cs-ii
TRANSCRIPT
EXP.NO:
DATE:
SIMULATION OF DCT BASED SPEECH/AUDIO
COMPRESSION METHOD
AIM:
To simulate and analyze an audio signal compression using discrete cosine transform.
EQUIPMENTS REQUIRED:
1. MATLAB 7.0.1
2. Personal Computer
THEORY:
Audio compression is removal of redundant or irrelevant information from the audio
signal. Audio compression allows efficient storage and transmission of audio signal. Discrete
cosine transform of an audio signal converts an audio block into its equivalent frequency
coefficients.
An audio sample is a sequence of real numbers X={x1,…xN}. The dct of this
audio sample is the sequence, DCT(X)=Y={y1,…,yN} such that
Y
where
1
w(k) =
The compression scheme
The coefficients of the DCT are amplitudes of cosines that are “within” the original
single. Small coefficients will result in cosines with small amplitudes, which we are less
likely to hear. So instead of storing the original sample we could take the DCT of the sample,
discard small coefficients, and keep that. We would store fewer numbers and so compress the
audio data.
Filling in the details
When compressing with DCTs we typically compress small slices (windows) of the
audio at once. This is partly so that seeking through the compressed stream is easier but
mostly because we want the coefficients in our window to represent frequencies we hear
(with large window the majority of the coefficients would represent frequencies well out of
the human hearing range).
ALGORITHM:
Initialize the Matlab.
Read the audio signal as input for compression.
Initialize the compression matrices for compression factors 2,4 & 8.
Compress the audio files by taking discrete cosine transform.
Plot the original and compressed audio signals.
Plot the expanded view of original and compressed audio signals.
Plot the spectrogram of original and compressed audio signal
2
FLOW CHART:
3
Compress the audio signal using discrete cosine transform
START
STOP
Initialize the compression matrices
Read the input signal
Display the original and compressed audio signal
PROGRAM:
function[]=myDCT()
[funky,f]=wavread('F:\SS\funky.wav');
windowsize=8192;
sampleshalf=windowsize/2;
samplesquarter=windowsize/4;
sampleseighth= windowsize/8;
funkycompressed2=[];
funkycompressed4=[];
funkycompressed8=[];
for i=1:windowsize:length(funky)-windowsize
windowDCT=dct(funky(i:i+windowsize-1));
funkycompressed2(i:i+windowsize-
1)=idct(windowDCT(1:sampleshalf),windowsize);
funkycompressed4(i:i+windowsize-1)=idct(windowDCT(1:samplesquarter),
windowsize);
funkycompressed8(i:i+windowsize-1)=idct(windowDCT(1:sampleseighth),
windowsize);
end
figure(1);
h1=subplot(4,1,1);
plot(funky)
title('original waveform');
subplot(4,1,2);
4
plot(funkycompressed2)
title('compression factor 2'),axis(axis(h1));
subplot(4,1,3);
plot(funkycompressed4)
title('compression factor 4'),axis(axis(h1));
subplot(4,1,4);
plot(funkycompressed8)
title('compression factor 8'),axis(axis(h1));
%expanded view of audio signal
figure(2)
h1=subplot(4,1,1);plot(funky(100000:120000)),title('portion of original
waveform');
subplot(4,1,2)
plot(funkycompressed2(100000:120000)),title('portion of compression factor2');
subplot(4,1,3)
plot(funkycompressed4(100000:120000)),title('portion of compression factor4');
subplot(4,1,4)
plot(funkycompressed8(100000:120000)),title('portion of compression factor8');
%spectogram of audio signals
figure(3)
subplot(4,1,1)
specgram('funky'),title('original waveform');
subplot(4,1,2)
specgram(funkycompressed2),title('compressionfactor2');
subplot(4,1,3)
specgram(funkycompressed4),title('compressionfactor4');
subplot(4,1,4)
specgram(funkycompressed8),title('compressionfactor8');
%saving to wave files
wavwrite(funkycompressed2,'funky2')
wavwrite(funkycompressed4,'funky4')
wavwrite(funkycompressed8,'funky8')
%playing files
5
disp('original');
wavplay(funky,f);
disp('compression factor2');
wavplay(funkycompressed2,f);
disp('compression factor4');
wavplay(funkycompressed4,f);
disp('compression factor8');
wavplay(funkycompressed8,f);
OUTPUT:
0 0.5 1 1.5 2 2.5
x 104
-0.50
0.5Portion of Original Waveform
0 0.5 1 1.5 2 2.5
x 104
-0.50
0.5Portion of Compression Factor 2
0 0.5 1 1.5 2 2.5
x 104
-0.50
0.5Portion of Compression Factor 4
0 0.5 1 1.5 2 2.5
x 104
-0.50
0.5Portion of Compression Factor 8
6
0 0.5 1 1.5 2 2.5 3 3.5 4
x 105
-0.50
0.5Original Waveform
0 0.5 1 1.5 2 2.5 3 3.5 4
x 105
-0.50
0.5Compression Factor 2
0 0.5 1 1.5 2 2.5 3 3.5 4
x 105
-0.50
0.5Compression Factor 4
0 0.5 1 1.5 2 2.5 3 3.5 4
x 105
-0.50
0.5Compression Factor 8
Time
Fre
quen
cy
Original Waveform
2 4 6 8 10 12 14 16 18
x 104
00.5
1
Time
Fre
quen
cy
Compression Factor 2
2 4 6 8 10 12 14 16 18
x 104
00.5
1
Time
Fre
quen
cy
Compression Factor 4
2 4 6 8 10 12 14 16 18
x 104
00.5
1
Time
Fre
quen
cy
Compression Factor 8
2 4 6 8 10 12 14 16 18
x 104
00.5
1
7
RESULT:
Thus the given audio signal has been compressed using discrete cosine transform.
And its output was verified successfully.
EXP.NO:
DATE:
SIMULATION OF DWT BASED SPEECH /AUDIO
COMPRESSION METHOD
AIM:
To compress and provide substantial improvements in audio quality at higher compression ratios using Wavelet Transform.
APPARATUS REQUIRED:
1. MATLAB 7.0.1
2. Personal Computer
THEORY:
WAVELET COMPRESSION:
8
The wavelet transform has emerged as a cutting edge technology, Wavelet
compression is a form of data compression well suited for image compression (sometimes
also video compression and audio compression). Notable implementations are MPEG, MP1,
MP2 and MP3 for Audio signals. The goal of audio compression is to encode audio data to
take up less storage space and less bandwidth for transmission .Wavelet compression can be
either lossless or lossy.
Using a wavelet transform, the wavelet compression methods are adequate for
representing transients, such as percussion sounds in audio, or high-frequency components in
two-dimensional images, for example an image of stars on a night sky. This means that the
transient elements of a data signal can be represented by a smaller amount of information
than would be the case if some other transform, such as the more widespread discrete cosine
transform, had been used.
METHOD OF COMPRESSION:
In order to determine what information in an audio signal is perceptually irrelevant,
most lossy compression algorithms use transforms such as the (MDCT) to convert sampled
waveforms into a transform domain. Once transformed, typically into the, component
frequencies can be allocated bits according to how audible they are. Audibility of spectral
components is determined by first calculating a, below which it is estimated that sounds will be
beyond the limits of human perception.
ALGORITHM:
Initialize the Matlab
Read the input audio given for compression
Add the multiplicative noise to the audio signal
Transform the image using HAAR Transform
Get the decomposition level from the user
Compression ratio is calculated in percentage
The image is compressed using the ratio
Finalize by displaying the compressed audio
9
FLOW CHART:
10
Transform the Audio using Haar Transform
Get the decomposition level
Add multiplicative noise to the Audio
START
Initialize by reading input Audio file
PROGRAM:
clc;
clear all;
close all;
[y, Fs, nbits, readinfo] = wavread('C:\Documents and Settings\WELCOME\Desktop\
jjj.wav');
subplot(1,3,1);
plot(y);
n=input('enter the decomposition level');
[Lo_D,Hi_D,Lo_R,Hi_R]=wfilters('haar');
[c,s]=wavedec2(y,n,Lo_D,Hi_D);
disp('the decomposition level is');
[THR,NKEEP]=wdcbm2(c,s,1.5,3*prod(s(1)));
[compressed_image,TREED,comp_ratio,PERFL2]=wpdencmp(THR,'s',n,'haar','threshol
d',5,1);
disp('compression ratio in percentage');
disp(comp_ratio);
11
Calculate the compression ratio
STOP
Display compression ratio and compressed Audio
subplot(1,3,2);
plot(compressed_image);
re_im1=waverec2(c,s,'haar');
subplot(1,3,3);
plot(re_im1);
OUTPUT:
12
Enter the decomposition level: 5
Compression ratio in percentage is: 20
RESULT:
Thus the given Audio signal has been compressed using the Wavelet Transform
and its output was verified successfully.
EXP.NO:
DATE:
SIMULATION OF LPC BASED SPEECH /AUDIO
COMPRESSION METHOD
AIM:
To simulate and analyze an audio signal compression using linear predictive coding algorithm.
EQUIPMENTS REQUIRED:
1. MATLAB 7.0.1
2. Personal Computer
THEORY:
LPC:
13
Linear predictive coding (LPC) is a tool used mostly in audio signal processing and
speech processing for representing the spectral envelope of a digital signal of speech in
compressed form, using the information of a linear predictive model. It is one of the most
powerful analysis methods for encoding good quality speech at a low bit rate and provides
extremely accurate estimates of speech parameters. It expresses each sample of the signal as a
linear combination of previous samples. Such an equation is called a linear predictor, which
is called as Linear Predictive Coding. The coefficients of the difference equation characterize
the formants, so the LPC system needs to estimate these coefficients. The estimate is done by
minimizing the mean-square error between the predicted signal and the actual signal. It
involves the computation of a matrix of coefficient values and the solution of a set of linear
equations may be used to assure convergence to a unique solution with efficient computation.
ALGORITHM:
Initialize the Matlab.
Read the audio signal as input for compression.
Take transpose to the product of window signal and filtered input signal.
Computation of a matrix of coefficient vaules used for convergence.
Convergence of audio signal may also be obtained by set of linear
equations.
Plot the durbin algorithm for linear prediction coefficients.
Plot the predictor residual energy
14
FLOW CHART:
15
Express each sample as a linear combination of previous
Transpose the product of window and the filtered input signal
START
Initialize by reading input image
PROGRAM:
clc;
close all;
clear all;
[x,fs]=wavread('C:\Documents and Settings\WELCOME\desktop\123.wav');% read
into the data
% Preemphasis filter
xx=double(x);
y=filter([1 -0.9495],1,xx);
N=160;
y1=y(1:N);
w1=hamming(1,N);
y2=(y1.*w1)';
p=30;% predict the order of
r=zeros(1,p+1);
16
Estimation of coefficients by minimizing mean square error
STOP
Display original and compressed signal
for k=1:p+1
sum=0;
for m=1:N+1-k
sum=sum+y2(m).*y2(m-1+k)';
end
r(k)=sum;
end
k=zeros(1,p);
k(1)=r(2)/r(1);
a=zeros(p,p);
a(1,1)=k(1);
e=zeros(1,p);
e(1)=(1-k(1)^2)*r(1);
for i=2:p
c=zeros(1,i);
sum=0;
for j=1:i-1
sum=sum+(a(i-1,j).*r(i+1-j));
end
c(i)=sum;
k(i)=(r(i+1)-c(i))/e(i-1);
if find(abs(k)>1)
disp('default')
else
subplot(413);plot(abs(k));title('|k(i)|<=1')
end
a(i,i)=k(i);
for j=1:i-1
a(i,j)=a(i-1,j)-k(i).*a(i-1,i-j);
end
e(i)=(1-k(i)^2)*e(i-1);
subplot(414);plot(e);
title('predictor residual energy E(i)');
end
17
d=zeros(1,p);
for t=1:p
d(t)=a(p,t);
end
z=zeros(1,N);
for i=1:p
z(i)=y2(i);
end
figure(1);
subplot(411);
plot(y2);
title('Original Data');
subplot(412);
plot(z);
title('durbin algorithm for linear prediction coefficients');
OUTPUT:
18
0 5 10 15 20 25 300
0.2
0.4|k(i)|<=1
0 5 10 15 20 25 300.5
1
1.5x 10
-3 predictor residual energy E(i)
0 20 40 60 80 100 120 140 160-0.01
0
0.01Original Data
0 20 40 60 80 100 120 140 160-1
0
1durbin algorithm for linear prediction coefficients
RESULT:
Thus the compression of given audio signal using linear predictive coding was
simulated and its output has been plotted.
EXP.NO: SIMULATION OF SUBBAND BASED SPEECH/ AUDIO
19
DATE: COMPRESSION METHOD
AIM:
To simulate audio and speech compression algorithm of subband coding using MATLAB.
APPARATUS REQUIRED:
1. MATLAB 7.0.1
2. Personal computer
THEORY:
A popular approach to decomposing the image into different frequency bands without
the imposition of an arbitrary block structure is sub band coding. After the input has been
decomposed into its constituents, we can use the coding technique best suited to each
constituent to improve compression performance. Furthermore, each component of the source
output may have different perceptual characteristics. Quantization error that is perceptually
objectionable in one component may be acceptable in a different component of the source
output. Therefore, a coarser quantizer may be used for perceptually less important
components. This is how the concept of sub-band coding comes into picture
ALGORITHM:
Initialize the Matlab.
Read the audio file given for sub band coding.
Plot the signals of speech and filter in time domain.
Take Fourier transform for converting signals in time domain to frequency
domain.
Plot the signals of speech and filter in frequency domain.
Decimate the signals to get the four bands in synthesis.
Compare the original band with synthesized band.
FLOW CHART:
20
PROGRAM:
21
Decimate the signals to get the bands in synthesis
Compare the original band with synthesized band
Convert the signals to frequency domain.
START
STOP
Initialize by reading the audio files.
Display the output
waveforms
clc;
close all;
clear all;
num=36000;
[x,fs,nbits] = wavread(' sub1.wav',num);
x=x(:,1)';
lnx=length(x);
L = 2;
len = 25;
wc = 1/L; %cut-off frequency is pi/2.
freq=-pi:2*pi/(lnx-1):pi;% the frequency vector
lp = fir1(len-1, wc,'low');
hp = fir1(len-1, wc,'high');
yl=conv(x,lp);
yh=conv(x,hp);
%Time domain plots of signal and filters
figure(1);
subplot(311);
plot(x);axis([0 lnx min(x) max(x)]);ylabel('speech');
Title('Speech and filters in time domain');
subplot(312);
stem(lp);axis([0 length(lp) (min(lp)+0.1) (max(lp)+0.1)]);
ylabel('lp');
subplot(313);
stem(hp);axis([0 length(hp) min(hp)+0.1 max(hp)+0.1]);
ylabel('hp');
pause
%plotting filter response of filters and the two speech bands(lower and upper) in freq
domian
figure(2);
X=fftshift(fft(x,lnx));
Lp=fftshift(fft(lp,lnx));
Hp=fftshift(fft(hp,lnx));
YL=fftshift(fft(yl,lnx));
22
Yh=fftshift(fft(yh,lnx));
subplot(3,2,1);
plot(freq/pi, abs(X));
ylabel('|X|');
axis([0 pi/pi min(abs(X)) max(abs(X))]);
title('Freq domain representation of speech and the two bands');
subplot(3,2,3);
plot(freq/pi, abs(Lp),'g');
ylabel('|Lp|');
axis([0 pi/pi min(abs(Lp)) max(abs(Lp))]);
subplot(3,2,4);
plot(freq/pi, abs(Hp), 'g');
ylabel('|Hp|');
axis([0 pi/pi min(abs(Hp)) max(abs(Hp))]);
subplot(3,2,5);
plot(freq/pi, abs(YL), 'y');
ylabel('|YL|');
axis([0 pi/pi min(abs(YL)) max(abs(YL))]);
legend('Low bandafter filtering');
subplot(3,2,6);
plot(freq/pi, abs(Yh), 'y');
ylabel('|Yh|');
axis([0 pi/pi min(abs(Yh)) max(abs(Yh))]);
legend('High band after filtering');
pause
ydl =yl(1:2:length(yl));
ydh=yh(1:2:length(yh));
s0=conv(ydl,lp);
s1=conv(ydl,hp);
s2=conv(ydh,lp);
s3=conv(ydh,hp);
% now finally decimating to get the four bands
b0 =s0(1:2:length(s0));
b1=s1(1:2:length(s1));
23
b2 =s2(1:2:length(s2));
b3=s3(1:2:length(s3));
%freq plots of decimated signals(four bands)
figure(3);
title('Four bands in freq domain');
subplot(4,1,1);
plot(freq/pi,abs(fftshift(fft(b0,lnx))));
ylabel('|B0|');
axis([0 pi/pi min(abs(fft(b0))) max(abs(fft(b0)))]);
title('Four bands in freq domain');
subplot(4,1,2);
plot(freq/pi,abs(fftshift(fft(b1,lnx))));
ylabel('|B1|');
axis([0 pi/pi min(abs(fft(b0))) max(abs(fft(b1)))]);
subplot(4,1,3);
plot(freq/pi,abs(fftshift(fft(b2,lnx))));
ylabel('|B2|');
axis([0 pi/pi min(abs(fft(b2))) max(abs(fft(b2)))]);
subplot(4,1,4);
plot(freq/pi,abs(fftshift(fft(b3,lnx))));
ylabel('|B3|');
axis([0 pi/pi min(abs(fft(b3))) max(abs(fft(b3)))]);
pause;
% now synthesizing
L=2;
N1=length(b0);
Ss0=zeros(1,L*N1);
Ss1=zeros(1,L*N1);
Ss2=zeros(1,L*N1);
Ss3=zeros(1,L*N1);
Ss0(L:L:end)=b0;
Ss1(L:L:end)=b1;
Ss2(L:L:end)=b2;
Ss3(L:L:end)=b3;
24
%Passing through reconstruction filters
% making a low pass filter with cutoff at 1/L and gain L
reconst_fil=L*fir1(len-1,1/L);
% finding the freq response of the filter
sb0=conv(reconst_fil,Ss0);
sb1=conv(reconst_fil,Ss1);
sb2=conv(reconst_fil,Ss2);
sb3=conv(reconst_fil,Ss3);
Slow=sb0-sb1;
Shigh=sb2-sb3;
subl=zeros(1,length(Slow)*2);
subh=zeros(1,length(Shigh)*2);
subl(L:L:end)=Slow;
subh(L:L:end)=Shigh;
subll=conv(reconst_fil,subl);
subhh=conv(reconst_fil,subh);
sub=subll-subhh;
%Freq plots of final two bands and their merging into a single band
figure(4);
subplot(3,1,1);
plot(freq/pi,abs(fftshift(fft(subll,lnx))));
ylabel('|low band|');
axis([0 pi/pi min(abs(fft(subll))) max(abs(fft(subll)))]);
title('Final two bands in synthesis');
subplot(3,1,2);
plot(freq/pi,abs(fftshift(fft(subhh,lnx))));
ylabel('|High band|');
axis([0 pi/pi min(abs(fft(subhh))) max(abs(fft(subhh)))]);
subplot(3,1,3);
plot(freq/pi,abs(fftshift(fft(sub,lnx))));
ylabel('|Band|');
axis([0 pi/pi min(abs(fft(sub))) max(abs(fft(sub)))]);
pause
25
%Comparison
figure(5);
subplot(2,1,1);
plot(freq/pi, abs(X));
ylabel('|X|');
axis([0 pi/pi min(abs(X)) max(abs(X))]);
title('Comparison');
legend('original band');
subplot(2,1,2);
plot(freq/pi,abs(fftshift(fft(sub,lnx))),'r');
ylabel('|Band|');
axis([0 pi/pi min(abs(fft(sub))) max(abs(fft(sub)))]);
legend('Synthesized Band');
OUTPUT:
FIGURE 1:
26
FIGURE2:
FIGURE 3:
27
FIGURE 4:
FIGURE 5:
28
RESULT:
Thus audio and speech compression algorithm of subband coding using MATLAB
was simulated.
29
EXP.NO:
DATE:
SIMULATION OF EZW IMAGE COMPRESSION
ALGORITHM
AIM:
To compress an image using simulate EZW image coding algorithm.
APPARATUS REQUIRED:
1. MATLAB 7.0.1
2. Personal Computer
THEORY:
EZW Algorithm:
Embedded Zerotrees of Wavelet Transforms is a lossy compression algorithm . At low bit
rates i.e. high compression ratios most of the coefficients produced by a such as the will be
zero, or very close to zero. This occurs because "real world" images tend to contain mostly
low frequency information
By considering the transformed coefficients as a with the lowest frequency coefficients at
the root node and with the children of each tree node being the spatially related coefficients in
the next higher frequency subband, there is a high probability that one or more subtrees will
consist entirely of coefficients which are zero or nearly zero, such subtrees are called
zerotrees. Due to this, we use the terms node and coefficient interchangeably, and when we
refer to the children of a coefficient, we mean the child coefficients of the node in the tree
where that coefficient is located. We use children to refer to directly connected nodes lower
in the tree and descendants to refer to all nodes which are below a particular node in the tree,
even if not directly connected.
In zerotree based image compression scheme such as EZW and, the intent is to use the
statistical properties of the trees in order to efficiently code the locations of the significant
coefficients. Since most of the coefficients will be zero or close to zero, the spatial locations
of the significant coefficients make up a large portion of the total size of a typical compressed
30
image. A coefficient is considered significant if its magnitude is above a particular threshold.
By starting with a threshold which is close to the maximum coefficient magnitudes and
iteratively decreasing the threshold, it is possible to create a compressed representation of an
image which progressively adds finer detail. Due to the structure of the trees, it is very likely
that if a coefficient in a particular frequency band is insignificant, then all its descendants will
also be insignificant.
ALGORITHM:
Initialize the Matlab
Read the input image given for compression
Specify the maximum number of steps for the compression algorithm.
Compress the image using EZW algorithm.
Uncompress the compressed image.
Finalize by plotting the compressed and uncompressed image
FLOW CHART:
31
PROGRAM:
32
Compress the image using EZW algorithm
Uncompress the compressed image.
Specify the number of input levels for compression
START
STOP
Initialize by reading input
image
Display original image and compressed image
clc;
clear all;
close all;
X = imread('wpeppers.jpg');
image(X)
axis square
colormap(pink(255))
title('Original Image: peppers')
meth = 'gbl_mmc_h'; % Method name
option = 'c'; % 'c' stands for compression
[CR,BPP] = wcompress(option,X,'peppers.wtc',meth,'BPP',0.5);
option = 'u'; % 'u' stands for uncompression
Xc = wcompress(option,'peppers.wtc');
colormap(pink(255))
figure(1)
subplot(1,2,1); image(X);
axis square;
title('Original Image')
subplot(1,2,2); image(Xc);
axis square;
title('Compressed Image')
xlabel({['Compression Ratio: ' num2str(CR,'%1.2f %%')], ...
['BPP: ' num2str(BPP,'%3.2f')]})
meth = 'ezw'; % Method name
wname = 'haar'; % Wavelet name
nbloop = 6; % Number of loops
[CR,BPP] = wcompress('c',X,'peppers.wtc',meth,'maxloop', nbloop, ...
'wname','haar');
Xc = wcompress('u','peppers.wtc');
colormap(pink(255))
figure(2)
subplot(1,2,1); image(X);
axis square;
title('Original Image')
33
subplot(1,2,2); image(Xc);
axis square;
title('Compressed Image - 6 steps')
xlabel({['Compression Ratio: ' num2str(CR,'%1.2f %%')], ...
['BPP: ' num2str(BPP,'%3.2f')]})
[CR,BPP] = wcompress('c',X,'peppers.wtc',meth,'maxloop',9,'wname','haar');
Xc = wcompress('u','peppers.wtc');
colormap(pink(255))
figure(3)
subplot(1,2,1); image(Xc);
axis square;
title('Compressed Image - 9 steps')
xlabel({['Compression Ratio: ' num2str(CR,'%1.2f %%')],...
['BPP: ' num2str(BPP,'%3.2f')]})
[CR,BPP] = wcompress('c',X,'peppers.wtc',meth,'maxloop',12,'wname','haar');
Xc = wcompress('u','peppers.wtc');
subplot(1,2,2); image(Xc);
axis square;
title('Compressed Image - 12 steps')
xlabel({['Compression Ratio: ' num2str(CR,'%1.2f %%')], ...
['BPP: ' num2str(BPP,'%3.2f')]})
[CR,BPP] = wcompress('c',X,'peppers.wtc','ezw','maxloop',12, ...
'wname','bior4.4');
Xc = wcompress('u','peppers.wtc');
colormap(pink(255))
figure(4)
subplot(1,2,1); image(Xc);
axis square;
title('Compressed Image - 12 steps - bior4.4')
xlabel({['Compression Ratio: ' num2str(CR,'%1.2f %%')], ...
['BPP: ' num2str(BPP,'%3.2f')]})
[CR,BPP] = wcompress('c',X,'peppers.wtc','ezw','maxloop',11, ...
34
'wname','bior4.4');
Xc = wcompress('u','peppers.wtc');
subplot(1,2,2); image(Xc);
axis square;
title('Compressed Image - 11 steps - bior4.4')
xlabel({['Compression Ratio: ' num2str(CR,'%1.2f %%')], ...
['BPP: ' num2str(BPP,'%3.2f')]})
[CR,BPP] = wcompress('c',X,'peppers.wtc','spiht','maxloop',12, ...
'wname','bior4.4');
Xc = wcompress('u','peppers.wtc');
colormap(pink(255))
OUTPUT:
35
Original Image
100 200 300 400 500
100
200
300
400
500
Compressed Image - 6 steps
Compression Ratio: 0.06 %BPP: 0.02
100 200 300 400 500
100
200
300
400
500
Original Image
100 200 300 400 500
100
200
300
400
500
Compressed Image
Compression Ratio: 1.57 %BPP: 0.38
100 200 300 400 500
100
200
300
400
500
36
Compressed Image - 9 steps
Compression Ratio: 0.81 %BPP: 0.19
100 200 300 400 500
100
200
300
400
500
Compressed Image - 12 steps
Compression Ratio: 7.47 %BPP: 1.79
100 200 300 400 500
100
200
300
400
500
Compressed Image - 12 steps - bior4.4
Compression Ratio: 4.92 %BPP: 1.18
100 200 300 400 500
100
200
300
400
500
Compressed Image - 11 steps - bior4.4
Compression Ratio: 2.51 %BPP: 0.60
100 200 300 400 500
100
200
300
400
500
RESULT:
Thus the given image has been compressed using the EZW algorithm.
37
EXP.NO:
DATE:
SIMULATION OF SPIHT IMAGE COMPRESSION
ALGORITHM
AIM:
To compress an image using simulate SPIHT image coding algorithm.
APPARATUS REQUIRED:
1. MATLAB 7.0.12. Personal Computer
THEORY:
SPIHT ALGORITHM:
One of the most efficient algorithms in the area of image compression is the Set
Partitioning in Hierarchical Trees (SPIHT). It uses a sub-band coder, to produce a pyramid
structure where an image is decomposed sequentially by applying power complementary low
pass and high pass filters and then decimating the resulting images. These are one-
dimensional filters that are applied in cascade (row then column) to an image whereby
creating four-way decomposition: LL (low-pass then another low pass), LH (low pass then
high pass), HL (high and low pass) and finally HH (high pass then another high pass). The
resulting LL version is again four-way decomposed. This process is repeated until the top of
the pyramid is reached. This pyramid structure is commonly known as spatial orientation
tree.
ALGORITHM:
Initialize the Matlab
Read the input image given for compression
Specify the maximum number of steps for the compression algorithm.
Compress the image using SPIHT algorithm.
Uncompress the compressed image.
Finalize by plotting the compressed and uncompressed image.
38
FLOW CHART:
39
Compress the image using SPIHT algorithm
Uncompress the compressed image.
Specify the number of input levels for compression
START
STOP
Initialize by reading input image
Display original image and compressed image
PROGRAM:
clc;
clear all;
close all;
x=imread(‘wpeppers.jpg’);
[cr,bpp]=wcompress(‘c’,x,’wpeppers.wtc’,’spiht’,’maxloop’,12);
xc=wcompress (‘u’,’wpeppers.wtc’);
Colormap (pink(255));
Subplot(1,2,1);
Image(x);
Axis square;
Title(‘original image’);
Subplot(1,2,2);
Image(xc);
Axis square;
Title(‘compressed image-12-steps-bior 4.4’);
xlabel({[‘compression ratio:’num2str(cr,’%1.2f%%’)]…[‘bpp:’num2str(bpp,’%3.2f’)]});
delete(‘wpeppers.wtc’);
40
OUTPUT:
Original Image
100 200 300 400 500
100
200
300
400
500
Compressed Image - 12 steps - bior4.4
Compression Ratio: 1.65 %BPP: 0.40
100 200 300 400 500
100
200
300
400
500
RESULT:
41
Thus the given image has been compressed using the SPIHT algorithm and its
output was verified successfully.
EXP.NO:
DATE:S- PARAMETER ESTIMATION OF COUPLER
AIM:
To design and analyze the characteristics of a coupler using ADS.
APPARATUS REQUIRED:
1. ADS2. Personal Computer
THEORY:
A very commonly used basic element in microwave system is the directional coupler.
Its basic function is to sample the forward and reverse travelling waves through a
transmission line or a waveguide. The common use of this element is to measure the power
level of a transmitted or received signal. The model of a directional coupler is shown in
Figure 1.
42
As seen in the figure, the coupler is a four-ports device. The forward travelling wave goes
into port 1 and exit from port 2. A small fraction of it goes out through port 4. In a perfect
coupler, no signal appears in port 4. Since the coupler is a lossless passive element, the sum
of the signals power at ports 1 and 2 equals to the input signal power. The reverse travelling
wave goes into port 2 and out of port 1. A small fraction of it goes out through port 3. In a
perfect coupler, no signal appears in port 4. The directional coupler S-parameters matrix is:
Where k is the coupling factor (a linear value).
One popular realization technique of the directional coupler is the coupled lines directional
coupler; two quarter wavelength line are placed close to each other. The wave travelling
through one line is coupled to the other line. Such a coupler is shown in Figure 2.
43
Since there is no ideal coupler available, some of the forward travelling wave is coupled into
port 3. This mean that we may think that there is a reverse travelling wave when there isn’t.
This is very critical in application where the directional coupler is used to measure the return
loss of the
device. By calculating 20 log(S31/S41) we can find the return loss of the device connected to
port 2. If out coupler has no perfect directivity then out measurement is not accurate.
There are few simple parameters to describe the functionality of a coupler:
• Insertion Loss: 20 log(S21) or 10 log(1 − k2).
• Return Loss: 20 log(S11).
• Coupling: 20 log(S31) or 20 log(k).
• Directivity: 20 log(S31) − 20 log(S41).
CIRCUIT DIAGRAM:
44
OUTPUT:
45
RESULT:
THUS THE COUPLER WAS DESIGNED AND ANALYZED USING ADS AND ITS OUTPUT WAS VERIFIED SUCCESSFULLY.
46
EXP.NO:
DATE:DESIGN OF OSCILLATOR
AIM:
To Design the oscillator using ADS.
APPARATUS REQUIRED:
1. ADS SOFTWARE
2. Personal Computer.
THEORY:
MICROWAVE OSCILLATOR:
An electronic oscillator is an electronic circuit that produces a repetitive electronic
signal, often a sine wave or a square wave. They are widely used in many electronic devices.
Common examples of signals generated by oscillators include signals broadcast by radio and
television transmitters, clock signals that regulate computers and quartz clocks, and the
sounds produced by electronic beepers and video games.
Oscillators are often characterized by the frequency of their output signal: an audio
oscillator produces frequencies in the audio range, about 16 Hz to 20 kHz. An RF oscillator
produces signals in the radio frequency (RF) range of about 100 kHz to 100 GHz. A low-
frequency oscillator (LFO) is an electronic oscillator that generates a frequency below ≈20
Hz. This term is typically used in the field of audio synthesizers, to distinguish it from an
audio frequency oscillator.
Oscillators designed to produce a high-power AC output from a DC supply are
usually called inverters. There are two main types of electronic oscillator: the harmonic
oscillator and the relaxation oscillator.
47
PROCEDURE:
1. Initialize the Advanced Design System software
2. Create a new project and save it.
3. Select the simulation format.
4. Select an application type as oscillator.
5. Select the required sample design.
6. Specify the simulation template for oscillator.
7. Simulate the project.
CIRCUIT DIAGRAM:
48
OUTPUT:
RESULT:
Thus the Oscillator has been designed using ADS software and its output was
verified successfully .
49
EXP.NO:
DATE:DESIGN OF FILTER
AIM:
To stimulate the performance of a Filter using ADS
APPARATUS REQUIRED:
1. Personal Computer
2. ADS software
THEORY:
A filter is a two port network used to control the frequency response at a certain point
in a system by providing transmission within the passband of the filter and attenuation in the
stop band of the filter. The basic filter types are low-pass, high-pass, bandpass and band-
reject (notch) filters.
CIRCUIT DIAGRAM:
50
Digital Filter Impulse Response
SW_DFILT_FIRX1
ImpulseFloatI1
Delay=0Period=0Level=1.0
NumericSinkN1
ControlSimulation=YESStop=DefaultNumericStopStart=DefaultNumericStartPlot=Rectangular
Numeric
1 2 3
DFDF
DefaultNumericStop=100DefaultNumericStart=0
PROCEDURE:
Step1: Open the ADS software.
Step2: Create a new project from the file menu.
Step3: Open the schematic window of ADS.
Step4: From the components library select the appropriate necessary fo the required model.
Step5: Click on the necessary components and place them on the schematic windows of ADS.
Step6: Design the filters using discrete elements
Step7: Determine the SWR of each filter using hand analysis
51
Step8: Compare experimental results to theory and simulation
Step9: Comment on your result
OUTPUT:
500 100
0.0
0.1
0.2
0.3
-0.1
0.4
Index
N1
52
RESULT:
Thus the Filter was simulated using ADS and its output was verified successfully.
EXP.NO:
DATE: DESIGN OF MIXER USING ADS
AIM:
To stimulate the performance of a Mixer using ADS
APPARATUS REQUIRED:
1. Personal Computer2. ADS software
THEORY:
Mixers are three port active or passive devices, are designed to yield both a sum and a
difference frequency at a single output port when two distinct input frequencies are inserted
into the other two ports. This process, called frequency conversion (or heterodyning), is found
in most communications gear, and is used so that we may increase or decrease a signal’s
53
frequency. One of the two input frequencies will normally be a CW wave, produced within
the radio by a local oscillator (LO), while the other input will be the RF signal received from
the antenna. If we would like to produce an output frequency within the mixer circuit that is
lower than the input RF signal, then this is called down conversion; if we would like to
produce an output signal that is at a higher frequency than the input signal, it is referred to as
up conversion. Indeed, most AM, SSB, and digital transmitters require mixers to convert up
to a higher frequency for transmission into space, while superheterodyne receivers require a
mixer to convert a received signal to a much lower frequency. This lower received frequency
available at the mixer’s output port is called the intermediate frequency (IF). Receivers use
this lower-frequency IF signal because it is much easier to efficiently amplify and filter with
all the IF stages tuned and optimized for a single, low band of frequencies, which increases
the receiver’s gain and selectivity. Again, the frequency conversion process within the
nonlinear mixer stage produces the intermediate frequency by the RF input signal
heterodyning, or beating, with the receiver’s own internal LO. This heterodyning mixer
circuit will consist of either a diode, BJT, or FET that is overdriven, or biased to run within
the nonlinear area of its operation. However, the beating of the mixer’s RF and LO input
signals yields not only the RF, the LO, and the sum and difference frequencies of these two
primary signals, but also many spurious frequencies at the mixer’s output port. Most of these
undesired frequencies will be filtered out within the receiver’s IF stages, resulting in the new
desired signal frequency, consisting of the converted carrier and any sidebands, now at the
difference frequency. This new, lower difference frequency will then be amplified and further
filtered as it passes through the fixed-tuned IF strip. There are three basic classifications for
both active and passive mixers: Unbalanced mixers have an IF output consisting of fS,fLO,
fS − fLO, fS + fLO, and other spurious outputs. They will also exhibit little isolation between
each of the mixer’s three ports, resulting in undesired signal interactions and feedthroughs to
another port. Singlebalanced mixers will at least strongly attenuate either the original input
signal or the LO (but not both), while sending less of the above mixing products on to its
output than the unbalanced type. A double-balanced mixer, or DBM for short, supplies
superior IF-RF-LO inter-port isolation, while outputting only the sum and difference
frequencies of the input signal and the local oscillator, while attenuating both the LO and RF
signals, and significantly attenuating three quarters of the possible mixer spurs at the output
of the IF port. This makes the job of filtering and selecting a frequency plan a much easier
task.
54
CIRCUIT DIAGRAM:
55
PROCEDURE:
56
Step1: Open the ADS software.
Step2: Create a new project from the file menu.
Step3: Open the schematic window of ADS.
Step4: From the components library select the appropriate necessary of the required model.
Step5: Click on the necessary components and place them on the schematic windows of ADS.
Step6: Design the Mixer using discrete elements
Step7: Determine the SWR of each filter using hand analysis
Step8: Compare experimental results to theory and simulation
Step9: Comment on your result
OUTPUT:
57
RESULT:
Thus the Mixer was simulated using ADS and its output was verified successfully.
EXP.NO: DESIGN OF AMPLIFIER
58
DATE:
AIM:
To design and analyze the characteristics of Amplifier using ADS.
APPARATUS REQUIRED:
1. ADS software
2. Personal Computer
THEORY:
An amplifier is an electronic device that increases the voltage, current, or power of a
signal. Amplifiers are used in wireless communications and broadcasting, and in audio
equipment of all kinds. They can be categorized as either weak-signal amplifiers or power
amplifiers. Weak-signal amplifiers are used primarily in wireless receivers. They are also
employed in acoustic pickups, audio tape players, and compact disc players. A weak-signal
amplifier is designed to deal with exceedingly small input signals, in some cases measuring
only a few nano volts (units of 10-9 volt). Such amplifiers must generate minimal internal
noise while increasing the signal voltage by a large factor. The most effective device for this
application is the field-effect transistor. The specification that denotes the effectiveness of a
weak-signal amplifier is sensitivity, defined as the number of micro volts (units of 10-6 volt)
of signal input that produce a certain ratio of signal output to noise output (usually 10 to 1).
Power amplifiers are used in wireless transmitters, broadcast transmitters, and hi-fi
audio equipment. The most frequently-used device for power amplification is the bipolar
transistor. However, vacuum tubes, once considered obsolete, are becoming increasingly
popular, especially among musicians. Many professional musicians believe that the vacuum
tube (known as a "valve" in England) provides superior fidelity.
59
CIRCUIT DIAGRAM:
PROCEDURE:
1. Initialize the Advanced Design System software
2. Create a new project and save it.
3. Select simulation format.
4. Select an application type as amplifier.
5. Select the required sample design.
6. Specify the simulation template for Amplifier.
7. Simulate the project.
60
OUTPUT:
RESULT:
Thus the Amplifier was simulated using ADS and its output was verified successfully.
61
EXP.NO:
DATE:SIMULATION OF GPS
AIM: To Simulate the GPS system using MATLAB
APPARATUS REQUIRED:
1. MATLAB 7.0.1
2. Personal Computer
THEORY:
Trilateration is a method of determining the relative position of objects using the
geometry of triangles in a similar fashion as triangulation. Unlike triangulation, which uses
angle measurements to calculate the subject’s location, triangulation uses the known locations
of two or more reference points, and the measured distance between the subject and each
reference point. To accurately and uniquely determine the relative location of a point on a 2D
plane using trilateration alone, generally at least 3 reference points are needed.
Standing at B, you want to know your location relative to the reference points P1, P2
and P3 on a 2D plane. Measuring r1 narrows your position down to a circle. Next, measuring
r2 narrows it down to two points, A and B. A third measurement, r3, gives your coordinates
at B. A fourth measurement could also be made to reduce error.
A mathematical derivation for the solution of a three-dimensional trilateration
problem can be found by taking the formulae for three spheres and setting them equa;l to
each other. To do this, we must apply three constraints to the centers of these spheres; all
three must be on the z=0 plane, one must be on the origin, and one other must be on the x-
axis.
Starting with three spheres,
62
and
We subtract the second from the first and solve for x:
Substituting this back into the formula for the first sphare produces the formula for a circle,
the solution to the intersection of the first two spheres:
Setting this formula equal to the formula for the third sphere finds:
Now that we have the x-and y- coordinates of the solution point, we can simply rearrange the
formula for the first sphere to find the z- coordinate:
Now we have the solution to all three points x, y and z. because z is expressed as a square
root, it is possible for there to be zero, one or two solutions to the problem.
ALGORITHM:
Initialize the Matlab
63
Get the co-ordinate values for x,y and z
Determine the absolute location of the points
Locate the area of intersections of three spheres
Display the latitude and longitude values
PROGRAM:clc;
clear all;
close all;
x=input('the x-coordinate value=');
if(x>100)
disp('i/p exceeds the axis value');
return
end
y=input('the y-coordinate value=');
if(y>100)
disp('i/p exceeds the axis value');
return
end
z=input('the z-coordinate value=');
if(z>100)
disp('i/p exceeds the axis value');
return
end
a=6378137;
b=6356752.31425;
f=(a-b)/b;
display(f);
doubletemp=0;
doubletemp1=0;
temp=((a*a)-(b*b))/(b*b);
e1=sqrt(temp);
disp('the value of e1 is');
display(e1);
64
temp=2*f-(f*f);
e=sqrt(temp);
disp('the value of e is');
disp(e);
temp=(x*x)+(y*y);
p=sqrt(temp);
disp('the value of p is');
display(p);
theta=atan(z*a/(p*b));
display(theta);
temp=z+(e1*e1*b*sin(theta)*sin(theta)*sin(theta));
disp('the value of temp is');
display(temp);
temp1=p-(e*e*a*cos(theta)*cos(theta)*cos(theta));
disp('the value of temp1 is');
display(temp1);
fi=atan(temp/temp1);
disp('the value of fi is');
display(fi);
lam=atan2(y,x);
disp('the value of lam is');
display(lam);
temp=1-(e*e*sin(fi)*sin(fi));
temp1=sqrt(temp);
n=a/temp1;
h=(p/cos(fi))-n;
disp('The value of Altitiude (h) is');
display(h);
OUTPUT:
the x-coordinate value=5
the y-coordinate value=4
65
the z-coordinate value=3
f =0.0034
the value of e1 is
e1 =0.0821
the value of e is
0.0820
the value of p is
p =6.4031
theta =0.4394
the value of temp is
temp =3.3018e+003
the value of temp1 is
temp1 = -3.1747e+004
the value of fi is
fi = -0.1036
the value of lam is
lam = 0.6747
The value of Altitiude (h) is
h =-6.3784e+006
66
RESULT:
Thus the GPS was simulated using MATLAB and its output was verified successfully.
EXP.NO:PERFORMANCE EVALUATION OF SIMULATION OF
CDMA SYSTEMDATE:
AIM:
To design and analyze the performance evaluation of simulation of CDMA system.
APPARATUS REQUIRED:
1. MATLAB Version 7.0.1
2. Personal computer
THEORY:
DMA is a spread spectrum multiple access technique. A spread spectrum technique
spreads the bandwidth of the data uniformly for the same transmitted power. A spreading
code is a pseudo-random code that has a narrow Ambiguity function, unlike other narrow
pulse codes. In CDMA a locally generated code runs at a much higher rate than the data to be
transmitted. Data for transmission is combined via bitwise XOR (exclusive OR) with the
faster code. Code division multiple access (CDMA) is a channel access method used by
various radio communication technologies. It should not be confused with the mobile phone
standards called cdmaOne, CDMA2000 (the 3G evolution of cdma One) and WCDMA (the
3G standard used by GSM carriers), which are often referred to as simply CDMA, and use
CDMA as an underlying channel access method.One of the concepts in data communication
is the idea of allowing several transmitters to send information simultaneously over a single
communication channel. This allows several users to share a band of frequencies (see
bandwidth). This concept is called multiple access.
CDMA employs spread-spectrum technology and a special coding scheme (where
each transmitter is assigned a code) to allow multiple users to be multiplexed over the same
67
physical channel. By contrast, time division multiple access (TDMA) divides access by time,
while frequency-division multiple access (FDMA) divides it by frequency. CDMA is a form
of spread-spectrum signalling, since the modulated coded signal has a much higher data
bandwidth than the data being communicated.An analogy to the problem of multiple access is
a room (channel) in which people wish to talk to each other simultaneously. To avoid
confusion, people could take turns speaking (time division), speak at different pitches
(frequency division), or speak in different languages (code division). CDMA is analogous to
the last example where people speaking the same language can understand each other, but
other languages are perceived as noise and rejected. Similarly, in radio CDMA, each group of
users is given a shared code. Many codes occupy the same channel, but only users associated
with a particular code can communication.
BLOCK DIAGRAM OF CDMA SYSTEM:
MULTI USER:
68
TRANSMITTER SIDE SYSTEM:
RECEIVER SIDE SYSTEM:
69
SINGLE USER:
70
PROCEDURE:
1. Convert input bits to bipolar bits.. 1 to 1 and 0 to -1 for user1 and user2
71
2. Take 100 samples per bit for both user1 and user2 and then plot base band
signal which is in bipolar NRZ format.
3. Then BPSK modulate the signal. Take care that sampling rate of sinusoidal
carrier matches the sampling rate per bit. Here it is 100 samples per carrier and then
plot the BPSK signal
4. Multiply the BPSK modulated signal with the PN code. Here again the care
should be taken to match the sampling rate. i.e. no. of chip per bit* no of samples per
chip = no of samples per bit of BPSK modulated signal.
5. Same procedure is carried out for user2 bits.
6. The channel is AWGN channel with SNR 5 dbs. In channel the signal from
user1 is added to signal from user2 and white Gaussian noise is added.
7. At receiver end , first received signal is multiples with PN then BPSK
demodulated by multiplying with the carrier(coherent demod)
8. Then the samples over 1 bit interval are summed. And if the sum is greater
than 0 than the received bit is 1 else rx bit is 0. Summation is used in place of
integration because it is a discrete time system
9. Same procedure is repeated for user2.
OUTPUT:
72
73
RESULT:
Thus the performance evaluation of simulation of CDMA was simulated using MATLAB and its output was verified successfully.
74
EXP.NO:
DATE:DESIGN AND TESTING OF A MICROSTRIP COUPLER
AIM:
To design and analyze the characteristics of a microstrip coupler using MATLAB.
APPARATUS REQUIRED:
3. MATLAB 7.0.14. Personal Computer
THEORY:
Mini-Circuits microstrip couplers are reactive devices featuring very low insertion
loss. Most models have 3 ports, and are manufactured with an internal 50-ohm termination.
In the case, power coupled from any power incident to the output port (the reflected power) is
absorbed and not available to the user. However, all 4-port (bi-microstrip) models have both
the incident and reflected coupled power available. Examples are the ZFDC-20-1H and the
BD-suffix models. The basic function of a microstrip coupler is to operate on an input so that
two input signals are available. However, when the input is applied to the opposite port of an
internally terminated coupler, only one output signal is produced.
MICROSTRIP COUPLER CHARACTRISTICS
1. The output signals are unequal in amplitude. The larger signal is at the main-line
output port. The smaller signal is at the coupled port.
2. The main-line insertion loss depends upon the signal level at the coupled port, as
determined by design.
75
3. There is high isolation between the coupled port and the output of the main-line.
Key characteristics of a microstrip coupler include coupling coefficient, coupling
flatness, main-line loss and directivity, defined in the next page. Mini-Circuits full line of
microstrip couplers, spanning 5 KHz to 2GHz, provide excellent performance. They feature:
1. flat coupling over a broad bandwidth
2. low main-line loss, as low as 0.1 dB
3. directivity as high as 55 dB and
4. A wide range of coupling values, from 6dB to 30dB.
MICROSTRIP COUPLER APPLICATIONS
The high performance characteristics of these units enable the following signal processing
functions to be accomplished:
1. Measure incident and reflected power to determine VSWR
2. Signal sampling
3. Signal injection
PROGRAM:
clc;
clear all;
close all;
for(f=10^8:10^8:10^11)
C=47*10^-12;
L=1542*10^-9*((sqrt(f)^-1));
Rs=4.8*sqrt(f)*10^-6;
Re=33.9*10^12*(f^-1);
76
impedance1=abs((i*2*pi*f*C)^-1);
impedance=abs(i*2*pi*f*L+Rs+Re*((1+i*2*pi*f*C*Re)^-1));
axis on;
grid on;
hold on;
axis auto;
xmin=10^5;
xmax=10^11;
ymin=0;
ymax=3.5;
axis([xmin,xmax,ymin,ymax]);
xlabel('frequency');
ylabel('impedance');
plot(f,impedance,'red');
plot(f,impedance1,'blue');
end
77
OUTPUT:
1 2 3 4 5 6 7 8 9 10
x 1010
0
0.5
1
1.5
2
2.5
3
3.5
frequency
impe
danc
e
RESULT:
78
Thus the microstrip coupler was simulated using MATLAB and its output was verified successfully.
AIM:
To simulate the micro strip antenna using MATLAB.
EQUIPMENTS REQUIRED:
1. Personal computer.
2. MATLAB 7.0 version.
THEORY:
In telecommunication, there are several types of micro strip antennas (also known as
printed antennas) the most common of which is the micro strip patch antenna or patch
antenna. A patch antenna is a narrowband, wide-beam antenna fabricated by etching the
antenna element pattern in metal trace bonded to an insulating dielectric substrate, such as a
printed circuit board, with a continuous metal layer bonded to the opposite side of the
substrate which forms a ground plane.
Common micro strip antenna shapes are square, rectangular, circular and elliptical,
but any continuous shape is possible. Some patch antennas do not use a dielectric substrate
and instead made of a metal patch mounted above a ground plane using dielectric spacers; the
resulting structure is less rugged but has a wider bandwidth. Micro strip antennas are
relatively inexpensive to manufacture and design because of the simple 2-dimensional
physical geometry. They are usually employed at UHF and higher frequencies because the
size of the antenna is directly tied to the wavelength at the resonant frequency.
A single patch antenna provides a maximum directive gain of around 6-9 dB. It is relatively easy to print an array of patches on a single (large) substrate using lithographic techniques. The directivity of patch antennas is approximately 5-7 dB
79
EXP.NO: SIMULATION OF MICROSTRIP ANTENNA
USING MATLABDATE:
ALGORITHM:
Start the program.
Calculate the width, effective dielectric constant, length, effective length of
microstrip as follows;
w= ((sqrt (2/er+1))*c)/(2*fr)
preff =((er+1)/2)+(((er-1)/2)*(1+12*1/wbyh))
len=(c/(2*fr*sqrt(preff)))-(2*incleng)
eff=len+(2*incleng)
Where er=dielectric constant value
fr=resonant frequency
Stop the program.
80
FLOWCHART
81
ENTER THE DIELECTRIC CONSTANT,RESONANT FREQUENCY,HEIGHT OF MICROSTRIP ANTENNA
FIND THE WIDTH OF MICROSTRIP ANTENNA
CALCULATE EFFECTIVE DIELECTRIC CONSTANT,LENGTH,EFFECTIVE LENGTH OF MICROSTRIP ANTENNA
STOP
START
CODING:
clc;
close all;
clear all;
er=input('the dielectric constant value');
fr=input('the resonant frequency value in Ghz');
h=input('the height of microstrip antenna in cm');
c=30;
w=((sqrt(2/er+1))*c)/(2*fr);
disp('width of microstrip in cm');
display(w);
wbyh=w/h;
preff=((er+1)/2)+((er-1)/2)*(1+12*1/wbyh);
disp('effective dielectric constant of microstrip');
disp(preff);
a=((preff+0.3)/(preff-0.258));
b=((wbyh+0.264)/(wbyh+0.813));
incleng=0.4128*h*a*b;
disp('increase in length of microstrip in cm');
disp(incleng);
len=((c/(2*fr+sqrt(preff)))-(2*incleng));
disp('length of microstrip in cm');
disp(len);
eff=len+(2*incleng);
disp('effective length of microstrip in cm');
disp(eff);
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OUTPUT:
the dielectric constant value 1
the resonant frequency value in Ghz 50
the height of micro strip antenna in cm 5
width of micro strip in cm
w = 0.5196
effective dielectric constant of micro strip
1
increase in length of micro strip in cm
1.4510
length of micro strip in cm
-2.6050
effective length of micro strip in cm
0.2970
RESULT:
Thus the micro strip antenna using MATLAB has been simulated.
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