7etc_dsp

8/8/2019 7ETC_DSP

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G.H.RAISONI COLLEGE OF ENGINEERING,NAGPUR

Department:-Electronics & Communication Engineering

Branch:-7th

Semester[Electronics & Telecommunication]

Subject:-Digital Signal Processing

List of Experiments

CYCLE-I

1. Write a MATLAB program to generate standard discrete time signals and to plot

them.

2. Write a MATLAB program to evaluate the convolution between two givensequences.

3. Write a MATLAB program to find the poles, zeros and express H[z] in factored

form.H[z] = (z4

+ 8z3

+ 20z2

+ 25z +16)/(z4+ 2z

3-8z

2+12z-10)

4. (a) Write a MATLAB program to evaluate the impulse response of following

difference equation.

y[n] – 0.25y[n-1]+0.45y[n-2] = 1.55x[n] + 1.95x[n-1]+2.15x[n-2]

(b) To study the block diagrammatic representation of FIR systems using DF-Iand DF-II forms.

5. Write a MATLAB program to evaluate linear convolution using DFT for twofinite sequences. Also compute errors between convolution by DFT and direct

linear convolution. CYCLE-II

5. Write am MATLAB program to to obtain original sequence x[n] by IDFT for

given k point DFT.X[k] = k/ K 0 k K-1

0 elsewhere

7. Write a MATLAB program to design a FIR low pass filter with following

specification using Keiser Window. M = 61, = 4.95 , 0.35 (actully0.35 ).

8. To implement convolution on fixed point DSP processor

9. To study the effects of low pass filter on floating point DSP processor

10. To study the effects of high pass filter on floating point DSP processor

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Experiment No:-1

Aim:- Write a MATLAB program to generate standard discrete time signals & plot

them

Problem:-To generate the following waveforms:-

a) Unit impulse Function

b) Unit step Function

c) Ramp Functiond) Delayed unit impulse Function

e) Delayed unit step Function

f) Sinusoidal Function

Theory:-A discrete signal is a signal defined only for integer values of the independent

variable(s). Several representations, including explicit sequences of values, formulas, andpiecewise formulas are available for use in Signals and Systems. Digital signals are thus a

subset of discrete signals, and both are handled identically by Signals and Systems.The second-most important discrete-time signal is the unit sample, which is defined to be

(n) = 1 if n=00 otherwise

Discrete-time systems can act on discrete-time signals in ways similar to those found inanalog signals and systems. In fact, a special class of analog signals can be converted into

discrete-time signals, processed with software, and converted back into an analog signal,

all without the incursion of error.

A discrete-time signal is represented symbolically as s(n), where n={…,-

1,0,1,…}. We usually draw discrete-time signals as stem plots to emphasize the fact theyare functions defined only on the integers.

We can delay a discrete-time signal by an integer just as with analog ones. Adelayed unit sample has the expression (n−m), and equals one when n=m.

The unit step function is equal to zero when its index is negative and equal toone for non-negative indexes

unit step: u(n) = 1 if n=00 otherwise

Program:-

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Simulation Results:-

Viva questions:-

1. What is the difference between discrete and digital signal?

2. Define a system and a signal.3. What is the impulse response of the system?

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Experiment No:-2

Aim:- Write a MATLAB program to evaluate the convolution between two sequences.

Problem:- The given sequences are

1) x1(n) = { 1 ,2 ,3 ,4 }2) x1(n) = { 3 ,6 ,1 ,1 }

Theory:-Convolution is used in DSP to find the system response of Linear Time-

Invariant [LTI] systems, to arbitrary inputs.

As with signals, convolution exists in both discrete-time and continuous timedomains. The focus of this document is simply on convolution in the discrete time

domain. Assume a system with

1. Impulse response of h[n]

2. Input forcing signal x[n]3. Output response y[n]

We symbolically write the system response of the convolution of two sequences as

y[n]= x[n]*h[n]. This is equivalent to

y[n]= [0,N-1] (x[k] X h[n-k]),

where n varies from 0,1,2,3..N-1.

If we have the following sequences :-

1. Impulse response of h[n] of length N2. Input forcing signal x[n] of length M

3. And are required to find out the value of the output system response y[n].

4. You are supposed to use the convolution of x[n] and h[n] to get y[n].

5. y[n]= convolution(x[n],h[n]) = x[n]*y[n]6. y[n] is of length M+N-1

Program:-

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Simulation Results:-

Viva questions:-

1. What is convolution? And what are the methods of convolution.

2. Quote any Two applications of convolution.

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Experiment No.3

Aim: Write a MATLAB program to find the poles, zeros of given system.

Problem: find the poles, zeros of given systems.

H [z] = 1/(Z-1)

H[z] = Z/(Z-2)2

H[z] = Z/(Z2-Z-1)

H[z] = (Z+2)/ (Z2-Z-1) (Z-2)

Theory:

The general system function is

1

0

1

0( ) 1

M

k k

N

k k

b Z

H z a Z

−

=

−

=

=

+

Poles: The poles of the systems are values of variable Z for which system function H(z)becomes infinite.

Zeros: The Zeros of the systems are values of variable Z for which system function H(z)

becomes zero.

Program:-

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Simulation result:-

-1 -0.5 0 0.5 1

-1

-0.5

0

0.5

1

Real Part

ImaginaryPa

rt

pole zero plot 1

-1 0 1 2

-1

-0.5

0

0.5

1

2

Real Part

ImaginaryPa

rt

pole zero plot 2

-1 -0.5 0 0.5 1

-1

-0.5

0

0.5

1

Real Part

ImaginaryPa

rt

pole zero plot 3

-2 -1 0 1 2

-1

0

1

Real Part

ImaginaryPa

rt

pole zero plot 4

Discussion questions:-Q1. What are Poles?

Q2. What are Zeroes?Q3. What is the necessity to study Pole-Zero plot of any systems.?

Q4. Where should poles lies in pole-zero plot for a stable system?Q5. What is difference between Pole-zero plot of Laplas Transform & in Z-Transform?

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Experiment No:-4

Aim:- (a)Write a MATLAB program to evaluate the impulse response of the system

(b)To study block diagrammatic representation of FIR system using DF- I &

DF-II System.

Problem:-The Difference equation is given as-

y[n]-0.25y[n-1]+0.45y[n-2]=1.55x[n]+1.95x[n-1]+ 2.15x[n]

Theory:-LTI Discrete time system is completely specified by its impulse response i.e. knowingthe impulse response we can compute the output of the system to any arbitrary input.

Let h[n] denotes the impulse response of the LTI discrete time systems. Since discrete

time system is time invariant, its response to [n-1] will be h[n-1] .Likewise theresponse to [n+2] , [n-4] and [n-6] will be h[n+2], h[n-4] and h[n-6] .

From the above result arbitrary input sequence x[n] can be expressed as a weighted

linear combination of delayed and advanced unit sample in the form k=+

X[n] = x[k] [n-k]k=-

where weight x[k] on the right hand side denotes specifically the k th sample value of

the sequence. The response of the LTI discrete time system to the sequencex[k] [n-k] will be x[k] h [n-k].

As a result, the response y[n] of the discrete time system to x[n] will be given by

k=+

y[n] = x[k] h [n-k] …………..(1)k=-

Which can be alternately written as

k=+ y[n] = x[n-k] h [k]…………(2)

k=-

The above equation (1) and (2) is called the convolution sum of the sequences x[n]and h[n] and represented compactly as y[n]=x[n] * h[n] Where the notation *

denotes the convolution sum.

Structure for Realization of Linear Time Invariant systems:Let us consider the first order system Y(n)=-a 1y(n-1)+b0 x(n) +b1 x(n-1)

This realization uses separate delays(memory) for both the input and output samplesand it is called as Direct form one structure.A close approximation reveals that the two delay elements contain the same input

w(n) and hence the same output w(n-1).consequently these two elements can be

merged into one delay. In contrast to the direct form I structure , this new realization

requires only one delay for auxiliary quantity w(n) ,and it is more efficient in termsof memory requirements. It is called the direct form II structure and it is used

extensively.

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Program:-

Simulation result:-

Discussion questions:-

1) Differentiate between linear and circular convolution.

2) Determine the unit step response of the linear time invariant system with impulseresponse h(n)=a n u(n) a<1 & -a<1

3) Determine the range of values of the parameter a for which linear time invariant

system with impulse response h(n)=a n u(n) is stable.

4) Consider the special case of a finite duration sequence given asX(n)={2 4 0 3}, resolve the sequence x(n) into a sum of weighted sequences.

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Experiment no 5:-

Aim:- Write a program to evaluate the convolution using DFT for two finite sequences

Also compute error between convolution by DFT and direct linear convolution

Problem:-The sequences are given as

x1(n) = {1 ,2 ,3,4}

x2(n)={1, 1, 1,1}

Theory:-

Discrete Convolution

Convolution, as just described using integrals

Steps Involved in Convolution

1) Time reverse the sequenceh[k] arriving at h[-k]

2) Shift h[-k] to the right by n sampling periods if n> 0 ,or to the left by n samplingperiod to form the sequence h[n-k] .

3) Product sequence:

v [k] = x[k] .h[n-k]4) Summing all samples of v [k] then yields the nth sample y[n] of the

5) The process is implemented for each value of n in the range -<n<+.6) The computation of output sequence is simply arithmetic operation such as addition

, multiplication and delays.7) In case of discrete time system with an infinite length sequence, the output

sequence is also of infinite length.

Program:-

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Simulation result:-

Discussion questions:-

1) Differentiate between time variant and time invariant system.2) If x 1(n)={1,2,3,4} and x 2(n)={1,2,3}

Find the convolution using tabular representation.

3) Draw all elementary standard discrete time signals.

4) Differentiate between causal and Non causal system.5) If x 1(n)={1,2,3,4} and x 2(n)={5,6,7,8}

Find the circular representation for the above sequences.

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Experiment no. :-6

Aim:- Write a MATLAB program to obtain original sequence x[n] by IDFT for given k

point DFT.X[K]= k/K 0<=k<=K-1

0 elsewhere

Problem:- Find the original sequence x[n] if DFT is X[K]= X{2,1+j,0,1-j}

Theory:-

For the analysis of discrete time sequence normally we convert it from time

domain to frequency domain sequence X(w). but X(w) is a continuous function of frequency and therefore not convenient for computing using DSP processor. So, in orderto make X(w) ,we sample it. The fourier transform we get is discrete in nature and is

called Discrete Fourier Transform.

If time domain sequence is denoted by x[n], its fourier transform by X(W), then sampledversion of X(W)is DFT of x[n].

DFT can be defined as , a finite duration sequence that is obtained by sampling one time

period of FT. Sampling is done at N equally spaced points over the period extending from

0<=w<=2Π.

X[K]= x[n] e- j2Πnk/N

Mathematically, inverse DFT i.e. IDFT is given as,

x[n] = 1/N{ X[K] e

j2Πnk/N

}The above two equations are called DFT pair. The term e- j2

Π /N is called Twiddle factor

WN

Program:-

X1[n]

Length= L

X2[n]

Length=

M

C2= L-1Zeropadding

C2 = L-1Ze C2= L-1

Zero padding

C2 = L-1Zero

padding

X2zp[n]

C1 = M-1

Zero

padding

X1zp[n]

C point

IDFT Z[n]

Linear

Convolution

C2= L-1

Zero padding

C2= L-1

Zero padding

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Simulation result:-

Discussion questions:-1. Prove the linearity property of DFT.

2. Explain the concept of circular shift.

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Experiment no.:- 7

Aim:- Write a MATLAB program to design a FIR low pass filter

Problem:- Design a FIR low pass filter using Kaiser window for the followingparameters.:-

M= 61, Beta= 4.95, Wc =0.35(Actually 0.35pi)

Theory:-In practice all the signals are mixed up with unwanted signals To remove, or

to reduce the strength of these unwanted signal and to improve quality of required signal,

we go for filtering. Filters can be Analog or digital. A digital filter is nothing but

mathematical algorithm implemented in hardware or software.In Digital signal processing we have two categories types of filters.

1. IIR filter

2. FIR filter.

Both filters are characterized by its impulse response sequences. Input/ outputrelationship is given by the convolution formula.

For IIR filter

y[n] = h[k]x[n-k] for causal sequence k ranges from 0 to ∞;or

y[n] = x[n]x[n-k] 0<k<∞;

For FIR filter

y[n] = h[k]x[n-k] for causal sequence k ranges from 0 to N-1;or

y[n] =

x[n]x[n-k] 0<k<N-1;Alternate form of FIR filter is:

H[z] = h[k]z-k for k ranging from 0 to ∞;One should use FIR filter for the given specification if

1. No phase distortion is desired

2. Number of filter coefficients are not too large.

There are several methods to design FIR filter, listed as follows:1. Fourier series method

2. Windowing method

3. DFT method

4. Frequency sampling methods.

We have fourier series ranging from minus infinity to plus infinity, but we only look orwindowed some part of the sequence ranging from –Q to +Q., where q is any positive

integer. Hence this method is called as windowing technique. The various windowingsequences available are:

1. Hamming sequence.

2. Hanning sequence3. Triangular sequence.

4. Kaiser sequence

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5. Blackman sequence.

Program:-

Simulation result:-

H[z] = { 0.0282-0.1409z-1+0,2817z-2-0.2817z-3+0.1409z-4-0.0282z-5} /

{1+0.9437z-1+1.44z-2+0.9629z-3+0.5301z-4+0.1620z-5}

Discussion questions:-1. Explain what is finite precision effect?2. Give the relative comparison between IIR and FIR filter for Implementation.

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Experiment No. 08

Aim: To Study the Circular convolution and download it on TMS320C6713 DSK

(DSP Starter Kit)

Problem: To perform circular convolution of the following sequences

x1(n) = [ 1,2,3,4]x2(n) = [1 ,1, 2, 1]

Apparatus: TMS320C6713 DSK

Theory:1. Circular convolution:

Convolution, as just described as

Steps Involved in Convolution1) Time reverse the sequence

h[k] arriving at h[-k]

2) Shift h[-k] to the right by n sampling periods if n> 0 ,or to the left by n samplingperiod to form the sequence h[n-k] .

3) Product sequence:

v [k] = x[k] .h[n-k]4) Summing all samples of v [k] then yields the nth sample y[n] of the

5) The process is implemented for each value of n in the range -<n<+.

6) The computation of output sequence is simply arithmetic operation such as addition

, Multiplication and delays.7) In case of discrete time system with an infinite length sequence, the output

sequence is also of infinite length.

8) In circular convolution the length of the sequences are same .If they are not same thenthe length is made equal by zero padding

2. The C6713DSK:

The C6713DSK is the low-cost standalone development platform that enables customers

to evaluate and develop applications for the TI C67XX DSP family. The DSK also servesas a hardware reference design for the TMS3206713 DSP.

A programmable logic device called CPLD is used to implement glue logic that lies theboard component together. The CPLD register based user interface that lets the userconfigure the board by reading and writing to the CPLD registers.

The DSK includes 4 LEDs and 4 DIPswitches as a simple way to provide the user with

interactive feedback.A 5v power supply is used to power the board. Core composer communicates with the

DSK through the embedded JTAG emulator with a USB host interface.

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Procedure:

1) Open Code Composer Studio, make sure the DSP kit is turned on.

2) Start a new project using “Project -new” pull down menu, save it in a separate

directory(c:\ti\my\projects) with name circonv.pjt.3) Add the source files Circular convolution to the project using ‘project ---- add

files to project’ pull down menu

4) Add linker command file hello.cmd

(Path:c:\ti\tutorial\dsk6713\hello1\hello.cmd)5) Add the run time support library file rts6700.lib

(Path:c:\ti\c6000\cgtools\lib\rts6700.lib)

6) Compile the program using the ‘project –compile’ pull down menu.7) Build the program using the ‘project –Build’ pull down menu

8) Load the program (lconv.out) in program memory of DSP chip using the ‘Field –

load program’ pull down menu.

Program:

Simulation Results:

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x =1 8 20 25 16

y =1 2 -8 12 -10

z =

-4.7463-1.7506

-0.7516 + 1.1666i

-0.7516 - 1.1666i

p =

-4.48851.3622

0.5632 + 1.1482i

0.5632 - 1.1482i

k = 1

Discussion questions:

1. What are the basic conditions to be satisfied to perform the circular convolution.2. What id DSP processor .

3. What are the main features of DSK TMS320C6713

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Experiment. No. 9

Aim: To design & implement digital Kaiser low pass FIR filter and observe its

frequency response.

Problem: To find Fir filter coefficients using MATLAB & design digital Kaiser low

pass FIR filter and observe its frequency response.Filter specifications are:

Order= 30; Sampling rate = 8000samples per second; Cut off frequency =400 Hz.

Equipments: • TMS 320C5416 architecture & instruction set.

• Host (PC )with windows 95/98/Me/XP/NT/2000.

• DSP kit with chip and device driver

• Oscilloscope with function generator

Formulae :

Cut-off frequency , Wc= 2*pi*fc/Fs;Desired Impulse Response: hdn (n using particular window) ,

b_rect1= fir1(order , Wc,’high’,boxcar(31));

Convolution= x[n]*h[n]

Theory:The finite Impulse response (FIR )filter possesses an output response to an

impulse which is of infinite duration.. The Impulse response is finite since there is no

feedback in the filter that is if you put in an impulse then its output must produced forfinite duration of time.

Algorithm:We need to realize the Kaiser low pass filter by implementing the difference

equation y[n]= box[n]+ b1x[n-1]+ b2x[n-2]+…………….+ b25x[n-25], where bo to b25

are feed forward coefficients . the coefficients are calculated using MATLAB. A direct

form Implementation is taken.

Step 1: Initialise the McBSP, the DSP board and the on board coded.

Step2: Initialise the discrete time system that is specify the initial conditions .

Generally zero initial conditions are assumed.

Step 3: Take sampled data from Coded. While input is fed to DSP kit from the signalgenerator since codec is stereo, take average of the input data, read from left and right

channel. Store sampled data at a memory location.

Step 4: Perform filter operation using above said difference equation. Store filter output

at a memory location

Step 5: Output the value to codec.(left channel and right channel) and view the output at

oscilloscope.

Step 6: GO to step 3.

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Matlab program to generate ‘FIR filter –Low Pass coefficients using

fir1. :

C Program to Implement FIR filter:

Procedure:1) Switch on the DSP board.

2) Open the code composer studio.

3) Create a new project.

4) Initialize the McBSP, the DSP board and the on board coded.5) Add the above given c source file to the current project.

6) Connect the speaker jack to the input of the CRO.

7) Build the program.8) Load the generated object file on to target board.

9) Run the program using F5.10) Observe the waveform that appears on the CRO screen.

Simulation Results:

Results: FIR filter coefficients were designed using MATLAB, the program wassuccessfully downloaded on the DSP processor. The resultant waveforms were observed

on the CRO.

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Experiment. No. 9

Aim: To design & implement digital Butterworth high pass IIR filter and observe its

frequency response.

Problem: To find IIR filter coefficients using MATLAB & design digital Butterworth

high pass IIR filter and observe its frequency response.

Filter specifications are: Fc=8000 Hz

Equipments: • TMS 320C5416 architecture & instruction set.

• Host (PC )with windows 95/98/Me/XP/NT/2000.

• DSP kit with chip and device driver

•Oscilloscope with function generator

Formulae :

Cut-off frequency , Wc= 2*pi*fc/Fs;Desired Impulse Response: hdn (n using particular window) ,

b_rect1= iir1(order , Wc,’high’,boxcar(31));Convolution= x[n]*h[n]

Theory:The finite Impulse response (FIR )filter possesses an output response to an

impulse which is of infinite duration.. The Impulse response is finite since there is no

feedback in the filter that is if you put in an impulse then its output must produced forfinite duration of time.

Algorithm:We need to realize the Kaiser low pass filter by implementing the difference

equation y[n]= box[n]+ b1x[n-1]+ b2x[n-2]+…………….+ b25x[n-25], where bo to b25

are feed forward coefficients . the coefficients are calculated using MATLAB. A direct

form Implementation is taken.

Step 1: Initialise the McBSP, the DSP board and the on board coded.

Step2: Initialise the discrete time system that is specify the initial conditions .

Generally zero initial conditions are assumed.

Step 3: Take sampled data from Coded. While input is fed to DSP kit from the signalgenerator since codec is stereo, take average of the input data, read from left and right

channel. Store sampled data at a memory location.

Step 4: Perform filter operation using above said difference equation. Store filter outputat a memory location

Step 5: Output the value to codec.(left channel and right channel) and view the output at

oscilloscope.

Step 6: GO to step 3.

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Matlab program to generate ‘FIR filter –Low Pass coefficients using

fir1. :

C Program to Implement FIR filter:

Procedure:11) Switch on the DSP board.

12) Open the code composer studio.

13) Create a new project.

14) Initialize the McBSP, the DSP board and the on board coded.15) Add the above given c source file to the current project.

16) Connect the speaker jack to the input of the CRO.

17) Build the program.18) Load the generated object file on to target board.

19) Run the program using F5.20) Observe the waveform that appears on the CRO screen.

Simulation Results:

Results: FIR filter coefficients were designed using MATLAB, the program wassuccessfully downloaded on the DSP processor. The resultant waveforms were observed

on the CRO.

7etc_dsp

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