DIGITAL SIGNAL PROCESSING (DSP) LAB MANUAL

EC 453 By RAM NAGESWARA RAO

DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING CHALAPATHI INSTITUTE OF ENGINEERING AND TECHNOLOGY (CIET) LAM, GUNTUR - 522034 (AFFILIATED TO ACHARYA NAGARJUNA UNIVERSITY)

LIST OF EXPERIMENTS Experiments Based On Tool Boxes 1. Simulation of AM. 2. Simulation of FM. 3. Simulation of LPF and HPF. 4. Fourier Transforms. 5. Simulation of M-ary PSK. 6. Simulation of DPCM. 7. Evaluation of DFT and IDFT of 16 Sample Sequence using DIT Algorithm. 8. Evaluation of DFT and IDFT of 16 Sample Sequence using DIF Algorithm. 9. Design of IIR Butterworth Filter using Impulse Invariant Method. 10. Design of FIR Filter using Windowing Technique. 11. Convolution of Two Signals. 12. Correlation of Two Signals. 13. DFT Analysis of a Noise Corrupted Signal.

NOTE: A minimum of 10(Ten) experiments have to be performed and recorded by the candidate to attain eligibility for University Practical Examination

SOFTWARE PACKAGE USED : MATLAB version 6.5 TOOL BOXES USED : SIGNAL PROCESING COMMUNICATIONS

REVISION HISTORY

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MATLAB stands for MATRIX LABORATORY MATLAB is a software program that allows you to do data manipulation and visualization. MATLAB is a product of MATHWORKS INC. The fact that MATLAB is an interpreted language means that commands to it are parsed and executed as they are entered; there is no need for the compilation /link/run phase.

Starting MATLAB Start  All Programs  Matlab Or Start  run  in dialog box type matlab and press Enter

MATLAB screen when launched

After launching MATLAB set the current working directory to the directory where your programs have to be stored. As seen in the screen shot we have three major sub windows one is command window where we type our commands. Second one is Workspace where we see created variables by us by their name size and type. Third sub window contains history of commands we have used still now. DSP LAB

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BASIC MATLAB COMMANDS : Command Prompt in MATLAB looks like commands after the prompt and press ENTER

>>

command window. Type your

>> command and Press Enter GETTING HELP >>help command : for getting help for that particular command >>lookfor string : if you don’t have any idea which command for particular operation then just look for how many commands are there related to that operation. This command lists out all commands with the string. Choose appropriate command suitable for our operation Eg : >> lookfor modulation

>>ver >> ls >>cd directoryname >> pwd >>mkdir directoryname >>clc >>clear >>clear variable-name >>exit >>load workspacename >>save workspacename >>who >>whos

: Lists version of MATLAB and its toolboxes : Lists contents of current directory : Changing Directory : Presently Working Directory : create directory by given name directoryname : CLear Command window : Clear all variables – clears allocated space for all variables and this can be seen in workspace also. : to clear particular variable eg: >>clear x : to quit from MATLAB : to load previously stored workspace : store present variables in workspacename : lists all variables : lists all variables with their properties

TOOLBOXES : Collection of Functions written for special applications such as Image Processing, statistics, Control system design, Neural Networks. Each type of functions grouped according to their category. TOOLBOXES used by us mostly are Communication Toolbox and Signal Processing Toolbox apart from common toolboxes such as mathematical toolbox. To get help for these toolboxes type >>help comm

>>help signal

To suppress output of a command from displaying in command window append command with a semi-colon eg : >>a=1:10 will appear in command window as a= 1 2 3 4 5 6 7 8 9 10 >>a=1:10; >> no display here Will do the same job but without any display output to command window To watch some of the demos type >>demos >>sigdemo1 >>sigdemo2 >>phone DSP LAB

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Basic building block of MATLAB is MATRIX fundamental data type is ARRAY Creating a vector with elements >>x=[1 2 3] x= 1 2 3 x is row vector with 3 elements >>y=[1;2;3] y= 1 2 3 Y is a column vector with 3 elements Accessing particular element in array is just indexing element number >>x(2) >>2

press ENTER % this is nothing but second element of x

Entering a 2*3 matrix >>a=[1 2 3;4 5 6] a= 1 2 3 4 5 6 Entering a 3*3 matrix >> b=[1 2 3;4 5 6;7 8 9] b= 1 2 3 4 5 6 7 8 9 Accessing 2nd row 3rd element >>b(2,3) gives you 5 Appending row or column b=[b y] appends a column b=[b;u] append a row to delete particular row or column >>b(:,3)=[ ] will delete third column >>b(2,:) =[ ] will delete 2nd row of matrix b Here : operator used to give range of rows or columns say if you want to delete only third row to eigth row of a matrix then specify the range as b(3:8 , : ) only : means all columns or rows >>zeros(m,n) gives matrix of m*n wil zeros >>ones(m,n) gives matrix of m*n wil ones >>rand(m,n) generates a matrix of m*n random numbers

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Creating Vectors X= initial value : Increment : Final value >>a=1:2:10 a= 1 3 5

7

9

If you do not mention any increment then it will assume by default increment as one (1) >>u=linspace(0,20,5) Will generate 5 elements between 0 and 20 To Print any string on to command window use function display >>display(‘www.RAMNAGRAO.com’) www.RAMNAGRAO.com >>display(a) Will display value of variable a

PLOTTING SIMPLE GRAPHS plot(x,y) : stem(x,y) : xlabel(‘ x- axis name’) : ylabel(‘y –axis name’) : title(‘my plot title’) : clf : figure(n) : hold on : hold off : subplot(m,n,p) : :

plot x Vs y plot x Vs y with stem style discrete points x- axis name in current plot y- axis name in current plot title of the graph clear current figure create new figure window with id number n to draw current plot in the same figure window to draw current plot in the same different window divide figure window into m*n blocks and activate block P for present plot.

PLOT Linear plot.PLOT(X,Y) plots vector Y versus vector X. Plot(var1,var2,’style option’); Style options

Eg to plot x,y in color red and values as stars and in dashed lines then use command as >>plot(x,y,’r*- -‘); DSP LAB

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MATLAB SCRIPT FILES MATLAB script files are group of instructions arranged inside a file line by line these files have extension as .m ( M- files) after execution of each command in this file output is displayed on to command window. These files are created in MATLAB Editor which is invoked by File New  M-file or by simply type >>EDIT at command window. Creating custom functions Start by opening editor and insert first line as template given below function [output variable] = function_name(input variables); Code related to this function % comments Save this file as same as function_name

Eg :

function [total,interest,duration] = bankamount(p,q,r) This file must be saved by name bankamount.m to run this function >>[t,I,d] =bankamount(1000,8,10);

CONTROL STATEMENTS For loop for m=1:100 num=1/(m+1) end While Loop While i < 100 num=2^I; end IF if I > 4 k=I; elseif (i>20) & (j ==8) k=5*i*j; else k=1; end switch switch flag case value1 block code1; case value2 block code2; otherwise last default block; end

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INTERACTIVE INPUT N=input(‘enter the matrix size: ‘); Enter the value of N in command window . until you enter the value program will stop there

IF after any command MATLAB runs into any kind of infinite loop or it hangs then press CTRL+C or CTRL+Z

Save Graphical Result of the Program After generating figure window of a program. Goto FILE  Export in dialog box give name similar to program name and change extension as .jpg

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EXPERIMENT 1 : SIMULATION OF AMPLITUDE MODULATION(AM) AIM : Simulation of AM. APPARATUS & TOOLS : PC with OS windows XP/ 2000 MATLAB 6.1 Tool Boxes – Signal Processing, Communications PROGRAM : %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % AIM

: AMPLITUDE MODULATION SIMULATION

% AUTHOR

: RN RAO

% PARAMETERS: % DATE

: 21 Sep 2012

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% t=0:0.001:1;

% time duration of 1 sec and smpling frequency 1000

mesg=sin(2*pi*5*t);

% modulating signal of 5 HZ

subplot(311); plot(t,mesg); title('modulating signal m(t)'); xlabel('

time t ');

ylabel('AMPLITUDE'); carr=sin(2*pi*60*t);

%carrier frequency 60Hz

subplot(312); plot(t,carr); title('Carrier signal c(t)'); xlabel('

time t ');

ylabel('AMPLITUDE'); modsig=amod(mesg,60,1000,'am');

% modulated signal

subplot(313); plot(t,modsig); title('modulated signal s(t)'); xlabel('

time t ');

ylabel('AMPLITUDE'); % Frequency components of modulated signals modsigf=abs(fft(modsig)); f=0:1:511; modsigf=modsigf(1:512); figure(3); stem(f,modsigf); axis([50 70 0 500]); title('frequency components of modulated signals');

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xlabel('frequency'); ylabel('amplitude'); figure(2); % demodulation of am signal figure(2); dmodsig=ademod(modsig,60,1000,'am'); subplot(211); plot(t,dmodsig); title('de modulating signal dm(t)'); xlabel('

time t ');

ylabel('AMPLITUDE'); subplot(212); plot(t,dmodsig); hold on plot(t,mesg,'r'); title('modulated and demodulated signals'); xlabel('

time t ');

ylabel('AMPLITUDE'); legend('Demodulated','original')

RESULT :

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EXPERIMENT 2 : SIMULATION OF FREQUENCY MODULATION (FM) AIM : Simulation of FM. APPARATUS & TOOLS : PC with OS windows XP/ 2000 MATLAB 6.1 Tool Boxes – Signal Processing, Communications %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %

AIM : Simulation of Frequency Modulation (FM)

% AUTHOR

: RN RAO

% PARAMETERS

:

% DATE

: Sep 2012

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% clc; clear all; close all; t=0:0.001:1; Fs=1000; Fc=20; x=sin(2*pi*t*5); y=amod(x,Fc,Fs,'fm',5); subplot(311); plot(t,y); hold on; plot(t,x,'r'); grid on; legend('modulated','message'); xlabel('time'); ylabel('amplitude'); title('FREQUENCY MODULATED WAVE'); z=ademod(y,Fc,Fs,'fm',5); subplot(312); plot(t,z); hold on; plot(t,x,'r'); legend('demodulated wave','message'); xlabel('

time');

ylabel('amplitude'); subplot(313); L=length(y); NFFT=2^nextpow2(L);

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f=Fs/2*linspace(0,1,NFFT/2+1); Y=fft(y,NFFT)/L; stem(f,2*abs(Y(1:NFFT/2+1))); axis([0 70 0 0.8]); grid MINOR title('spectrum of modulated wave'); xlabel('frequency'); ylabel('amplitude');

RESULT :

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EXPERIMENT 3 : SIMULATION OF LPF AND HPF AIM : Simulation of LPF and HPF. APPARATUS & TOOLS : PC with OS windows XP/ 2000 MATLAB 6.1 Tool Boxes – Signal Processing, Communications %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % AIM :

Simulation of LPF and HPF

% AUTHOR

: RN RAO

% PARAMETERS : % DATE

: 21- 09 - 2012

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% clc; clear all; close all; alphap=input('enter the value of passband ripple= ');

%passband attenuation in db =0.4

alphas=input('enter the value of stopband ripple= ');

%stopband attenuation in db =40

fp=input('enter the value of passband frequency= ');

%passband frequency in hz =200

fs=input('enter the value of stopband frequency= ');

%stopband frequency in hz=700

F=input('enter the value of sampling frequency= ');

%sampling frequency in hz = 2000

omp=2*fp/F; oms=2*fs/F; %TO FIND CUTOFF FREQUENCY & ORDER OF THE FILTER [n,wn]=buttord(omp,oms,alphap,alphas) %SYSTEM FUNCTION OF THE FILTER [b,a]=butter(n,wn) w=0:0.01:pi; [h,om]=freqz(b,a,w,'whole'); m=abs(h); an=angle(h); subplot(211); plot(om/pi,20*log(m)); grid on title(' LPF - Magnitude Response') ylabel('gain in dB'); xlabel('Normalised frequency'); subplot(212); plot(om/pi,an); grid on title(' LPF - Phase Response')

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ylabel('phase in radians'); xlabel('Normalised frequency'); %H P F figure(2); [bh,ah]=butter(n,wn,'high') wh=0:0.01:pi; [hh,omh]=freqz(bh,ah,wh,'whole'); mh=abs(hh); anh=angle(hh); subplot(211); plot(omh/pi,20*log(mh)); grid on title(' HPF- Magnitude Response') ylabel('gain in dB'); xlabel('Normalised frequency'); subplot(212); plot(omh/pi,anh); grid on title('HPF - Phase Response') ylabel('phase in radians'); xlabel('Normalised frequency');

RESULTS Input at command prompt enter the value of passband ripple= 0.4 enter the value of stopband ripple= 30 enter the value of passband frequency= 200 enter the value of stopband frequency= 700 enter the value of sampling frequency= 2000 n=

3

wn = 0.3537 b= 0.0736

0.2207

0.2207 0.0736

1.0000 -0.8468

0.5245 -0.0892

a=

bh = 0.3076 -0.9227

0.9227 -0.3076

ah = 1.0000 -0.8468

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0.5245 -0.0892

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EXPERIMENT 4 : FOURIER TRANSFORM AIM : Simulation of Fourier Transform APPARATUS & TOOLS : PC with OS windows XP/ 2000 MATLAB 6.1 Tool Boxes – Signal Processing, Communications %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % AIM : :

Fourier Transforms.

% AUTHOR

: RN RAO

% PARAMETERS : % DATE

: 21- 09 - 2012

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %fourier transform of rectangular pulse clc; clear all; close all; Fs=1000; T=1/Fs; L=1000; t=(0:L-1)*T; y=rectpuls(t,200/L); subplot(2,1,1); plot(Fs*t(1:200),y(1:200)); title('rectangular pulse in time domain'); xlabel('time in milliseconds'); ylabel('Amplitude'); NFFT=2^nextpow2(L); y=fft(y,NFFT)/L; f=Fs/2*linspace(0,1,NFFT/2+1); subplot(2,1,2); plot(f,2*abs(y(1:NFFT/2+1))); title('single sided amplitude spectrum of y(t)'); xlabel('frequency hz'); ylabel('|y(f)|'); %Rectangular pulse of less duration y1=rectpuls(t,20/L); figure(2); subplot(2,1,1); plot(Fs*t(1:200),y1(1:200));

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title('Rectangular pulse of less width in time domain'); xlabel('time in milliseconds'); NFFT=2^nextpow2(L); y1=fft(y1,NFFT)/L; f=Fs/2*linspace(0,1,NFFT/2+1); subplot(2,1,2); plot(f,2*abs(y1(1:NFFT/2+1))); title('single sided Amplitude spectrum of y(t)'); xlabel('frequency Hz'); ylabel('|y(f)|'); %change in N figure y1=rectpuls(t,20/L); NFFT=64; for i=1:1:4 NFFT=i*NFFT y2=fft(y1,NFFT)/L; f=Fs/2*linspace(0,1,NFFT/2+1); subplot(2,2,i); stem(f,2*abs(y2(1:NFFT/2+1))); title(strcat(' N= ',num2str(NFFT))); end

RESULT :

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EXPERIMENT 5 : SIMULATION OF M-ARY PSK AIM : Simulation of M-ary Phase Shift Keying. APPARATUS & TOOLS : PC with OS windows XP/ 2000 MATLAB 6.1 Tool Boxes – Signal Processing, Communications %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % AIM : :

Simulation of M-ary PSK.

% AUTHOR

: RN RAO

% PARAMETERS : % DATE

: 21 - Sep - 2012

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% clc; close all; clear all; m=16; Fd=1

%original msg sample

Fs=3

%modulate signal will be modulated

x=randint(100,1,m);

%random digital signal

y=dmodce(x,Fd,Fs,'PSK',m); % ADD SOME GAUSSIAN NOISE % ynoisy=y+.04*randn(300,1); ynoisy=awgn(y,40); % CREATE SCATTER PLOT FOR NOISE DATA scatterplot(ynoisy,1,0,'b*'); % DEMODULATE z=ddemodce(ynoisy,Fd,Fs,'PSK',m) ser=symerr(x,z) %%check for any symbol error rate [ber,per]=biterr(x,z)

After running once note down the values of ser, ber values change program by removing clear all instruction ( we are operating on same message ) now change value of SNR in AWGN function for every change in SNR run the program and note down the ser,ber values plot SNR vs BER as a graph for that particular m value say 16 Repeat the above process for m=8,4

Observations : DSP LAB

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For M=16

SNR

For M=4

BER

SNR

BER

RESULT :

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EXPERIMENT 6 : SIMULATION OF DPCM AIM : Simulation of Differential Pulse Code Modulation APPARATUS & TOOLS : PC with OS windows XP/ 2000 MATLAB 6.1 Tool Boxes – Signal Processing, Communications %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % AIM : :

Simulation of Differential Pulse Code Modulation

% AUTHOR

: RN RAO

% PARAMETERS : % DATE

: 21 - 09 - 2012

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% clc; clear all; close all; predictor=[0 1]; partition=[-1:0.1:0.9]; codebook=[-1:.1:1]; t=[0:pi/50:2*pi]; x=sawtooth(3*t);

% use other wave shapes also

%QUANTIZE WITH DPCM encodedx=dpcmenco(x,codebook,partition,predictor); %RECOVER x FROM MODULATED SIGNAL decodedx=dpcmdeco(encodedx,codebook,predictor); plot(t,x,t,decodedx,'r--'); title('DPCM') legend('original','estimated') distor=sum((x-decodedx).^2)/length(x) msgbox(strcat('Error is ',num2str(distor)));

RESULT

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EXPERIMENT 7 : DESIGN OF FIR FILTER USING WINDOWING TECHNIQUE AIM : Design of FIR Filter using Windowing Technique APPARATUS & TOOLS : PC with OS windows XP/ 2000 MATLAB 6.1 Tool Boxes – Signal Processing, Communications PROGRAM : %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % AIM : :

Design of FIR Filter using Windowing Technique.

% AUTHOR

: RN RAO

% PARAMETERS : % DATE

: 14-09 - 2012

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

clc; clear all; close all; n=20; fp=200; fq=300; fs=1000; fn=2*fp/fs; window=hamming(n+1); %window=rectwin(n+1); stem(window); title(' WINDOW - HAMMING '); xlabel('n'); b=fir1(n,fn,window); [H W]=freqz(b,1,128); figure subplot(211); plot(W/pi,abs(H)); title('magnitude response of lpf'); xlabel('normalised frequency'); ylabel('gain in db'); subplot(212); DSP LAB

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plot(W/pi,angle(H)); title('phase response of lpf'); xlabel('normalised frequency'); ylabel('angle');

RESULT

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EXPERIMENT 8 : CONVOLUTION OF TWO SIGNALS AIM : Convolution of Two Signals. APPARATUS & TOOLS : PC with OS windows XP/ 2000 MATLAB 6.1 Tool Boxes – Signal Processing, Communications %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % AIM : :

Convolution of Two Signals.

% AUTHOR

: RN RAO

% PARAMETERS : % DATE

: 14 -09 - 2012

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% clc; clear all; close all; %input with square braces and command between elements % x= input('enter the i/p sequence x(n)='); x=[1,0,1,2,-1,3,2]; N1=length(x); n=0:1:N1-1; subplot(221); stem(n,x); title('SIGNAL 1'); xlabel(strcat('x(n)=',num2str(x))); ylabel('x(n)'); %h input ('enter the input sequence h(n)='); h=[1,1,2,2,1,1] N2=length(h); n1=0:1:N2-1; subplot(222); stem(n1,h); xlabel(strcat('h(n)=',num2str(h))); title('SIGNAL 2'); ylabel('h(n)'); y=conv(x,h);

% convolution of two sequences

n2=0:1:N1+N2-2; subplot(212); stem(n2,y); xlabel(strcat('y(n)=',num2str(y))); ylabel('y(n)');title('Convolution of two sequences x(n)& h(n)');

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RESULT

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EXPERIMENT 9 : CORRELATION OF TWO SIGNALS AIM : Correlation of Two Signals. APPARATUS & TOOLS : PC with OS windows XP/ 2000 MATLAB 6.1 Tool Boxes – Signal Processing, Communications %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % AIM : :

Correlation of Two Signals.

% AUTHOR

: RN RAO

% PARAMETERS : % DATE

: 14-09 - 2012

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% clc; clear all; close all; xn=[1,-1,1,1,2] hn=[1,2,1,-1] subplot(311); stem(xn); xlabel('->n'); ylabel('amplitude'); title('sequence x(n)'); subplot(312); stem(hn); xlabel('n'); ylabel('amplitude'); title('sequence h(n)'); rxh=xcorr(xn,hn); subplot(313); stem(rxh); xlabel('->n'); ylabel('amplitude'); title('cross correlation');

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RESULT

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EXPERIMENT 10 : DFT ANALYSIS OF A NOISE CORRUPTED SIGNAL AIM : DFT Analysis of a Noise Corrupted Signal. APPARATUS & TOOLS : PC with OS windows XP/ 2000 MATLAB 6.1 Tool Boxes – Signal Processing, Communications %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % % AIM : :

DFT Analysis of a Noise Corrupted Signal.

% AUTHOR

: RN RAO

% PARAMETERS : % DATE

: 14 -09 - 2012

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% clc clear all fsa=2000; t=0:1/fsa:0.1; x=sin(2*pi*200*t); xn=sin(2*pi*200*t)+rand(size(t)); subplot(211); plot(t,x); hold on plot(t,xn,'r--') title(' Signals in Time Domain '); xlabel('time'); ylabel('x(t)'); legend('without noise','with noise') L=length(t); NFFT=2^nextpow2(L); %NEXT POWER OF 2 FROM LENGTH OF 'Y' y=fft(x,NFFT)/L; yn=fft(xn,NFFT)/L; f=fsa/2*linspace(0,1,NFFT/2+1); subplot(212); %PLOT SINGLE - SIDED AMPLITUDE SPECTRUM plot(f,2*abs(y(1:NFFT/2+1))); hold on plot(f,2*abs(yn(1:NFFT/2+1)),'r--'); title('spectrum of Signals without and with Noise'); xlabel('frequency (Hz)'); ylabel('x(f)'); legend('without noise','with noise')

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RESULT

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MISCELLANEOUS PROGRAMS

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TO GENERATE DIFFERENT TYPES OF SIGNALS

Aim: To generate different types of signals EQUIPMENTS: PC with windows (XP/2000), MATLAB Software Program : clc;

%clear command window

close all;

% close all other figures

clear all;

% clear all variables

% unit step sequence N=21;

% number of samples

x=ones(1,N);

% all samples with 1

n=0:1:N-1; subplot(2,2,1);stem(n,x); xlabel('n');ylabel('x(n)'); title('unit step sequence'); % exponential Sequence x1=.8.^(n); subplot(2,2,2),stem(n,x1); xlabel('n'),ylabel('x1(n)'); title('exponential sequence'); %analog sin signal x2=sin(.1*pi*n); subplot(2,2,3);plot(n,x2); xlabel('n');ylabel('x2(n)'); title('analog sin signal'); %disrete sin signal x3=sin(.2*pi*n); subplot(2,2,4);stem(n,x3); xlabel('n');ylabel('x3(n)'); title('discrete sin signal');

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RESULT

::

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TO GENERATE SUM OF SINUSOIDAL SIGNALS

Aim: To generate sum of sinusoidal signals EQUIPMENTS: PC with windows (XP/2000), MATLAB Software

Program: clc; close all; clear all; t=0:0.05:2*pi; x1=sin(t*5);

%sine wave with period 5

x2=sin(t*9);

%sine wave with period 7

x3=x1+x2;

%sum of x1 and x2

subplot(3,1,1); plot(t,x1) xlabel('time');ylabel('amplitude'); title('sin signal-1'); subplot(3,1,2); plot(t,x2); xlabel('time');ylabel('amplitude'); title('sin signal-2'); subplot(3,1,3); plot(t,x3); xlabel('time');ylabel('amplitude'); title('sum of sin signals');

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RESULT

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MISCELLANEOUS SIGNAL GENERATION AIM : Miscellaneous Signal Generation t1 = -8:-4; x1 = zeros(size(t1)); t2 = -4:3; x2 = t2+2; t3 = 3:8; x3 = t3-2; t = [t1 t2 t3]; x = [x1 x2 x3]; subplot(221),plot(t,x) xlabel('Time (sec)') ylabel('x(t)') title('a)') % a) t = t+1; subplot(222),plot(t,x) xlabel('Time (sec)') ylabel('x(t)') title('b)') % c) n1 = -6:1; x1 = zeros(size(n1)); n2 = 2:3; x2 = 2*n2-4; n3 = 4:8; x3 = 4-n3; n = [n1 n2 n3]; x = [x1 x2 x3]; subplot(223),stem(n,x) xlabel('n') ylabel('x[n]') title('c)') % d) n = n-1; subplot(224),stem(n,x) xlabel('n') ylabel('x[n]') title('d)'),subplot(111) DSP LAB

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RESULTS

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SINE WAVE GENERATION AIM : SINE WAVE GENERATION t = [ 0 : 1 : 40 ]; % Time Samples f = 500; % Input Signal Frequency fs = 8000; % Sampling Frequency x = sin(2*pi*f/fs*t); % Generate Sine Wave figure(1); stem(t,x,'r'); % View the samples figure(2); stem(t*1/fs*1000,x,'r'); % View the samples hold on; plot(t*1/fs*1000,x); % Plot Sine Wave

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AMPLITUDE MODULATION WITHOUT USING TOOLBOX FUNCTIONS %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

AIM : Amplitude Modulation Without using Toolbox functions. % AUTHOR

: RN RAO

% PARAMETERS : % DATE

: 14 Sep 2012

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %AM without using toolbox clc; clear all; close all; fm=20; fc=500; vm=1;vc=1;interval=0.001; t=0:0.00001:0.09999; f=0:1:99999; m=0.6; wc=2*pi*fc; wm=2*pi*fm; v1=vc*m+vm*sin(wm*t); v2=-(vc*m+vm*sin(wm*t)); vm=vm*sin(wm*t); vc=vc*sin(wc*t); vam=(1+m*sin(wm*t)).*sin(wc*t); vf=abs(fft(vam,10000))/10000; figure; plot(t,vam); hold on; plot(t,v1,'r'); plot(t,v2,'r'); title(' AMPLITUDE MODULATION WITHOUT TOOLBOX ') xlabel('======> Time '); ylabel('======> Amplitude '); figure;

vm=1;vc=1; for mi=1:1:5 m=2*mi/10; v1=vc*m+vm*sin(wm*t); v2=-(vc*m+vm*sin(wm*t));

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vam=(1+m*sin(wm*t)).*sin(wc*t); subplot(5,1,mi) plot(t,vam); hold on; plot(t,v1,'r'); plot(t,v2,'r'); ylabel(strcat('m=',num2str(m)));

end

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FILTERING FREQUENCY COMPONENTS USING FILTERS

AIM: To Filter Frequency components using LPF & HPF fsa=2000; t=0:1/fsa:0.1; x=sin(2*pi*200*t)+sin(2*pi*600*t)+sin(2*pi*900*t); subplot(211); plot(t,x); title('input to the filter x(t)'); xlabel('time'); ylabel('x(t)'); L=length(t); NFFT=2^nextpow2(L); %NEXT POWER OF 2 FROM LENGTH OF 'Y' y=fft(x,NFFT)/L; f=fsa/2*linspace(0,1,NFFT/2+1); subplot(212); %PLOT SINGLE - SIDED AMPLITUDE SOECTRUM plot(f,2*abs(y(1:NFFT/2+1))); title('spectrum of x(t)'); xlabel('frequency (Hz)'); ylabel('x(f)'); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% alphap=input('enter the value of passband ripple= ');

%passband attenuation in db

alphas=input('enter the value of stopband ripple= ');

%stopband attenuation in db

fp=input('enter the value of passband frequency= ');

%passband frequency in hz

fs=input('enter the value of stopband frequency= ');

%stopband frequency in hz

F=input('enter the value of sampling frequency= ');

%sampling frequency in hz

omp=2*fp/F; oms=2*fs/F; %TO FIND CUTOFF FREQUENCY & ORDER OF THE FILTER [n,wn]=buttord(omp,oms,alphap,alphas) %SYSTEM FUNCTION OF THE FILTER [b,a]=butter(n,wn) w=0:0.01:pi; [h,om]=freqz(b,a,w,'whole'); m=abs(h); an=angle(h); figure(2); subplot(211); plot(om/pi,20*log(m)); grid on

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ylabel('gain in dB'); xlabel('Normalised frequency'); subplot(212); plot(om/pi,an); grid on ylabel('phase in radians'); xlabel('Normalised frequency'); %APPLY FILTER TO THE WAVE yy=filter(b,a,x); figure(3); subplot(211); plot(yy); %legend('filtered') hold on; plot(x,'r'); legend('filtered','original') xlabel('time'); ylabel('amplitude'); title('signals before & after filtering'); subplot(212); L=length(yy); NFFT=2^nextpow2(L); %NEXT POWER OF 2 FROM LENGTH OF 'Y' y=fft(yy,NFFT)/L; f=fsa/2*linspace(0,1,NFFT/2+1); subplot(212); %PLOT SINGLE - SIDED AMPLITUDE SOECTRUM plot(f,2*abs(y(1:NFFT/2+1))); title('spectrum of filtered signal'); xlabel('frequency (Hz)'); ylabel('magnitude'); INPUT AT COMMAND PROMPT enter the value of passband ripple= 0.2 enter the value of stopband ripple= 30 enter the value of passband frequency= 200 enter the value of stopband frequency= 500 enter the value of sampling frequency= 2000 press enter n = 5 , wn = 0.2958 b=

0.0065

a=

1.0000 -2.0177

DSP LAB

0.0327

0.0655

0.0655

2.0732 -1.1455

0.0327

0.0065

0.3423 -0.0428

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DSP LAB

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DSP LAB

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