Basic simulation lab manual1


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Basic simulation lab manual1

  1. 1. DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING Siddharth Institute of Engineering and Technology (Affiliated to J.N.T.UNIVERSITY, ANANTAPUR) Narayanavanam, puttur, AP.II YEAR BTECH I SEMESTER BASIC SIMULATION LAB MANUAL PREPARED BY:VERIFIED BY: LIST OF EXPERIMENTS S.No Name of the Experiment Basic operations on matrices. 1. Generation on various signals and Sequences (periodic and a periodic), such as unit impulse, unit step, square, saw tooth, 2. triangular, sinusoidal, ramp, sinc. Operations on signals and sequences such as addition, multiplication, scaling, shifting, folding, computation of 3. energy and average power. Finding the even and odd parts of signal/sequence and real 4. and imaginary part of signal.
  2. 2. 5. Convolution between signals and sequences Auto correlation and cross correlation between signals and6. sequences. Verification of linearity and time invariance properties of a7. given continuous /discrete system. Computation of unit sample, unit step and sinusoidal response of the given LTI system and verifying its physical8. Reliability and stability properties. Gibbs phenomenon.9. Finding the Fourier transform of a given signal and plotting10. its magnitude and phase spectrum11. Waveform synthesis using Laplace Transform. Locating the zeros and poles and plotting the pole zero maps12. in s8plane and z8plane for the given transfer function. Generation of Gaussian Noise (real and complex),computation of its mean, M.S. Value and its skew,13. kurtosis, and PSD, probability distribution function.14. Sampling theorem verification.15. Removal of noise by auto correlation/cross correlation. Extraction of periodic signal masked by noise using16. correlation.17. Verification of Weiner8Khinchine relations.18. Checking a random process for stationary in wide sense. 1
  3. 3. EXP.NO:1
  4. 4. BASIC OPERATIONS ON MATRICESAim: To generate matrix and perform basic operation on matrices UsingMATLAB Software.EQUIPMENTS:PC with windows (95/98/XP/NT/2000).MATLAB SoftwareCONCLUSION:EXP.NO: 2 GENERATION OF VARIOUS SIGNALS AND SEQUENCES (PERIODIC AND APERIODIC), SUCH AS UNIT IMPULSE, UNIT STEP, SQUARE, SAWTOOTH, TRIANGULAR, SINUSOIDAL, RAMP, SINC.Aim: To generate different types of signals Using MATLAB Software.EQUIPMENTS:PC with windows(95/98/XP/NT/2000).MATLAB SoftwareMatlab program:%unit impulsegeneration clcclose alln1=-3;n2=4;n0=0;n=[n1:n2];x=[(n-n0)==0]stem(n,x)% unit stepgeneration n1=-4;n2=5;n0=0;
  5. 5. 9
  6. 6. [y,n]=stepseq(n0,n1,n2);stem(n,y); xlabel(n) ylabel(amplitude); title(unit step);
  7. 7. % square wave wavegenerator fs = 1000;t = 0:1/fs:1.5;x1 = sawtooth(2*pi*50*t); x2 =square(2*pi*50*t);subplot(2,2,1),plot(t,x1), axis([0 0.2 -1.21.2])xlabel(Time (sec));ylabel(Amplitude); title(Sawtooth Periodic Wave)subplot(2,2,2),plot(t,x2), axis([0 0.2 -1.2 1.2])xlabel(Time (sec));ylabel(Amplitude); title(Square Periodic Wave);subplot(2,2,3),stem(t,x2), axis([0 0.1 -1.2 1.2])xlabel(Time (sec));ylabel(Amplitude);% sawtooth wavegenerator fs = 10000;t = 0:1/fs:1.5;x = sawtooth(2*pi*50*t);subplot(1,2,1);plot(t,x), axis([0 0.2 -11]);xlabel(t),ylabel(x(t))title(sawtooth signal);N=2; fs = 500;n =0:1/fs:2; x =sawtooth(2*pi*50*n);subplot(1,2,2);
  8. 8. stem(n,x), axis([0 0.2 -11]);xlabel(n),ylabel(x(n))title(sawtoothsequence);To generate a trianguular pulseA=2; t = 0:0.0005:1;x=A*sawtooth(2*pi*5*t,0.25); %5 Hertz wave with duty cycle 25%plot(t,x);gridaxis([0 1 -3 3]);%%To generate a trianguularpulse fs = 10000;t = -1:1/fs:1;x1 = tripuls(t,20e-3); x2 = rectpuls(t,20e-3);subplot(211),plot(t,x1), axis([-0.1 0.1 -0.2 1.2])xlabel(Time (sec));ylabel(Amplitude); title(Triangular Aperiodic Pulse)subplot(212),plot(t,x2), axis([-0.1 0.1 -0.2 1.2])
  9. 9. xlabel(Time (sec));ylabel(Amplitude); title(Rectangular Aperiodic Pulse)set(gcf,Color,[1 1 1]),%%To generate a rectangular pulset=-5:0.01:5;pulse = rectpuls(t,2); %pulse of width 2 time unitsplot(t,pulse)axis([-5 5 -1 2]);grid
  10. 10. % sinusoidal signalN=64; % Define Number of samplesn=0:N-1; % Define vectorn=0,1,2,3,...62,63 f=1000; % Definethe frequencyfs=8000; % Define the samplingfrequency x=sin(2*pi*(f/fs)*n); %Generate x(t) plot(n,x); % Plot x(t) vs.ttitle(Sinewave [f=1KHz,fs=8KHz]); xlabel(SampleNumber); ylabel(Amplitude);% RAMPclcclose alln=input(enter the length of ramp);t=0:n; plot(t); xlabel(t);
  11. 11. ylabel(amplitude);title (ramp)
  12. 12. % sincx = linspace(-5,5); y =sinc(x);subplot(1,2,1);plot(x,y) xlabel(‘time’);ylabel(‘amplitude’);title(‘sinc function’);subplot(1,2,2);stem(x,y); xlabel(‘time’);ylabel(‘amplitude’);title(‘sinc function’);
  13. 13. CONCLUSION:
  14. 14. EXP.NO: 3 OPERATIONS ON SIGNALS AND SEQUENCES SUCH AS ADDITION, MULTIPLICATION, SCALING, SHIFTING, FOLDING, COMPUTATION OF ENERGY AND AVERAGE POWERAim: To perform arithmetic operations different types of signals UsingMATLAB Software.EQUIPMENTS:PC with windows(95/98/XP/NT/2000).MATLAB Softwar%plot the 2 Hz sine wave in the top panel t = [0:.01:1]; % independent (time) variable A = 8; % amplitudef1 = 2; % create a 2 Hz sine wave lasting 1 sec s1 = A*sin(2*pi*f1*t);f2 = 6; % create a 4 Hz sine wave lasting1 sec s2 = A*sin(2*pi*f2*t);figure subplot(4,1,1) plot(t, s1)title(1 Hz sine wave)ylabel(Amplitude)%plot the 4 Hz sine wave in the middle panel subplot(4,1,2)plot(t, s2)title(2 Hz sine wave)ylabel(Amplitude)%plot the summed sine waves in the bottom panel subplot(4,1,3)plot(t, s1+s2) title(Summed sine waves) ylabel(Amplitude) xlabel(Time (s))xmult=s1.*s2;subplot(4,1,4); plot(xmult); title(multiplication); ylabel(Amplitude) xlabel(Time (s))
  15. 15. %signal folding clc; clear all t=0:0.1:10; x=0.5*t; lx=length(x); nx=0:lx-1;xf=fliplr(x);nf=-fliplr(nx); subplot(2,1,1); stem(nx,x); xlabel(nx); ylabel(x(nx));title(original signal); subplot(2,1,2); stem(nf,xf); xlabel(nf); ylabel(xf(nf));title(folded signal); 23
  16. 16. %plot the 2 Hz sine wave scallingt = [0:.01:1]; % independent (time) variable A = 8; % amplitudef1 = 2; % create a 2 Hz sine wavelasting 1 sec s1 = A*sin(2*pi*f1*t);subplot(3,2,1) plot(s1); xlabel(t);ylabel(amplitude); s2=2*s1; subplot(3,2,2) plot(s2);xlabel(t);ylabel(amplitude);
  17. 17. s3=s1/2; subplot(3,2,3) plot(s3); xlabel(t);ylabel(amplitude); subplot(3,2,4) stem(s1);xlabel(t); ylabel(amplitude); s2=2*s1; subplot(3,2,5) stem(s2);xlabel(t); ylabel(amplitude); s3=s1/2; subplot(3,2,6) stem(s3);xlabel(t);ylabel(amplitude);Excersize questions: Sketch the following questions using MATLAB 1. x(t)= u(-t+1)
  18. 18. 2. x(t)=3r(t-1) 3. x(t)=U(n+2-u(n-3) 4. x(n)=x1(n)+x2(n)where x1(n)={1,3,2,1},x2(n)={1,-2,3,2} 5. x(t)=r(t)-2r(t-1)+r(t-2) 6. x(n)=2δ(n+2)-2δ(n-4), -5≤ n ≥5. 7. X(n)={1,2,3,4,5,6,7,6,5,4,2,1} determine and plot the following sequence a. x1(n)=2x(n-5-3x(n+4)) b. x2(n)=x(3-n)+x(n)x(n- 2)CONCLUSION: Inthis experiment the various oprations on signalshave been performedUsing MATLAB have been demonstrated.
  19. 19. EXP.NO: 4 FINDING THE EVEN AND ODD PARTS OF SIGNAL/SEQUENCE AND REAL AND IMAGINARY PART OF SIGNALAim: program for finding even and odd parts of signals Using MATLABSoftware.EQUIPMENTS:PC with windows(95/98/XP/NT/2000). MATLABSoftware%even and odd signals program:t=-4:1:4; h=[ 2 1 1 2 0 1 2 2 3 ]; subplot(3,2,1) stem(t,h); xlabel(time); ylabel(amplitude); title(signal); n=9;
  20. 20. for i=1:9 x1(i)=h(n); n=n-1;end subplot(3,2,2)stem(t,x1);xlabel(time); ylabel(amplitude);title(foldedsignal); z=h+x1subplot(3,2,3);stem(t,z); xlabel(time);ylabel(amplitude); title(sumof two signal); subplot(3,2,4);stem(t,z/2);xlabel(time); ylabel(amplitude);title(even signal); a=h- x1; subplot(3,2,5); stem(t,a); xlabel(time); ylabel(amplitude);title(difference of two signal); subplot(3,2,6);stem(t,a/2);xlabel(time); ylabel(amplitude);title(odd signal);
  21. 21. % energy clc;close all; clear all; x=[1,2,3]; n=3e=0;for i=1:n; e=e+(x(i).*x(i));end% energy clc;close all; clear all; N=2 x=ones(1,N) for i=1:N y(i)=(1/3)^i.*x(i);end n=N; e=0;for i=1:n; e=e+(y(i).*y(i));end
  22. 22. %powerclc;close all;clear all;N=2x=ones(1,N) fori=1:N y(i)=(1/3)^i.*x(i);endn=N;e=0;for i=1:n; e=e+(y(i).*y(i)) ;end p=e/(2*N+ 1);% powerN=input(type a value forN); t=-N:0.0001:N;x=cos(2*pi*50*t).^2;disp(the calculated power p of thesignal is); P=sum(abs(x).^2)/length(x)plot(t,x);axis([0 0.1 0 1]);disp(the theoretical power of thesignal is); P_theory=3/8CONCLUSION:
  23. 23. EXP.NO:5 LINEAR CONVOLUTIONAim: To find the out put with linear convolution operation Using MATLABSoftware.EQUIPMENTS:PC with windows(95/98/XP/NT/2000). MATLABSoftwareProgram:clc;close all;clear all;x=input(enter inputsequence); h=input(enterimpulse response);y=conv(x,h);subplot(3,1,1);stem(x);xlabel(n);ylabel(x(n)); title(input signal)subplot(3,1,2);stem(h);xlabel(n);ylabel(h(n)); title(impulseresponse)subplot(3,1,3);
  24. 24. stem(y);xlabel(n);ylabel(y(n)); title(linearconvolution)disp(The resultant signal is);disp(y)linear convolutionoutput:enter input sequence[1 4 32] enter impulse response[10 2 1] The resultant signalis 1 4 5 11 10 7 2
  25. 25. CONCLUSION:
  26. 26. EXP.NO: 66. AUTO CORRELATION AND CROSS CORRELATION BETWEENSIGNALS AND SEQUENCES.………………………………………………………………………………………………Aim: To compute auto correlation and cross correlation between signals andsequencesEQUIPMENTS: PC with windows (95/98/XP/NT/2000). MATLAB Software% CrossCorrelation clc;close all;clear all;x=input(enter input sequence);h=input(enter the impulse suquence);subplot(3,1,1); stem(x);xlabel(n);ylabel(x(n));title(input signal);subplot(3,1,2); stem(h);xlabel(n);ylabel(h(n));title(impulsesignal);y=xcorr(x,h);subplot(3,1,3);stem(y);xlabel(n);ylabel(y(n));disp(the resultant signal is);disp(y);title(correlation signal);
  27. 27. % autocorrelation clc;close all;clear all;x = [1,2,3,4,5]; y = [4,1,5,2,6];subplot(3,1,1); stem(x);xlabel(n);ylabel(x(n));title(inputsignal);subplot(3,1,2);stem(y);xlabel(n);ylabel(y(n));title(inputsignal);z=xcorr(x,x);subplot(3,1,3);stem(z);xlabel(n);ylabel(z(n));title(resultant signal signal);
  28. 28. CONCLUSION: In this experiment correlation of various signalshave been performed Using MATLABApplications:it is used to measure the degree to which the two signals aresimilar and it is also used for radar detection by estimating the time delay.itis also used in Digital communication, defence applications and soundnavigationExcersize questions: perform convolution between the following signals 1. X(n)=[1 -1 4 ], h(n) = [ -1 2 -3 1] 2. perform convolution between the. Two periodic sequences x1(t)=e-3t{u(t)-u(t-2)} , x2(t)= e -3t for 0 ≤ t ≤ 2
  29. 29. EXP.NO: 7 VERIFICATION OF LINEARITY AND TIME INVARIANCE PROPERTIES OF AGIVEN CONTINUOUS /DISCRETE SYSTEM.Aim: To compute linearity and time invariance properties of a given continuous/discrete systemEQUIPMENTS:PC with windows (95/98/XP/NT/2000).MATLAB SoftwareProgram1:clc;clear all;close all;n=0:40; a=2; b=1;x1=cos(2*pi*0.1*n);x2=cos(2*pi*0.4*n);x=a*x1+b*x2; y=n.*x;y1=n.*x1;y2=n.*x2;yt=a*y1+b*y2;
  30. 30. d=y-yt;d=round(d) if d disp(Given system is not satisfy linearity property);else disp(Given system is satisfy linearity property);endsubplot(3,1,1), stem(n,y);grid subplot(3,1,2),stem(n,yt); gridsubplot(3,1,3), stem(n,d);gridProgram2:clc;clear all;close all;n=0:40; a=2; b=-3;x1=cos(2*pi*0.1*n);x2=cos(2*pi*0.4*n); x=a*x1+b*x2;y=x.^2;y1=x1.^2;y2=x2.^2;yt=a*y1+b*y2;
  31. 31. d=y-yt;d=round(d); if d disp(Given system is not satisfy linearity property);else disp(Given system is satisfy linearity property);endsubplot(3,1,1), stem(n,y); gridsubplot(3,1,2), stem(n,yt); gridsubplot(3,1,3), stem(n,d); gridProgramclc;close all;clear all;x=input(enter the sequence);N=length(x);n=0:1:N-1;
  32. 32. y=xcorr(x,x);subplot(3,1,1); stem(n,x);xlabel( n----->);ylabel(Amplitude--->);title(inputseq);subplot(3,1,2);N=length(y);n=0:1:N-1;stem(n,y);xlabel(n---->);ylabel(Amplitude----.); title(autocorr seq for input);disp(autocorr seq for input);disp(y)p=fft(y,N);subplot(3,1,3); stem(n,p);xlabel(K----->);ylabel(Amplitude--->);title(psd ofinput); disp(thepsd fun:);disp(p)Program1:clc;closeall;clearall;n=0:40;
  33. 33. D=10;x=3*cos(2*pi*0.1*n)-2*cos(2*pi*0.4*n);xd=[zeros(1,D)x];y=n.*xd(n+D);n1=n+D;yd=n1.*x;d=y-yd;if d disp(Given system is not satisfy time shifting property);else disp(Given system is satisfy time shifting property);endsubplot(3,1,1),stem(y),grid;subplot(3,1,2),stem(yd),grid;subplot(3,1,3),stem(d),grid;
  34. 34. Program2:clc;closeall;clearall;n=0:40;D=10;x=3*cos(2*pi*0.1*n)-2*cos(2*pi*0.4*n);xd=[zeros(1,D)x]; x1=xd(n+D);y=exp(x1);n1=n+D;yd=exp(xd(n1));d=y-yd;if d disp(Given system is not satisfy time shifting property);else disp(Given system is satisfy time shifting property);endsubplot(3,1,1),stem(y),grid;subplot(3,1,2),stem(yd),grid;subplot(3,1,3),stem(d),grid;
  35. 35. CONCLUSION:
  36. 36. EXP.NO:8 COMPUTATION OF UNIT SAMPLE, UNIT STEP AND SINUSOIDAL RESPONSE OF THE GIVEN LTI SYSTEM AND VERIFYING ITS PHYSICAL REALIZABILITY AND STABILITY PROPERTIES.Aim: To Unit Step And Sinusoidal Response Of The Given LTI System AndVerifyingIts Physical Realizability And StabilityProperties.EQUIPMENTS:PC with windows(95/98/XP/NT/2000).MATLABSoftware%calculate and plot the impulse response and stepresponse b=[1];a=[1,-1,.9];x=impseq(0,-20,120); n = [-20:120]; h=filter(b,a,x); subplot(3,1,1);stem(n,h);title(impulse response); xlabel(n);ylabel(h(n));=stepseq(0,-20,120); s=filter(b,a,x); s=filter(b,a,x); subplot(3,1,2); stem(n,s);title(step response); xlabel(n);ylabel(s(n)) t=0:0.1:2*pi;x1=sin(t);%impseq(0,-20,120); n = [-20:120]; h=filter(b,a,x1); subplot(3,1,3);stem(h);title(sin response); xlabel(n);ylabel(h(n)); figure;zplane(b,a);
  37. 37. CONCLUSION: I
  38. 38. EXP.NO: 9 GIBBS PHENOMENONAim: To verify the Gibbs Phenomenon.EQUIPMENTS:PC with windows (95/98/XP/NT/2000).MATLAB SoftwareGibbs Phenomina Program :t=0:0.1:(pi*8); y=sin(t); subplot(5,1,1); plot(t,y); xlabel(k);ylabel(amplitude); title(gibbs phenomenon); h=2;%k=3;for k=3:2:9 y=y+sin(k*t)/k; subplot(5,1,h);plot(t,y); xlabel(k); ylabel(amplitude); h=h+1;end
  39. 39. CONCLUSION: In this experiment Gibbs phenomenon have beendemonstrated Using MATLAB
  40. 40. EXP.NO: 10. FINDING THE FOURIER TRANSFORM OF A GIVEN SIGNAL AND PLOTTING ITS MAGNITUDE AND PHASE SPECTRUMAim: to find the fourier transform of a given signal and plotting itsmagnitude and phase spectrumEQUIPMENTS: PC with windows (95/98/XP/NT/2000). MATLAB SoftwareEQUIPMENTS: PC with windows (95/98/XP/NT/2000).
  41. 41. MATLAB Software Program: clc;close all;clear all;x=input(enter the sequence); N=length(x);n=0:1:N-1; y=fft(x,N) subplot(2,1,1); stem(n,x);title(input sequence); xlabel(time index n----->); ylabel(amplitude x[n]----> ); subplot(2,1,2);stem(n,y);title(output sequence);xlabel( Frequency index K---->);ylabel(amplitude X[k]------>);
  42. 42. FFT magnitude and Phase plot:clcclose all x=[1,1,1,1,zeros(1,4)]; N=8;X=fft(x,N); magX=abs(X),phase=angle(X)*180/pi; subplot(2,1,1)plot(magX); grid xlabel(k)ylabel(X(K)) subplot(2,1,2) plot(phase);
  43. 43. grid xlabel(k) ylabel(degrees)
  44. 44. CONCLUSION: In this experiment the fourier transform of a given signaland plotting its magnitude and phase spectrum have been demonstratedusing matlab
  45. 45. Exp:11 LAPLACE TRNASFORMSAim: To perform waveform synthesis using Laplece Trnasforms of a givensignalProgram for Laplace Transform: f=t syms f t; f=t; laplace(f) Program for nverse Laplace Transform f(s)=24/s(s+8) invese LT syms F s F=24/(s*(s+8)); ilaplace(F) y(s)=24/s(s+8) invese LT poles and zeros
  46. 46. Signal synthese using Laplace Tnasform:clear all clc t=0:1:5 s=(t);subplot(2,3,1) plot(t,s); u=ones(1,6) subplot(2,3,2) plot(t,u); f1=t.*u;subplot(2,3,3) plot(f1);s2=-2*(t-1); subplot(2,3,4); plot(s2);u1=[0 1 1 1 1 1]; f2=-2*(t-1).*u1; subplot(2,3,5); plot(f2);u2=[0 0 1 1 1 1]; f3=(t-2).*u2; subplot(2,3,6); plot(f3); f=f1+f2+f3; figure;plot(t,f);% n=exp(-t);% n=uint8(n);% f=uint8(f);% R = int(f,n,0,6)laplace(f);
  47. 47. CONCLUSION: In this experiment the Triangular signal synthesised usingLaplece Trnasforms using MATLAB
  48. 48. EXP.NO: 12 LOCATING THE ZEROS AND POLES AND PLOTTING THE POLE ZEROMAPS IN S-PLANE AND Z-PLANE FOR THE GIVEN TRANSFER FUNCTION.Aim: To locating the zeros and poles and plotting the pole zero maps ins-plane and z- plane for the given transfer functionEQUIPMENTS:PC with windows (95/98/XP/NT/2000).MATLAB Softwareclc; close all clear all;%b= input(enter the numarator cofficients)%a= input(enter the denumi cofficients)b=[1 2 3 4] a=[1 2 1 1 ] zplane(b,a); Result: :
  49. 49. EXP.NO: 13 13. Gaussian noise %Estimation of Gaussian density and Distribution Functions %% Closing and Clearing all clc; clear all; close all; %% Defining the range for the Random variable dx=0.01; %delta x x=-3:dx:3; [m,n]=size(x); %% Defining the parameters of the pdf mu_x=0; % mu_x=input(Enter the value of mean); sig_x=0.1; % sig_x=input(Enter the value of varience); %% Computing the probability density function px1=[]; a=1/(sqrt(2*pi)*sig_x); for j=1:n px1(j)=a*exp([-((x(j)-mu_x)/sig_x)^2]/2); end %% Computing the cumulative distribution function cum_Px(1)=0; for j=2:n cum_Px(j)=cum_Px(j-1)+dx*px1(j); end %% Plotting the results figure(1) plot(x,px1);grid axis([-3 3 0 1]); title([Gaussian pdf for mu_x=0 and sigma_x=, num2str(sig_x)]); xlabel(--> x) ylabel(--> pdf) figure(2) plot(x,cum_Px);gri d axis([-3 3 0 1]); title([Gaussian Probability Distribution Function for mu_x=0 and sigma_x=, num2str(sig_x)]); title(ite^{omegatau} = cos(omegatau) + isin(omegatau))xlabel(--> x) ylabel(--> PDF)
  50. 50. EXP.NO: 14 14. Sampling theorem verificationAim: To detect the edge for single observed image using sobel edge detectionand canny edge detection.EQUIPMENTS:PC with windows (95/98/XP/NT/2000).MATLAB Software
  51. 51. Figure 2: (a) Original signal g(t) (b) Spectrum G(w)δ (t) is the sampling signal with fs = 1/T > 2fm.Figure 3: (a) sampling signal δ (t) ) (b) Spectrum δ (w)Let gs(t) be the sampled signal. Its Fourier Transform Gs(w) isgiven byFigure 4: (a) sampled signal gs(t) (b) Spectrum Gs(w)
  52. 52. To recover the original signal G(w):1. Filter with a Gate function, H2wm(w) of width 2wmScale it by T.Figure 5: Recovery of signal by filtering with a fiter of width 2wmAliasing{ Aliasing is a phenomenon where the high frequency components of thesampled signal interfere with each other because of inadequate samplingws < 2wm.Figure 6: Aliasing due to inadequate sampling
  53. 53. Aliasing leads to distortion in recovered signal. This is thereason why sampling frequency should be atleast twice thebandwidth ofthe signal. Oversampling{ In practice signal are oversampled, where fs issigni_cantly higher than Nyquist rate to avoidaliasing.Figure 7: Oversampled signal-avoids aliasing t=-10:.01:10; T=4; fm=1/T; x=cos(2*pi*fm*t); subplot(2,2,1); plot(t,x); xlabel(time);ylabel(x(t)) title(continous time signal) grid; n1=-4:1:4 fs1=1.6*fm; fs2=2*fm; fs3=8*fm;x1=cos(2*pi*fm/fs1*n1); subplot(2,2,2); stem(n1,x1); xlabel(time);ylabel(x(n))title(discrete time signal with fs<2fm)hold on subplot(2,2,2); plot(n1,x1) grid; n2=-5:1:5; x2=cos(2*pi*fm/fs2*n2); subplot(2,2,3); stem(n2,x2); xlabel(time);ylabel(x(n))title(discrete time signal with fs=2fm) hold onsubplot(2,2,3); plot(n2,x2) grid; n3=-20:1:20;
  54. 54. x3=cos(2*pi*fm/fs3*n 3); subplot(2,2,4); stem(n3,x3); xlabel(time);ylabel(x( n))title(discrete time signal with fs>2fm) hold onsubplot(2,2,4);plot(n3,x3)grid;CONCLUSION: In this experiment the sampling theorem have been verified Using MATLAB
  55. 55. EXP.No:15
  56. 56. REMOVAL OF NOISE BY AUTO CORRELATION/CROSS CORRELATIONAim: removal of noise by auto correlation/cross correlationEQUIPMENTS:PC with windows (95/98/XP/NT/2000).MATLAB Softwarea)auto correlation clear allclc t=0:0.1:pi*4; s=sin(t);k=2; subplot(6,1,1) plot(s); title(signal s); xlabel(t);ylabel(amplitude); n = randn([1 126]); f=s+n; subplot(6,1,2) plot(f);title(signal f=s+n); xlabel(t); ylabel(amplitude); as=xcorr(s,s); subplot(6,1,3)plot(as);title(auto correlation of s); xlabel(t); ylabel(amplitude); an=xcorr(n,n);subplot(6,1,4)plot(an);title(auto correlation ofn); xlabel(t);ylabel(amplitude);cff=xcorr(f,f);subplot(6,1,5)plot(cff);title(auto correlation off); xlabel(t);ylabel(amplitude);hh=as+an;subplot(6,1,6)plot(hh);title(addition ofas+an); xlabel(t);ylabel(amplitude);
  57. 57. B)CROSS CORRELATION :clear all clct=0:0.1:pi*4;s=sin(t);k=2;%sk=sin(t+k);
  58. 58. subplot(7,1,1)plot(s);title(signal s);xlabel(t);ylabel(amplitude);c=cos(t); subplot(7,1,2) plot(c);title(signal c);xlabel(t);ylabel(amplitude);n = randn([1 126]); f=s+n; subplot(7,1,3) plot(f);title(signal f=s+n);xlabel(t);ylabel(amplitude);asc=xcorr(s,c); subplot(7,1,4) plot(asc);title(auto correlation of s and c);xlabel(t);ylabel(amplitude);anc=xcorr(n,c); subplot(7,1,5) plot(anc);title(auto correlation of n and c);xlabel(t);ylabel(amplitude);cfc=xcorr(f,c); subplot(7,1,6) plot(cfc);title(auto correlation of f and c);xlabel(t);ylabel(amplitude);hh=asc+anc; subplot(7,1,7) plot(hh);title(addition of asc+anc);xlabel(t);ylabel(amplitude); 76
  59. 59. Result:
  60. 60. EXP.No:16 Program:EXTRACTION OF Clear all; close all; clc; n=256; k1=0:n-1; P x=cos(32*pi*k1/n)+sin(48*pi*k1/n); E plot(k1,x) R %Module to find period of input signl k=2; I xm=zeros(k,1); ym=zeros(k,1); hold on O for i=1:k D [xm(i) ym(i)]=ginput(1); I plot(xm(i), ym(i),r*); C end period=abs(xm(2)-xm(1)); rounded_p=round(period); S m=rounded_p I % Adding noise and plotting noisy signal G N A L M A y=x+randn(1,n); S figure plot(k1,y) K E D B Y N O I S E U S I N G C O R R E L A T I O N Extraction of Periodic Signal Masked By Noise Using Correlation
  61. 61. % To generate impulse train with the period as that of input signald=zeros(1,n);for i=1:nif (rem(i-1,m)==0) d(i)=1;end end%Correlating noisy signal and impulse train cir=cxcorr1(y,d);%plotting the original and reconstructed signal m1=0:n/4;figurePlot (m1,x(m1+1),r,m1,m*cir(m1+1));
  62. 62. CONCLUSION: In this experiment the Weiner-Khinchine Relation havebeen verified using MATLAB.
  63. 63. EXP.No:17 VERIFICATION OF WIENER–KHINCHIN RELATIONAIM: Verification of wiener–khinchine relationEQUIPMENTS:PC with windows (95/98/XP/NT/2000).MATLAB SoftwarePROGRAM:Clcclear all;t=0:0.1:2*pi; x=sin(2*t); subplot(3,2,1); plot(x); au=xcorr(x,x); subplot(3,2,2);plot(au); v=fft(au); subplot(3,2,3); plot(abs(v)); fw=fft(x); subplot(3,2,4);plot(fw);fw2=(abs(fw)).^2;subplot(3,2,5); plot(fw2);Result:
  64. 64. EXP18. CHECKING A RANDOM PROCESS FOR STATIONARITY IN WIDE SENSE. AIM: Checking a random process for stationary in wide sense.EQUIPMENTS:PC with windows (95/98/XP/NT/2000).MATLAB SoftwareMATLAB PROGRAM:Clear allClcy = randn([1 40]) my=round(mean(y));z=randn([1 40]) mz=round(mean(z)); vy=round(var(y)); vz=round(var(z));t = sym(t,real); h0=3; x=y.*sin(h0*t)+z.*cos(h0*t); mx=round(mean(x));k=2;xk=y.*sin(h0*(t+k))+z.*cos(h0*(t+k));x1=sin(h0*t)*sin(h0*(t+k));x2=cos(h0*t)*cos(h0*(t+k)); c=vy*x1+vz*x1;% if we solve “c=2*sin (3*t)*sin (3*t+6)" we get c=2cos (6)% which is a costant does not depent on variable’t’% so it is wide sence stationaryResult: