dsp record for ece hit

8/10/2019 Dsp Record for Ece Hit

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Hindusthan Institute of TechnologyCoimbatore

DEPARTMENT OF ECE

CERTIFIC TE OF COMPLETION

It is certified that this is the bonafide record of work done by

Name:..

Register Number:.Year of Batch:.................

Year:..Semester:.

Lab Name: Digital Signal Processing Laboratory

STAFF INCHARGE HOD

CERTIFIC TE OF COMPLETION

We here by certify that the above record work was submitted for University

Practical Examination held on ..

INTERNAL EXAMINER EXTERNAL EXAMINER


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INDEX

SL. NO. DATE EXPERIMENT NAMEPAGE

NO.

MARK

(15)SIGN

CYCLE-I(USING MATLAB)

1. Generation of Discrete time signals

2. Verification of sampling theorem

3. FFT and IFFT

4.

Linear and Circular Convolution through

FFT

5. Design of FIR filters (window design)

6.Design of IIR Filters (Butterworth &

chebychev)

7. Decimation by poly phase decomposition.

CYCLE-II(USING DSP KIT)

8. Generation of signals

9. Linear convolution

10. Implementation of a FIR filter

11.

Implementation of a IIR filter

12. Calculation of FFT.

TOTAL

AVERAGE

COMPLETED DATE:STAFF SIGNATURE.........


3/66

AIM:

To write a MATLAB program to generate a following standard input signals (i)Unit step, (ii)Unit impulse ,(iii) Unit ramp, (iv) Sinusoidal signal, (v)Saw tooth wave, (vi) Square wave, (vii)

Exponential signal and plot their response in Discrete and continuous time domain.

APPARATUS REQUIRED:

HARDWARE: IBM PC (OR) Compatible PC

SOFTWARE: MATLAB 6.5 (OR) High version

A.UNIT STEP SEQUENCE:

MATHEMATICAL EQUATION:u(n) = 1 for n >= 0

= 0 for n < 0

THEORY:The unit step sequence is a signal that is zero everywhere expect at n >= 0 where its

value is unity. In otherwise integral of the impulse function is also a singularity function and called

the unit step function.

ALGORITHM:

Step 1: Start the program

Step 2: Get the dimension of nStep 3: Discrete output is obtained for n>= 0 and zeros for all other values.

Step 4: Output is generated in stem format

Step 5: Terminate the process

B.UNIT IMPLULSE SEQUENCE:

MATHEMATICAL EQUATION:

(n) = 1 for n = 0

= 0 for n 0THEORY:

The unit impulse (sample) sequence is a signal that is zero everywhere except at n=0 where

it is unity. This signal sometime referred to as unit impulse.

ALGORITHM:


Step 2: Get the dimension of nStep 3: Discrete output is obtained for n = 0 and zeros for all other values.

Step 4: Output is generated in stem formatStep 5: Terminate the process

EX. NO: GENERATION OF DISCRETE TIME SIGNALS

DATE:


4/66

C.UNIT RAMP SEQUENCE:


Ur (n) = n for n >= 0

= 0 for n< 0

THEORY:

This unit ramp sequence is signal that grows linearly when n>=0, otherwise it is zero.

ALGORITHM:


Step 2: Get the dimension of nStep 3: Discrete output is obtained for n>=0 and zeros for all other values

Step 4: Output is generated in stem format


D.SINUSOIDAL SEQUENCE:


X(n) = A sin (o n + )Where o frequency in radians/sec, and is the phase angle in radians.

ALGORITHM:

Step 1: Start the programStep 2: Get the dimension of nStep 3: For each value of n find the sine formatStep 4: Output is generated in stem(plot) format


E.SAWTOOTH WAVE:

ALGORITHM:

Step 1: Start the programStep 2: Get the dimension of nStep 3: For each value of n find the sawtooth format Step 4: Output is generated in stem(plot) format


F. SQUARE WAVE:

ALGORITHM:Step 1: Start the program

Step 2: Get the dimension of nStep 3: For each value of n find the square format Step 4: Output is generated in stem(plot) format



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G.EXPONENTIAL SEQUENCE:


X (n) = an for all n

THEORY:

When the values of a>1, the sequence grows exponentially and when the value is 0


6/66

A.UNIT STEP SEQUENCE :

PROGRAM:

%program to generate unit step sequencen = -10:10;

s = [zeros(1,10) 1 ones(1,10)];

stem (n,s);

title ('unit step sequence');

xlabel ('time index n');

ylabel ('amplitude');


PROGRAM:

%program to generate impulse sequencen = -20:20;

s = [zeros(1,20) 1 zeros(1,20)];

stem (n, s);

title ('unit impulse sequence');

xlabel ('time');



PROGRAM:

%program to generate unit ramp sequenceclf;

n =0:10;

s =n;

stem (n,s);

title ('unit ramp sequence');

xlabel ('time index');



PROGRAM:

%program to generate sine sequenceclf;

t=0:0.1:pi;

y=sin(2*pi*t);

stem(t,y);

grid;

title('sine sequence');

xlabel('time');

ylabel('amplitude');


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E.SAWTOOTH WAVE:

PROGRAM:

% sawtooth sequencet = 0:0.1:5;

y = sawtooth (2*pi*t);

stem (t,y);

title ('sawtooth sequence');

xlabel ('time');


F. SQUARE WAVE:

PROGRAM:

%square sequenceclf;

t=0:0.1:5;

y=square(2*pi*t);

figure(1);

stem(t,y);

title('square sequence in continuous domain');

xlabel('time');

ylabel('amplitude');%axis([0 20 -2 2]);


PROGRAM:

%program to generate exponential sequence

clf;t=0:10;

y=exp(0.3*t);

figure(1);

stem(t,y);

grid;

title('Exponential sequence');

xlabel('time');



8/66

A.UNIT STEP SEQUENCE :

INPUT: n = -10:10

OUTPUT:


INPUT: n = -20:20

OUTPUT:


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INPUT: n = 0:10

OUTPUT:


INPUT:n = 0: 0.1:pi

OUTPUT:


10/66

e.SAWTOOTH WAVE:

INPUT:n = 0 : 0.1: 5

OUTPUT:

F. SQUARE WAVE:

INPUT: n =0:0.1:5

OUTPUT


11/66


INPUT:n = 0:10

OUTPUT:

RESULT:

Thus the MATLAB programs for unit step, unit impulse, unit ramp, sinusoidal signal sawtooth, square wave, exponential signals were generated and their responses were plotted in discrete

and continuous time domain successfully.


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A.FFT(FAST FOURIER TRANSFORM)

AIM:(i) To write a MATLAB program to obtain Fast Fourier Transform for the system given in the

form of finite duration sequence as follows x(n) = {1, 1, 1, 0, 0, 0, 0, 0} using FFT algorithm.

APPARATUS REQUIRED:

HARD WARE: IBM PC (Or) Compatible PC

SOFTWARE: MATLAB 6.0 (Or) Higher version

THEORY:

FFT:

The implementation of DFT through digital computers requires memory to store x(n) and

values of coefficients WknN . The amount of accessing and storing of data in computation is directly

proportional to the number of arithmetic operations involved. Therefore, for direct computation of

N- point DFT the amount computation and computation time is proportional to N2. From equation

(1) observe that the direct calculation of the DFT requires N2complex multiplications and N (N-1)

complex additions. Direct computation of DFT is basically inefficient primarily because it does not

exploit the symmetry and periodicity properties of the twiddle or phase factor WN.

As the value of N increases, the direct computation of DFT becomes a time taking and

complex process, which also leads to very high memory capacity requirements.

The computationally efficient algorithms, known collectively as Fast Fourier Transform

(FFT) algorithms exploit the symmetry and periodicity properties of the twiddle or phase factor WN.

In particular these two properties are:

Wk+N/2N = -WkN

W

k+N

N = W

k

N

The FFT is a method for computing the DFT with reduced number of calculations. The

computational efficiency is achieved if we adopt a divide and conquer approach. This approach is

based on the decomposition of an N- point DFT into smaller DFTs.

In an N-point sequence, if N can be expressed as N= rm, then the sequence can be decimated

into r- point sequences. For each r- point sequence, r- point DFT can be computed. From the results

of r-point DFT, r2-point DFTs are computed. From the results of r2-point DFTs, the r3-point DFTs

are computed and so on, until we get rm-point DFT.In computing N-point DFT by this method a

number of stages of computation will be m times. The number r is called Radix of the FFT

algorithm.

EX.NO: FFT & IFFT

DATE


13/66

RADIX2 FFT ALGORIHM:

For performing radix-2 FFT, the value of N should be such that, N=2 m. Here the decimation

can be performed m times, where m=log N. In direct computation of N-point DFT, the total

numbers of complex additions are N (N-1) and the total number of complex multiplications is N2. In

radix-2 FFT, the total numbers of complex additions are reduced to N.log 2N and total numbers of

complex multiplications are reduced to (N/2). log 2N.

ALGORITHM:

Step 1: Start the program.

Step 2: Get the finite duration sequence x(n).

Step 3: Calculate the value of N.

Step 4: Using fftcommand, DFT is calculated.

Step 5: Calculate the magnitude and phase responses.

Step 6: Plot the magnitude and phase responses.

Step 6: Terminate the process.


14/66

PROGRAM:

xn=[1 1 1 0 0 0 0 0];

N=8;

Xk=fft(xn,N);

disp('DFT of the given sequence is');

disp(Xk);

%computation of magnitude response of X(k)

subplot(2,1,1);

z=abs(Xk);

disp('Magnitude response is');

disp(z);

stem(z);

grid;

title('plot of magnitude of X(k)');

xlabel('index k');

ylabel('magnitude');

%Enter the input x(n)xn=[1 1 1 0 0 0 0 0];

N=8;

Xk=fft(xn,N);disp('DFT of the given sequence is');

disp(Xk);

%computation ofphase responsesubplot(2,1,2);

t=angle(Xk);

disp('Phase response is');

disp(t);

stem(t);grid;

title('plot of phase of X(K)');

xlabel('index k');

ylabel('angle in radians');


15/66

OUTPUT:

FFT OF THE GIVEN SEQUENCE

[3.0000 1.7071 - 1.7071i 0 - 1.0000i 0.2929 + 0.2929i 1.0000

0.2929 - 0.2929i 0 + 1.0000i 1.7071 + 1.7071i]

Magnitude response is

[ 3.0000 2.4142 1.0000 0.4142 1.0000 0.4142 1.0000 2.4142 ]

Phase response is

[ 0 -0.7854 -1.5708 0.7854 0 -0.7854 1.5708 0.7854 ]

RESULT:

Thus the MATLAB programs for FFT for the given finite duration was generated usingFFT algorithm.


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B.IFFT (INVERSE FAST FOURIER TRANSFORM)

AIM

To write a MATLAB program to obtain Inverse Discrete Fourier Transform for the system

given in the form of finite duration sequence as follows Xk=[5 0 (1-j) 0 1 0 (1+j) 0 ]using FFT

algorithm. Also plot the magnitude and phase responses for the same.

APPARATUS REQUIRED:



THEORY:

COMPUTATION OF IDFT THROUGH FFT:

The Inverse Discrete Fourier Transform (IDFT) of the sequence X(k) of length N is defined as,

N-1

IDFT [X (k)] = x (n) = 1/N X(k) ej2nk /N, n = 0,1,2,3(N-1) (1)k = 0

Taking the conjugate of equation (1) multiplying by N, we getN-1

N. x*(n) = X*(k) e -j2nk /N, n = 0,1,2,3(N-1) (2)k = 0

The R.H.S of equation (2) the DFT of the sequence x*(n) and may be computed using FFT

algorithm. The desired output sequence x(n) is obtained by complex conjugating the equation (2)

and dividing by N to give

N-1

x(n) = 1/N [ X*(k) e -j2nk /N]*, n = 0,1,2,3(N-1) ..(3)

k = 0

In equation (3) the expression inside the brackets is same as the DFT computation of a sequence.

Hence in order to compute IDFT of X(k), the following procedure can be followed.

1.Take complex conjugate of X(k).

2. Compute the N-point DFT of X*(k) using radix2 FFT.

3. Take complex conjugate of the output sequence of FFT.

4. Divide the sequence obtained in step 3 by N. The resultant sequence is x(n).

EX.NO: FFT & IFFT

DATE


17/66

ALGORITHM:


Step 2: Get the finite duration sequence X(k).

Step 3: Calculate the value of N.

Step 4: Using ifftcommand, IDFT is calculated.

Step 5: Calculate the magnitude and phase responses.

Step 6: Plot the magnitude and phase responses.



18/66

PROGRAM:

%computation of IFFT

%Enter the input X(k)

Xk=[5 0 (1-j) 0 1 0 (1+j) 0 ];

N=8;

xn=ifft(Xk,N);

disp('IFFT of the given sequence is');

disp(xn);


19/66

INPUT:

X(K) =[5 0 (1-j) 0 1 0 (1+j) 0 ]

OUTPUT:

IFFT of the given sequence is

[1.0000 0.7500 0.5000 0.2500 1.0000 0.7500 0.5000 0.2500]

RESULT:Thus the MATLAB programs for IFFT for the given finite duration were executed.


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A. DECIMATION USING MATLAB

AIM:To write a MATLAB program to decimate the given sinusoidal sequence for a down sampling

factor of M = 2.

APPARATUS REQUIRED:



THEORY:

The process of reducing the sampling rate of a signal is called decimation

(Sampling rate compression). Decimation is also known as down sampling.

The decimated signal is given by

y(n)= x(Mn) , where M be the integer sampling rate reduction factor.

The general representation of decimation process can be

x(n) w(n) y(n)

F F F F1=F/MDecimator

ALGORITHM:


Step 2: Get the length of the sinusoidal input signal.

Step 3: Get the down sampling factor M.

Step 4: Get the frequency of sinusoidal signal.

Step 5: Compute the decimated signal using decimate command.

Step 6: Plot the output sequence.


h(n) M

EX.NO: VERIFICATION OF SAMPLING THEOREM

DATE :


21/66

PROGRAM:

%Decimation process

%Get the length of sinusoidal signal

N=input('Enter the length of sinusoidal signal :');

n=0:N-1;

%Get the value of Down sampling factor

M=input('Enter the Down-sampling factor :');

n=0:N-1;

%Generate the input sequence

f=input('Enter the input signal frequency :');

x=sin(2*pi*f*n);

%Generate the decimated output sequence

y=decimate(x,M,'fir');

%plot the input sequence

figure(1);

stem(n,x(1:N));

title('input sequence');

xlabel('time index n--->');


m=0:(N/M)-1;

figure(2);

stem(m,y(1:N/M));

title('Decimated output sequence');




22/66

INPUT:

Enter the length of sinusoidal signal :100

Enter the Down-sampling factor :2

Enter the input signal frequency :0.045

OUTPUT:

INPUT WAVEFORM

0 10 20 30 40 50 60 70 80 90 100-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

input sequence

time index n--->

amplitude

OUTPUT WAVEFORM

0 5 10 15 20 25 30 35 40 45 50

-1

-0.5

0

0.5

1

1.5

Decimated output sequence

time index n--->

amplitude


23/66


24/66

B.INTERPOLATION USING MATLAB

AIM:To write a MATLAB program to interpolate the given sinusoidal sequence for a

Up sampling factor of L = 3.

APPARATUS REQUIRED:



THEORY:

The process of increasing the sampling rate of a signal is called Interpolation (Sampling rate

expansion). Interpolation is also known as up sampling.

The interpolated signal is given by

y(n)= x(n/L) , where L be the integer sampling rate increasing factor.

The general representation of interpolation process can be

x(n) w(n) y(n)

F F1=LF F1

ALGORITHM:



Step 3: Get the Up sampling factor L.


Step 5: Compute the interpolated signal using interp command.

Step 6: Plot the output sequence.


L h(n)

EX.NO: VERIFICATION OF SAMPLING THEOREM

DATE :


25/66

PROGRAM:

%interpolation process

%Get the length of sinusoidal signal

N=input('Enter the length of sinusoidal signal:');

n=0:N-1;

%Get the value of Up sampling factor

L=input('Enter the Up-sampling factor:');

%Generate the input sequence

f=input('Enter the input signal frequency:');

x=sin(2*pi*f*n);

%Generate the interpolated output sequence

y=interp(x,L);

%plot the input sequence

figure(1);

stem(n,x(1:N));

title('input sequence');



figure(2);

m=0:(N*L)-1;

stem(m,y(1:N*L));

title('Interpolated output sequence');




26/66

INPUT:Enter the length of sinusoidal signal: 50

Enter the Up-sampling factor: 3

Enter the input signal frequency: 0.045

OUTPUT

INPUT WAVEFORM

OUTPUT WAVEFORM

0 50 100 150-1.5

-1

-0.5

0

0.5

1

1.5Interpolated output sequence

time index n--->

amplitude


27/66

RESULT:

Thus the MATLAB program for interpolate the given sinusoidal sequence for a Up

sampling factor of L = 3 was generated and executed successfully


28/66

LINEAR CONVOLUTION USING MATLAB

AIM:

To write a MATLAB program to obtain the linear convolution between two finite duration

sequences x(n) and h(n).

APPARATUS REQUIRED:



THEORY:

Convolution is a powerful way of characterizing the input-output relationship of time invariant linear systems. Convolution finds its application in processing signals especially analyzing

the output of the system.

The response or output y(n) of a LTI system for any arbitrary input is given by convolution

of input and the impulse response h(n) of the system.

y(n) = [x(k) h(n-k) ] (1)

k =

If the input has L samples and the impulse response h(n) has M s amples then the outputsequence y(n) will be a finite duration sequence consisting of L+ M-1 samples. The convolution

results in a non-periodic sequence. Hence this convolution is also called aperiodic convolution.

The convolution relation of equation (1) can also be expressed as

y(n) = x(n) *h(n) = h(n) * x(n)

where the symbol * indicates convolution operation.

ALGORITHM:


Step 2: Get the sequence x(n).

Step 3: Get the range of the sequence x(n).

Step 4: Get the sequence h(n).

Step 5: Get the range of the sequence h(n)..

Step 6: Find the convolution between the sequences x(n) and h(n) using conv command.

Step 7: Plot the convoluted sequence y(n).


EX.NO: LINEAR AND CIRCULAR CONVOLUTION USING MATLAB

DATE :


29/66


30/66

INPUT:Enter the input sequence x(n)[ 1 2 3 4]

Enter the range of x(n)0:3

Enter the input sequence h(n)[4 3 2 1]

Enter the range of h(n)-1:2

OUTPUT: Convoluted output: 4 11 20 30 20 11 4

0 0.5 1 1.5 2 2.5 30

1

2

3

4

input sequence x(n)

time

amplitude

-1 -0.5 0 0.5 1 1.5 20

1

2

3

4

impulse response sequence h(n)

time

amplitude

-1 0 1 2 3 4 50

5

10

15

20

25

30

output sequence

time

amplit

ude


31/66

RESULT:Thus the MATLAB program for Linear convolution was generated and their

responses were plotted in discrete time domain successfully.


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B.CIRCULAR CONVOLUTION USING MATLAB

AIM:

To write a MATLAB program to obtain the circular convolution between two finite duration


APPARATUS REQUIRED:



THEORY:

Convolution is a powerful way of characterizing the input-output relationship of time invariant linear systems. Convolution finds its application in processing signals especially analyzing

the output of the system.

The response or output y(n) of a LTI system for any arbitrary input is given by convolution

of input and the impulse response h(n) of the system.

y(n) = [x(k) h(n-k) ] (1)

k = If the input has L samples and the impulse response h(n) has M samples then the output

sequence y(n) will be a finite duration sequence consisting of L+ M-1 samples. The convolution

results in a non-periodic sequence. Hence this convolution is also called aperiodic convolution.

The convolution relation of equation (1) can also be expressed as

y(n) = x(n) *h(n) = h(n) * x(n)

where the symbol * indicates convolution operation.

ALGORITHM:


Step 2: Get the sequence x(n).

Step 3: Get the range of the sequence x(n).

Step 4: Get the sequence h(n).

Step 5: Get the range of the sequence h(n)..

Step 6: Find the convolution between the sequences x(n) and h(n) using conv command.

Step 7: Plot the convoluted sequence y(n).


EX.NO: LINEAR AND CIRCULAR CONVOLUTION USING MATLAB

DATE :


33/66

PROGRAM:

%program to find the circular convolution

seq1=input('enter the input sequence: ');

N1=length(seq1);

k1=0:N1-1;

subplot(2,1,1);

stem(k1,seq1);

title('first sequence ');

xlabel('time');


seq2=input('enter the second sequence: ');

N2=length(seq2);

k2=0:N2-1;

subplot(2,1,2);

stem(k2,seq2);

title('first sequence ');

xlabel('time');


seq3=[seq2(1) fliplr(seq2(2:N1))];

seq4=seq1.*seq3;

seq(1)=sum(seq4);

N=N1;

for n=1:N-1;

seq5=[seq3(N) seq3(1:N-1)];

seq6=seq5.*seq1;

seq(n+1)=sum(seq6);

seq3=seq5;end

disp('circular convolution sequence');

disp(seq);

figure(2);

stem(k2,seq);

title('circular convolution sequence ');

xlabel('time');



34/66

INPUT:enter the input sequence: [1 2 3 4]

enter the second sequence: [5 6 7 8]

OUTPUT: circular convolution sequence: 66 68 66 60

INPUT SEQUENCE

OUTPUT SEQUENCE


35/66

RESULT:Thus the MATLAB program for Circular convolution was generated and their

responses were plotted in discrete time domain successfully.


36/66

AIM:

To write a MATLAB program for the design of FIR Low Pass Filter (LPF) for the given cut

off frequency using Hamming window. Also plot the magnitude and log magnitude responses for

the same.

APPARATUS REQUIRED:



THEORY:

The filters designed by using finite number of samples of impulse response are called

FIR filters. These finite number of samples are obtained from the infinite duration desired impulse

response hd(n). Here hd(n)is the inverse Fourier transform of Hd(), where Hd() is the ideal

(desired) frequency response. The various methods of designing FIR filters are (i). Fourier series

method, (ii). Window method, (iii). Frequency Sampling method, (iv) Optimal filter design method.

Here we discuss about window method only.

DESIGN OF FIR FILTERS USING WINDOWS:

The desired frequency response Hd(ej

) of a filter is periodic in frequency and can be

expanded in a Fourier series. The resultant series is given by

Hd(e

j) = hd(n)e

-jn ..(1)n =

Where hd(n) = 1/2 H(ej) ejn d (2)

-And known as Fourier coefficients having infinite length. One possible way of obtaining

FIR filter is to truncate the infinite Fourier series at n= (N-1)/2, where N is the length of the

desired sequence. But abrupt truncation of the Fourier series results in oscillation in the pass band

and stop band. These oscillations are due to slow convergence of the Fourier series and this effect is

known as the Gibbs phenomenon. To reduce these oscillations, the Fourier coefficients of the filter

are modified by multiplying the infinite impulse response with a finite weighing sequence (n)

called a window.

Where

(n) = (-n) 0 for |n| (N-1)/2

= 0 for |n| > (N-1)/2

EX.NO: DESIGN OF FIR FILTER USING MATLAB

DATE :


37/66

After multiplying window sequejnce w(n) with Hed(n), we get a finite duration sequence

jh(n) that satisfies the desired magnitude respone,

h(n) = hd(n)(n) for all |n| (N-1)/2

= 0 for |n| > (N-1)/2

The frequency response H(ej) of the filter can be obtained by convolution of Hd(ej)) and

W(ej) given by

H(ej) = 1/2 Hd(Hd(e

j ) W(ej(-) ) d (2)-

= H(ej) * W(ej)

Because both Hd(ej) and W(ej) are periodic function, the operation often called as periodic

convolution.

HAMMING WINDOW:The Hamming window sequence is given by

H (n) = 0.54+0.46 Cos 2n /(N-1) for (N-1)/2 n (N-1) /2

= 0 otherwise

The frequency response of Hamming window is

WH(ej) = 0.54 Sin (N/2) + 0.23Sin (N/2 - N / N-1) + 0.23Sin (N/2 + N / N-1)

Sin (/2) Sin (/2 - / N-1) Sin (N/2 + / N-1)

LOW PASS FILTER:

The magnitude response of an ideal low pass filter allows low

frequencies in the pass band to pass, whereas the high frequencies in the stop band are blocked. The

frequency cbetween the two bands is the cutoff frequency.

ALGORITHM:


Step 2: Get the cutoff frequency.

Step 3: Get the value of N.

Step 4: Get the window function (n) for Hamming window.

Step 5: Design a linear phase FIR low pass filter using fir1 command.

Step 6: Compute the complex frequency response of digital transfer function at specified

frequency points using freqz command.

Step 7: Plot the magnitude response and log magnitude response.



38/66

PROGRAM:

%Design of Low pass FIR Filter using Hanning window

%Get the cutoff frequency

wc=input('Enter the cut off frequency :');

%Get the order of the filter(N)N=input('Enter the order of the filter :');

%calculation of filter co efficients

b=fir1(N,wc,hanning(N+1));

w=0:0.01:pi;

%compute the frequency response

h=freqz(b,1,w);

%plot the magnitude response of LPF

figure(1);

plot(w/pi,abs(h));

ylabel('magnitude');

xlabel('normalized frequency');

title('magnitude response of LPF');

%plot the log magnitude response of LPF

figure(2);

plot(w/pi,20*log10(abs(h)));

ylabel('magnitude in dB');

xlabel('normalized frequency');

title('Log magnitude response of LPF');


39/66

INPUT:

Enter the cut off frequency : 0.9

Enter the order of the filter : 25

OUTPUT:

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.2

0.4

0.6

0.8

1

1.2

1.4

magnitude

normalized frequency

magnitude response of LPF

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-60

-50

-40

-30

-20

-10

0

10

magnitudeindB

normalized frequency

Log magnitude response of LPF


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RESULT:

Thus the MATLAB program for the design of FIR LPF using Hamming window for the

given cut off frequency was designed and also magnitude and log magnitude responses for the same

were plotted successfully.


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AIM:

To write a MATLAB program to design (i) Butterworth low pass digital IIR filter

(ii) Butterworth high pass digital IIR filter from the given specifications.

APPARATUS REQUIRED:



THEORY:The filters designed by considering all the infinite samples of impulse response are

called IIR filters. IIR filters are of recursive type, whereby the present output sample depends on the

present input, past input samples and output samples.

DESIGN OF AN ANALOG BUTTERWORTH LOWPASS FILTER:

1. From the given specifications find the order of the filter N.

N log (/)log (s /P)

Where

= (100.1

s-1)1/2

= (100.1

p-1)1/2

s-minimum stop band attenuation in positive dBp-maximum pass band attenuation in positive dB

p-pass band frequency

s-stop band frequency

2. Round off it to the next higher integer.

3. Find the transfer function H (s) for c=1 rad/sec for the value of N.4. Calculate the value of cutoff frequency c.5. Find the transfer function H a(s) for the above value of cby

Substituting s s/ c in H (s).

DESIGN OF DIGITAL FILTERS FROM ANALOG FILTERS:

The most common technique used for designing IIR digital filters known as indirect method, involves first designing an analog prototypefilter and then transforming the prototype to a digital filter. For the given specifications of a digital filter, the derivation of the digital filter

transfer function requires three steps.

1. Map the desired digital filter specifications into those for an equivalent analog filter.

2. Derive the analog transfer function for the analog prototype.

3. Transform the transfer function of the analog prototype into an equivalent digital filter

transfer function.

The four most widely used methods for digitizing the analog filter into a digital filter include.

1 .Approximation of derivatives.2. The impulse invariant transformation

3. The bilinear transformation

4. The matched z-transformation technique.

EX.NO: DESIGN OF IIR FILTER USING MATLAB

DATE:


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FREQUENCY TRANSFORMATION IN DIGITAL DOMAIN:

As in the analog domain frequency transformations can be performed on a digital low pass

filter to convert it to band pass, band stop, or high pass filter.

LOW PASS TO LOW PASS TRANSFORMATION :Z-1 Z -1

1- Z -1 where = sin[(c1

+ c )/ 2]

sin[(c1- c )/ 2]50

LOW PASS TO HIFH PASS TRANSFORMATION :

Z-1 Z -1 +1+ Z -1 where = cos[(c

1+ c )/ 2]

cos[(c1

- c )/ 2]

DESIGN OF BUTTERWORTH LPF:

ALGORITHM:


Step 2: Get the Pass band and Stop band edge ripples.

Step 3: Get the Pass band and Stop band edge frequencies.

Step 4: Select Sampling frequencies to be 1K Hz.

Step 5: Calculate the order of the filter.

Step 6: Design a LOW pass filter using butter (N, n,low).

Step 7: Draw the magnitude response of low pass filter.



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PROGRAM:

%Design of Butterworth IIR LPF

rp=input('Enter passband ripple :');

rs=input('Enter stopband ripple :');

fp=input('Enter passband frequency :');

fs=input('Enter stopband frequency :');

Fs=input('Enter sampling frequency :');

wp=2*(fp/Fs);

ws=2*(fs/Fs);

[N,wn]=buttord(wp,ws,rp,rs);

[b,a]=butter(N,wn,'low');

[hl,ol]=freqZ(b,a,512,Fs);

ml=20*log10(abs(hl));

%plot(1);

plot(ol/pi,ml);

xlabel('normalised frequency is ---->');

ylabel('gain in db --->');

title('butterworth lowpass filter');


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DESIGN OF BUTTERWORTH HPF:

ALGORITHM:


Step 2: Get the Pass band and Stop band edge ripples.

Step 3: Get the Pass band and Stop band edge frequencies.

Step 4: Select Sampling frequencies to be 1K Hz.

Step 5: Calculate the order of the filter.

Step 6: Design a HIGH pass filter using butter (N, n,high).

Step 7: Draw the magnitude response of high pass filter.



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PROGRAM:

% Design of Butterworth IIR HPF

rp=input('Enter passband ripple :');

rs=input('Enter stopband ripple :');

fp=input('Enter passband frequency :');fs=input('Enter stopband frequency :');

Fs=input('Enter sampling frequency :');

wp=2*(fp/Fs);

ws=2*(fs/Fs);

[n,wn]=buttord(wp,ws,rp,rs);

[b,a]=butter(n,wn,'high');

[hh,oh]=freqZ(b,a,512,Fs);

mh=20*log10(abs(hh));

plot(oh/pi,mh);

xlabel('normalised frequency is ---->');

ylabel('gain in db --->');

title('butterworth highpass filter');


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INPUT:

Enter passband ripple :03

Enter stopband ripple :60

Enter passband frequency :40

Enter stopband frequency :150Enter sampling frequency :1000

OUTPUT:

0 20 40 60 80 100 120 140 160-180

-160

-140

-120

-100

-80

-60

-40

-20

0

20

normalised frequency is ---->

gainindb--->

butterworth highpass filter

RESULT:

Thus the MATLAB programs for the design of Butterworth LPF and HPF were designed

and also their magnitude responses were plotted successfully.


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AIM:To write a MATLAB program to 'Decimation of polyphase decomposition sequence response'

APPARATUS REQUIRED:



THEORY:

The process of reducing the sampling rate of a signal is called decimation(Sampling rate compression). Decimation is also known as down sampling.

The decimated signal is given by

y(n)= x(Mn) , where M be the integer sampling rate reduction factor.

The general representation of decimation process can be

x(n) w(n) y(n)

F F F F1=F/M

Decimator

ALGORITHM:



Step 3: Get the down sampling factor M.


Step 5: Compute the decimated signal using decimate command.

Step 6: Plot the output sequence.Step 7: Terminate the process.

h(n) M

EX.NO: 'DECIMATION OF POLYPHASE DECOMPOSITION SEQUENCE

DATE: RESPONSE'


49/66

PROGRAM:

%'Decimation of polyphase decomposition sequence response'

clear all;

clc;

close all;

x=input('enter the input sequence');h=input('enter the FIR filter coefficients');

M=input('enter the decimation factor');

N1=length(x);

N=0:1:N1-1;

subplot(2,1,1);

stem(N,x);

xlabel('time');


Title('X sequence response');

N2=length(h);

n=0:1:N2-1;

subplot(2,1,2);stem(n,h);

xlabel('time');


title('H sequence response');

H=length(h);

P=floor((H-1)/M)+1;

r=reshape([reshape(h,1,H),zeros(1,P*M-H)],M,P);

X=length(x);

Y=floor((X+H-2)/M)+1;

U=floor((X+M-2)/M)+1;

R=zeros(1,X+P-1);for m=1:M

R=R+conv(x(1,:),r(m,:));

end

Disp(R);

N=length(R);

n=0:1:N-1;

figure(2);

stem(n,R);

xlabel('time');


title('Decimation of polyphase decomposition sequence response');


50/66

INPUT:

Enter the input sequence:[1 2 3 4]

Enter the FIR filter coefficients [1 1 1 1]

Enter the decimation factor 3

OUTPUT:3 7 11 15 4

INPUT WAVEFORM

OUTPUT WAVEFORM


51/66

RESULT:Thus the MATLAB program for decimate the given sinusoidal sequence for a down

sampling factor of M = 2 was generated and executed successfully.


52/66

KIT EXPERIMENTS


53/66

AIM:

To write a assembly program to generate a following standard input signals Sinusoidalsignal, Saw tooth wave, Square wave and triangle wave

PROGRAM

;SINEWAVE GENERATION.

;*********************

FREQ .set 1

LENGTH .SET 360

AMPLITUDE .set 5

TEMP .set 0TEMP1 .set 1

.mmregs

.text

START:

LDP #100HSPLK #0C100H,TEMP ;load start address of table

lar AR2,#LENGTH

CONT:

LACC TEMP ;load address of sine value

TBLR TEMP1 ;read sine data to TEMP1LT TEMP1

MPY #AMPLITUDE

PAC

SACL TEMP1

OUT TEMP1,4 ;send sine data to DAC

LACC TEMP

ADD #FREQ ;increase table value

SACL TEMP ;store it

MAR *,AR2

BANZ CONT,*-

b START

.end

EX. NO: GENERATION OF SIGNALS

DATE:


54/66


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;triangle

AMPLITUDE .SET 5

FREQ .SET 175

TEMP .SET 0

;

.mmregs

.text

START:

LDP #100H

splk #0,TEMP

CONT1:

lar AR2,#FREQ

CONT:

out TEMP,4

LACC TEMP

ADD #AMPLITUDE

SACL TEMP

MAR *,AR2BANZ CONT,*-

LAR AR2,#FREQ

CONTx:

OUT TEMP,4

LACC TEMP

SUB #AMPLITUDE

SACL TEMP

MAR *,AR2

BANZ CONTx

B CONT1.end

RESULT:

Thus the Assembly programs for sinusoidal signal saw tooth, square wave triangle w were

plotted in discrete and continuous time domain successfully.


56/66

AIM:

To write a assembly program to obtain the linear convolution between two finite duration


PROGRAM:

;***************************************************************************

; LINEAR CONVALUTION

;***************************************************************************

.mmregs

.text

START:LDP #02H

LAR AR1,#8100H ; x(n) datas

lar ar0,#08200H ;h(n) datas

LAR AR3,#8300H ;y(n) starting

LAR AR4,#0007 ;N1+N2-1

;to fold the h(n) values

lar ar0,#08203H

lacc #0c100h

mar *,ar0

rpt #3

tblw *-;padding of zerros for x(n) values

lar ar6,#8104h

mar *,ar6

lacc #0h

rpt #3h

sacl *+

;convalution operation starts

LOP: MAR *,AR1

LACC *+

SACL 050H ;starting of the scope of multiplication

LAR AR2,#0153H ; end of the array, to be multiplied with h(n) {150+N1-1}MAR *,AR2

ZAP

RPT #03H ;N1-1 times so that N1 times

MACD 0C100H,*-

APAC ;to accmulate the final product sample

MAR *,AR3

SACL *+

MAR *,AR4

BANZ LOP,*-

H: B H

EX. NO: LINEAR CONVOLUTION USING TMS320C50


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;INPUT ( x(n) )

;8100 - 1

;8101 - 3

;8102 - 1

;8103 - 3

;INPUT ( h(n) )

; 8200 - 0

; 8201 - 1

; 8202 - 2

; 8203 - 1

;OUTPUT ( y(n) )

; 8300 - 1

; 8301 - 5; 8302 - 8

; 8303 - 8

; 8304 - 7

; 8305 - 3

; 8306 - 0

RESULT:

Thus the Assembly programs for linear convolution was successfully verified


58/66

AIM:

To write a assembly program to obtain the FFT

PROGRAM

;*********************************************************

; FFT(4 POINT)

;*********************************************************

IN .set 8010H

BITREV .set 8020H

REAL .set 8040H

IMG .set 8050H

.MMREGS.TEXT

LDP #100H

LAR AR1,#IN

LAR AR2,#BITREV

SPLK #2H,05H

LMMR INDX,#8005H

MAR *,AR2

RPT #3H

BLDD #IN,*BR0+

LAR AR2,#BITREVLAR AR3,#8030H

LAR AR0,#1H

FFT1: MAR *,AR2

LACC *+

SACB

LT *+

MPY #1H

APAC

MAR *,AR3

SACL *+

LACBSPAC

SACL *+,AR0

BANZ FFT1,*-

LAR AR3,#8030H

LAR AR4,#REAL

LAR AR5,#IMG

MAR *,AR3

LACC *

SACB

ADRK #2H

LT *-

MPY #1H

APAC

MAR *,AR4

EX. NO: FFT USING TMS320C50


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SACL *

ADRK #2H

LACC #0H

MAR *,AR5

SACL *

ADRK #2H

LACB

SPAC

MAR *,AR4

SACL *-

LACC #0H

MAR *,AR5

SACL *-,AR3

LACC *,AR4

SACL *

ADRK #2H

SACL *,AR3

ADRK #2H

LT *

MPY #0FFFFHMAR *,AR5

SPL *,AR3

LT *

MPY #1H

MAR *,AR5

ADRK #2H

SPL *

H: B H


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;INPUT:

; 8010-0001

; 8011-0001

; 8012-0000

; 8013-0000

;BIT_REV:

; 8020-0001

; 8021-0000

; 8022-0001

; 8023-0000

;FFT1:

; 8030-0001

; 8031-0001

; 8032-0001

; 8033-0001

;REAL:

; 8040-0002

; 8041-0001; 8042-0000

; 8043-0001

;IMG:

; 8050-0000

; 8051-FFFF

; 8052-0000

; 8053-0001

RESULT:

Thus the Assembly programs for FFT was successfully verified


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AIM:

To write a assembly program to obtain the FIR design.

PROGRAM

* FIR Filter, Created by Filter Design Package,

* (c) 1996, Vi Microsystems Pvt. Ltd.,

*

* Approximation type: Window design - Blackmann Window

* Filter type: Lowpass filter

* Filter Order: 52

* Cutoff frequency in KHz = 3.000000

.mmregs.text

B START

CTABLE:

.word 0FFE7H ;Filter coefficients n=0

.word 0FFD3H

.word 0FFC6H

.word 0FFC4H

.word 0FFD0H

.word 0FFECH

.word 018H

.word 051H

.word 08CH

.word 0B9H

.word 0C2H

.word 092H

.word 01AH

.word 0FF5FH

.word 0FE78H

.word 0FD9AH

.word 0FD10H

.word 0FD30H

.word 0FE42H

.word 071H

.word 03B5H

.word 07CAH

.word 0C34H

.word 01054H

.word 01387H

.word 01547H

.word 01547H

.word 01387H

.word 01054H

.word 0C34H

.word 07CAH

.word 03B5H

.word 071H

.word 0FE42H

EX. NO: FIR DESIGN USING TMS320C50


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.word 0FD30H

.word 0FD10H

.word 0FD9AH

.word 0FE78H

.word 0FF5FH

.word 01AH

.word 092H

.word 0C2H

.word 0B9H

.word 08CH

.word 051H

.word 018H

.word 0FFECH

.word 0FFD0H

.word 0FFC4H

.word 0FFC6H

.word 0FFD3H

.word 0FFE7H ;Filter coefficients n=52

** Move the Filter coefficients

* from program memory to data memory

*

START:

MAR *,AR0 ;This block moves the filter coefficient from pgm memory to

data memory.

LAR AR0,#0200H

RPT #33H

BLKP CTABLE,*+

SETC CNF

* Input data and perform convolutionISR: LDP #0AH

LACC #0

SACL 0

OUT 0,05

IN 0,06H

LAR AR7,#0

MAR *,AR7

BACK: BANZ BACK,*-

IN 0,4

NOP

NOPNOP

NOP

MAR *,AR1

LAR AR1,#0300H

LACC 0

AND #0FFFH

SUB #800H

SACL *

LAR AR1,#333H

MPY #0

ZAC

RPT #33H

MACD 0FF00H,*- ;CONVOLUTION OPERATION

APAC

LAR AR1,#0300H


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SACH *

LACC *

ADD #800h

SACL *

OUT *,4

LACC #0FFH

SACL 0

OUT 0,05

NOP

B ISR

.end

OUTPUT:

RESULTThus the Assembly programs for FIR design was successfully verified


64/66

AIM:

To write a assembly program to obtain the IIR design.

PROGRAM:.MMREGS

.TEXT

TEMP .SET 0

INPUT .SET 1

T1 .SET 2

T2 .SET 3

T3 .SET 4

;

K .SET 315eh

M .SET 4e9fh

;cut-off freq is 1Khz. = Fc

;sampling frequency is 100 s (ie) 0.1ms.

; a = 2 * (355/113) * 1000 = 6283.18/1000 = 6.28 ;; divide by 1000 for secs

; K = aT/(1+aT) = 6.28*0.1 / (6.28*0.1+1) = 0.3857

; M = 1/(1+aT) = 1 / (6.28*0.1+1) = 0.61425

;convert to Q15 format

; K = K * 32767 = 12638.23 = 315Eh

; M = M * 32767 = 20127.12 = 4E9Fh

;Sampling Rate is 100 s & Cut off Frequency is 1 Khz

LDP #100H

LACC #0

SACL T1

SACL T2

SACL TEMP

OUT TEMP,4 ;CLEAR DAC BEFORE START TO WORK

LOOP:

LACC #0

SACL TEMPOUT TEMP,5 ;OUTPUT LOW TO DAC2 TO CALCULATE TIMING

;

IN TEMP,06 ;SOC

;

LAR AR7,#30h ;CHANGE VALUE TO MODIFY SAMPLING FREQ.

;sampling rate 100 s.

MAR

*,AR7

BACK:

BANZ

BACK,*-;

IN INPUT,4 ;INPUT DATA FROM ADC1

NOP

NOP

EX. NO: IIR DESIGN USING TMS320C50


65/66

;

LACC INPUT

AND #0FFFH

SUB #800h

SACL INPUT

;

LT INPUT

MPY #K

PAC

SACH T1,1

;;;CALL MULT ----MULTIPLICATION TO BE DONE WITH K

;;RESULT OF MULT IN T1

;

LT T2 ;PREVIOUS RESULT IN T2

MPY #M

PAC

SACH T3 ,1

;;;CALL MULT ----MULTIPLICATION TO BE DONE WITH M

;;RESULT OF MULT IN T3+;

LACC T1

ADD T3

SACL T2

ADD #800h

SACL TEMP

OUT TEMP,4 ;OUTPUT FILTER DATA TO DAC1

;

LACC #0FFH

SACL TEMP

OUT TEMP,5 ;OUTPUT HIGH TO DAC2 TO CALCULATE TIMING;

B LOOP


66/66

OUTPUT:

0 20 40 60 80 100 120 140 160

-180

-160

-140

-120

-100

-80

-60

-40

-20

0

20

normalised frequency is ---->

gainindb--->

butterworth highpass filter

dsp record for ece hit

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