%P3.1 function [X] = dtft(x,nx,w) % Computes Discrete-time Fourier Transform % [X] = dtft(x,n,w) % % X = DTFT values are computed at w frequencies % x = finite duration sequence over n % n = sample position vector % w = frequency location vector M = 250; k = -M:M; % k = 501 points X = x*(exp(-j*pi/M)).^(nx'*k); % Computes DTFT

%P3.2 colordef white; clear; clc; M = 250; k = -M:M; w = (pi/M)*k;%[0, pi]axis divided into 501 points. [x,nx] = stepseq(0,-50,50); % sequence x1a(n) [x2,nx2] = stepseq(20,-50,50); % sequence x1b(n) [x,nx] = sigadd(x,nx,x2,nx2); x2 = 2*0.8.^nx2; [x,nx] = sigmult(x,nx,x2,nx2); X = dtft(x,nx,w); % Computes Discrete-Time Fourier Transform magX = abs(X); angX = angle(X); figure(1); subplot(3,2,1); stem(nx,x,'k'); xlabel('n'); title('Given Sequence'); ylabel('x1(n)') subplot(3,2,3); plot(w/pi,magX,'k'); xlabel('frequency in pi units'); title('Magnitude Part'); ylabel('Magnitude') subplot(3,2,5); plot(w/pi,angX,'k'); xlabel('frequency in pi units'); title('Angle Part'); ylabel('Radians') [x,nx] = stepseq(0,0,100); % sequence x1a(n) [x2,nx2] = stepseq(50,0,100); % sequence x1b(n) [x,nx] = sigadd(x,nx,x2,nx2); x2 = 0.9.^nx2; [x,nx] = sigmult(x,nx,x2,nx2); X = dtft(x,nx,w); % Computes Discrete-Time Fourier Transform magX = abs(X); angX = angle(X); figure(1); subplot(3,2,2); stem(nx,x,'k'); xlabel('n'); title('Given Sequence'); ylabel('x2(n)') subplot(3,2,4); plot(w/pi,magX,'k'); xlabel('frequency in pi units'); title('Magnitude Part'); ylabel('Magnitude') subplot(3,2,6); plot(w/pi,angX,'k'); xlabel('frequency in pi units'); title('Angle Part'); ylabel('Radians')

x = [4,3,2,1,2,3,4]; nx = 0:length(x)-1; X = dtft(x,nx,w); % Computes Discrete-Time Fourier Transform magX = abs(X); angX = angle(X); figure(2); subplot(3,2,1); stem(nx,x,'k'); xlabel('n'); title('Given Sequence'); ylabel('x3(n)') subplot(3,2,3); plot(w/pi,magX,'k'); xlabel('frequency in pi units'); title('Magnitude Part'); ylabel('Magnitude') subplot(3,2,5); plot(w/pi,angX,'k'); xlabel('frequency in pi units'); title('Angle Part'); ylabel('Radians') x = [4,3,2,1,1,2,3,4]; nx = 0:length(x)-1; X = dtft(x,nx,w); % Computes Discrete-Time Fourier Transform magX = abs(X); angX = angle(X); figure(2); subplot(3,2,2); stem(nx,x,'k'); xlabel('n'); title('Given Sequence'); ylabel('x4(n)') subplot(3,2,4); plot(w/pi,magX,'k'); xlabel('frequency in pi units'); title('Magnitude Part'); ylabel('Magnitude') subplot(3,2,6); plot(w/pi,angX,'k'); xlabel('frequency in pi units'); title('Angle Part'); ylabel('Radians')

x = 4:-1:-4; nx = 0:length(x)-1; X = dtft(x,nx,w); % Computes Discrete-Time Fourier Transform magX = abs(X); angX = angle(X); figure(3); subplot(3,2,1); stem(nx,x,'k'); xlabel('n'); title('Given Sequence'); ylabel('x5(n)') subplot(3,2,3); plot(w/pi,magX,'k'); xlabel('frequency in pi units'); title('Magnitude Part'); ylabel('Magnitude') subplot(3,2,5); plot(w/pi,angX,'k'); xlabel('frequency in pi units'); title('Angle Part'); ylabel('Radians') x = [4,3,2,1,-1,-2,-3,-4]; nx = 0:length(x)-1; X = dtft(x,nx,w); % Computes Discrete-Time Fourier Transform magX = abs(X); angX = angle(X); figure(3); subplot(3,2,2); stem(nx,x,'k'); xlabel('n'); title('Given Sequence'); ylabel('x6(n)') subplot(3,2,4); plot(w/pi,magX,'k'); xlabel('frequency in pi units'); title('Magnitude Part'); ylabel('Magnitude') subplot(3,2,6); plot(w/pi,angX,'k'); xlabel('frequency in pi units'); title('Angle Part'); ylabel('Radians')

clear; clc; %P3.3 M = 250; k = -M:M; w = (pi/M)*k; % [0, pi] axis divided into 501 points. [x,nx] = stepseq(0,-10,10); % sequence x1(n) x=3*0.9^3*x; X = dtft(x,nx,w); % Computes Discrete-Time Fourier Transform magX = abs(X); angX = angle(X); figure(1); subplot(3,2,1); stem(nx,x,'k'); xlabel('n'); title('Given Sequence'); ylabel('x1(n)') subplot(3,2,3); plot(w/pi,magX,'k'); xlabel('frequency in pi units'); title('Magnitude Part'); ylabel('Magnitude') subplot(3,2,5); plot(w/pi,angX,'k'); xlabel('frequency in pi units'); title('Angle Part'); ylabel('Radians') [x,nx] = stepseq(2,-10,10); % sequence x2(n) [x,nx] = sigmult(x,nx,2*0.8.^(nx+2),nx); X = dtft(x,nx,w); % Computes Discrete-Time Fourier Transform magX = abs(X); angX = angle(X); subplot(3,2,2); stem(nx,x,'k'); xlabel('n'); title('Given Sequence'); ylabel('x2(n)') subplot(3,2,4); plot(w/pi,magX,'k'); xlabel('frequency in pi units'); title('Magnitude Part'); ylabel('Magnitude') subplot(3,2,6); plot(w/pi,angX,'k'); xlabel('frequency in pi units'); title('Angle Part'); ylabel('Radians') [x,nx] = stepseq(0,-10,10); % sequence x3(n) [x,nx] = sigmult(x,nx,0.5.^nx,nx); [x,nx] = sigmult(x,nx,nx,nx); X = dtft(x,nx,w); % Computes Discrete-Time Fourier Transform magX = abs(X); angX = angle(X); figure(2); subplot(3,2,1); stem(nx,x,'k'); xlabel('n'); title('Given Sequence'); ylabel('x3(n)') subplot(3,2,3); plot(w/pi,magX,'k'); xlabel('frequency in pi units'); title('Magnitude Part'); ylabel('Magnitude') subplot(3,2,5); plot(w/pi,angX,'k'); xlabel('frequency in pi units'); title('Angle Part'); ylabel('Radians') [x,nx] = stepseq(2,-10,10); % sequence x4(n) [x,nx] = sigmult(x,nx,-0.7.^(nx-1),nx); [x,nx] = sigmult(nx+2,nx,x,nx); X = dtft(x,nx,w); % Computes Discrete-Time Fourier Transform magX = abs(X); angX = angle(X); subplot(3,2,2); stem(nx,x,'k'); xlabel('n'); title('Given Sequence'); ylabel('x4(n)') subplot(3,2,4); plot(w/pi,magX,'k'); xlabel('frequency in pi units'); title('Magnitude Part'); ylabel('Magnitude') subplot(3,2,6); plot(w/pi,angX,'k'); xlabel('frequency in pi units'); title('Angle Part'); ylabel('Radians')

[x,nx] = stepseq(0,-10,10); % sequence x5(n) [x,nx] = sigmult(cos(0.1*pi*nx),nx,x,nx); [x,nx] = sigmult(5*(-0.9).^nx,nx,x,nx); X = dtft(x,nx,w); % Computes Discrete-Time Fourier Transform magX = abs(X); angX = angle(X); figure(3); subplot(3,2,1); stem(nx,x,'k'); xlabel('n'); title('Given Sequence'); ylabel('x5(n)') subplot(3,2,3); plot(w/pi,magX,'k'); xlabel('frequency in pi units'); title('Magnitude Part'); ylabel('Magnitude') subplot(3,2,5); plot(w/pi,angX,'k'); xlabel('frequency in pi units'); title('Angle Part'); ylabel('Radians')

%P3.4 colordef white; clear; clc; M = 250; k = -M:M; w = (pi/M)*k; % [0, pi] axis divided into 501 points. N = 5; nx = [-N-10:N+10]; x = stepseq(-N,-N-10,N+10)-stepseq(N+1,-N-10,N+10); X = dtft(x,nx,w); % Computes Discrete-Time Fourier Transform magX = abs(X); magX = magX./max(magX); angX = angle(X); figure(1); subplot(3,2,1); stem(nx,x,'k'); xlabel('n'); title('Given Sequence at N = 5'); ylabel('x1(n)') subplot(3,2,3); plot(w/pi,magX,'k'); xlabel('frequency in pi units'); title('Magnitude Part'); ylabel('Magnitude') subplot(3,2,5); plot(w/pi,angX,'k'); xlabel('frequency in pi units'); title('Angle Part'); ylabel('Radians') N = 15; nx = [-N-10:N+10]; x = stepseq(-N,-N-10,N+10)-stepseq(N+1,-N-10,N+10); X = dtft(x,nx,w); % Computes Discrete-Time Fourier Transform magX = abs(X); magX = magX./max(magX); angX = angle(X); figure(1); subplot(3,2,2); stem(nx,x,'k'); xlabel('n'); title('Given Sequence at N = 15'); ylabel('x1(n)') subplot(3,2,4); plot(w/pi,magX,'k'); xlabel('frequency in pi units'); title('Magnitude Part'); ylabel('Magnitude') subplot(3,2,6); plot(w/pi,angX,'k'); xlabel('frequency in pi units'); title('Angle Part'); ylabel('Radians')

N = 25; nx = [-N-10:N+10]; x = stepseq(-N,-N-10,N+10)-stepseq(N+1,-N-10,N+10); X = dtft(x,nx,w); % Computes Discrete-Time Fourier Transform magX = abs(X); magX = magX./max(magX); angX = angle(X); figure(2); subplot(3,2,1); stem(nx,x,'k'); xlabel('n'); title('Given Sequence at N = 25'); ylabel('x1(n)') subplot(3,2,3); plot(w/pi,magX,'k'); xlabel('frequency in pi units'); title('Magnitude Part'); ylabel('Magnitude') subplot(3,2,5); plot(w/pi,angX,'k'); xlabel('frequency in pi units'); title('Angle Part'); ylabel('Radians') N = 100; nx = [-N-10:N+10]; x = stepseq(-N,-N-10,N+10)-stepseq(N+1,-N-10,N+10); X = dtft(x,nx,w); % Computes Discrete-Time Fourier Transform magX = abs(X); magX = magX./max(magX); angX = angle(X); figure(2); subplot(3,2,2); stem(nx,x,'k'); xlabel('n'); title('Given Sequence at N = 100'); ylabel('x1(n)') subplot(3,2,4); plot(w/pi,magX,'k'); xlabel('frequency in pi units'); title('Magnitude Part'); ylabel('Magnitude') subplot(3,2,6); plot(w/pi,angX,'k'); xlabel('frequency in pi units'); title('Angle Part'); ylabel('Radians')

%P3.4 colordef white; clear; clc; M = 250; k = -M:M; w = (pi/M)*k; % [0, pi] axis divided into 501 points. N = 5; nx = [-N-10:N+10]; x = stepseq(-N,-N-10,N+10)-stepseq(N+1,-N-10,N+10); x = (1-abs(nx)/N).*x; X = dtft(x,nx,w); % Computes Discrete-Time Fourier Transform magX = abs(X); magX = magX./max(magX); angX = angle(X); figure(1); subplot(3,2,1); stem(nx,x,'k'); xlabel('n'); title('Given Sequence at N = 5'); ylabel('x1(n)') subplot(3,2,3); plot(w/pi,magX,'k'); xlabel('frequency in pi units'); title('Magnitude Part'); ylabel('Magnitude') subplot(3,2,5); plot(w/pi,angX,'k'); xlabel('frequency in pi units'); title('Angle Part'); ylabel('Radians') N = 15; nx = [-N-10:N+10]; x = stepseq(-N,-N-10,N+10)-stepseq(N+1,-N-10,N+10); x = (1-abs(nx)/N).*x; X = dtft(x,nx,w); % Computes Discrete-Time Fourier Transform magX = abs(X); magX = magX./max(magX); angX = angle(X); figure(1); subplot(3,2,2); stem(nx,x,'k'); xlabel('n'); title('Given Sequence at N = 15'); ylabel('x1(n)') subplot(3,2,4); plot(w/pi,magX,'k'); xlabel('frequency in pi units'); title('Magnitude Part'); ylabel('Magnitude') subplot(3,2,6); plot(w/pi,angX,'k'); xlabel('frequency in pi units'); title('Angle Part'); ylabel('Radians')

N = 25; nx = [-N-10:N+10]; x = stepseq(-N,-N-10,N+10)-stepseq(N+1,-N-10,N+10); x = (1-abs(nx)/N).*x; X = dtft(x,nx,w); % Computes Discrete-Time Fourier Transform magX = abs(X); magX = magX./max(magX); angX = angle(X); figure(2); subplot(3,2,1); stem(nx,x,'k'); xlabel('n'); title('Given Sequence at N = 25'); ylabel('x1(n)') subplot(3,2,3); plot(w/pi,magX,'k'); xlabel('frequency in pi units'); title('Magnitude Part'); ylabel('Magnitude') subplot(3,2,5); plot(w/pi,angX,'k'); xlabel('frequency in pi units'); title('Angle Part'); ylabel('Radians') N = 100; nx = [-N-10:N+10]; x = stepseq(-N,-N-10,N+10)-stepseq(N+1,-N-10,N+10); x = (1-abs(nx)/N).*x; X = dtft(x,nx,w); % Computes Discrete-Time Fourier Transform magX = abs(X); magX = magX./max(magX); angX = angle(X); figure(2); subplot(3,2,2); stem(nx,x,'k'); xlabel('n'); title('Given Sequence at N = 100'); ylabel('x1(n)') subplot(3,2,4); plot(w/pi,magX,'k'); xlabel('frequency in pi units'); title('Magnitude Part'); ylabel('Magnitude') subplot(3,2,6); plot(w/pi,angX,'k'); xlabel('frequency in pi units'); title('Angle Part'); ylabel('Radians')

%P3.6 colordef white; clear; clc; M = 250; k = -M:M; w = (pi/M)*k; % [0, pi] axis divided into 501 points. N = 5; nx = [-N-10:N+10]; nx = [-N-10:N+10]; x = stepseq(-N,-N-10,N+10)-stepseq(N+1,-N-10,N+10); x = (0.5+0.5*cos(pi*nx/N)).*x; X = dtft(x,nx,w); % Computes Discrete-Time Fourier Transform magX = abs(X); magX = magX./max(magX); angX = angle(X); figure(1); subplot(3,2,1); stem(nx,x,'k'); xlabel('n'); title('Given Sequence at N = 5'); ylabel('x1(n)') subplot(3,2,3); plot(w/pi,magX,'k'); xlabel('frequency in pi units'); title('Magnitude Part'); ylabel('Magnitude') subplot(3,2,5); plot(w/pi,angX,'k'); xlabel('frequency in pi units'); title('Angle Part'); ylabel('Radians') N = 15; nx = [-N-10:N+10]; nx = [-N-10:N+10]; x = stepseq(-N,-N-10,N+10)-stepseq(N+1,-N-10,N+10); x = (0.5+0.5*cos(pi*nx/N)).*x; X = dtft(x,nx,w); % Computes Discrete-Time Fourier Transform magX = abs(X); magX = magX./max(magX); angX = angle(X); figure(1); subplot(3,2,2); stem(nx,x,'k'); xlabel('n'); title('Given Sequence at N = 15'); ylabel('x1(n)') subplot(3,2,4); plot(w/pi,magX,'k'); xlabel('frequency in pi units'); title('Magnitude Part'); ylabel('Magnitude') subplot(3,2,6); plot(w/pi,angX,'k'); xlabel('frequency in pi units'); title('Angle Part'); ylabel('Radians')

N = 25; nx = [-N-10:N+10]; nx = [-N-10:N+10]; x = stepseq(-N,-N-10,N+10)-stepseq(N+1,-N-10,N+10); x = (0.5+0.5*cos(pi*nx/N)).*x; X = dtft(x,nx,w); % Computes Discrete-Time Fourier Transform magX = abs(X); magX = magX./max(magX); angX = angle(X); figure(2); subplot(3,2,1); stem(nx,x,'k'); xlabel('n'); title('Given Sequence at N = 25'); ylabel('x1(n)') subplot(3,2,3); plot(w/pi,magX,'k'); xlabel('frequency in pi units'); title('Magnitude Part'); ylabel('Magnitude') subplot(3,2,5); plot(w/pi,angX,'k'); xlabel('frequency in pi units'); title('Angle Part'); ylabel('Radians') N = 100; nx = [-N-10:N+10]; nx = [-N-10:N+10]; x = stepseq(-N,-N-10,N+10)-stepseq(N+1,-N-10,N+10); x = (0.5+0.5*cos(pi*nx/N)).*x; X = dtft(x,nx,w); % Computes Discrete-Time Fourier Transform magX = abs(X); magX = magX./max(magX); angX = angle(X); figure(2); subplot(3,2,2); stem(nx,x,'k'); xlabel('n'); title('Given Sequence at N = 100'); ylabel('x1(n)') subplot(3,2,4); plot(w/pi,magX,'k'); xlabel('frequency in pi units'); title('Magnitude Part'); ylabel('Magnitude') subplot(3,2,6); plot(w/pi,angX,'k'); xlabel('frequency in pi units'); title('Angle Part'); ylabel('Radians')

% P3.7 colordef white; clear; clc; M = 250; k = -M:M; w = (pi/M)*k; % [0, pi] axis divided into 501 points. n = -50:50; x = exp(j*0.1*pi*n).*(stepseq(0,-50,50)-stepseq(20,-50,50)); [xe,xo,m] = evenoddcomplex(x,n); XE = dtft(xe,m,w); XO = dtft(xo,m,w); figure(1); subplot(2,2,1); plot(w/pi,abs(XE),'k'); axis tight; xlabel('frequency in pi units'); title('Conjugate Symmetric Part Fourier Transform'); ylabel('|XE|'); subplot(2,2,3); plot(w/pi,abs(XO),'k'); axis tight; xlabel('frequency in pi units'); title('Conjugate Antisymmetric Part Fourier Transform'); ylabel('|XO|'); subplot(2,2,2); plot(w/pi,abs(real(dtft(x,n,w))),'k'); axis tight; xlabel('frequency in pi units'); title('Real part of DTFT(x)'); ylabel('|Re(DTFT(x))|'); subplot(2,2,4); plot(w/pi,abs(j*imag(dtft(x,n,w))),'k'); axis tight; xlabel('frequency in pi units'); title('Imaginary part of DTFT(x)'); ylabel('|Im(DTFT(x))|');

% P3.8 colordef white; clear; clc; M = 250; k = -M:M; w = (pi/M)*k; % [0, pi] axis divided into 501 points. n = -50:50; x = exp(j*0.1*pi*n).*(stepseq(0,-50,50)-stepseq(20,-50,50)); [xe,xo,m] = evenoddcomplex(x,n); xr = real(x); xi = imag(x); XE = dft(xe,length(m)); XO = dft(xo,length(m)); fXE = idft(XE,length(XE)); fXO = idft(XO,length(XO)); figure(1); subplot(2,2,1); plot(m,fXE,'k'); axis tight; xlabel('frequency in pi units'); title('Conjugate Symmetric Part Inverse Fourier Transform'); ylabel('|XE-1|'); subplot(2,2,3); plot(m,fXO,'k'); axis tight; xlabel('frequency in pi units'); title('Conjugate Antisymmetric Part Inverse Fourier Transform'); ylabel('|XO-1|'); subplot(2,2,2); plot(m,xr,'k'); axis tight; xlabel('frequency in pi units'); title('Real part of x(n)'); ylabel('Re((x(n))'); subplot(2,2,4); plot(m,xi,'k'); axis tight; xlabel('frequency in pi units'); title('Imaginary part of x(n)'); ylabel('Im(x(n))');

% P3.9 colordef white; clear; clc; M = 250; k = -M:M; w = (pi/M)*k; % [0, pi] axis divided into 501 points. w0 = pi/2; figure(1); N = 5; n = [-N-10:N+10]; x = stepseq(-N,-N-10,N+10)-stepseq(N+1,-N-10,N+10); x = cos(w0*n).*x; X = dtft(x,n,w); subplot(3,3,1); plot(w/pi,abs(X),'k'); xlabel('frequency in pi units'); title('Fourier Transform Magnitude N = 5'); ylabel('|X|'); subplot(3,3,4); plot(w/pi,angle(X),'k'); xlabel('frequency in pi units'); title('Fourier Transform Phase N = 5'); ylabel('\theta'); N = 15; n = [-N-10:N+10]; x = stepseq(-N,-N-10,N+10)-stepseq(N+1,-N-10,N+10); x = cos(w0*n).*x; X = dtft(x,n,w); subplot(3,3,2); plot(w/pi,abs(X),'k'); xlabel('frequency in pi units'); title('Fourier Transform Magnitude N = 15'); ylabel('|X|'); subplot(3,3,5); plot(w/pi,angle(X),'k'); xlabel('frequency in pi units'); title('Fourier Transform Phase N = 15'); ylabel('\theta') N = 25; n = [-N-10:N+10]; x = stepseq(-N,-N-10,N+10)-stepseq(N+1,-N-10,N+10); x = cos(w0*n).*x; X = dtft(x,n,w); subplot(3,3,3); plot(w/pi,abs(X),'k'); xlabel('frequency in pi units'); title('Fourier Transform Magnitude N = 25'); ylabel('|X|'); subplot(3,3,6); plot(w/pi,angle(X),'k'); xlabel('frequency in pi units'); title('Fourier Transform Phase N = 25'); ylabel('\theta') N = 100; n = [-N-10:N+10]; x = stepseq(-N,-N-10,N+10)-stepseq(N+1,-N-10,N+10); x = cos(w0*n).*x; X = dtft(x,n,w); subplot(3,2,5); plot(w/pi,abs(X),'k'); xlabel('frequency in pi units'); title('Fourier Transform Magnitude N = 100'); ylabel('|X|'); subplot(3,2,6); plot(w/pi,angle(X),'k'); xlabel('frequency in pi units'); title('Fourier Transform Phase N = 100'); ylabel('\theta')

% P3.11 colordef white; clear; clc; M = 250; k = -M:M; w = (pi/M)*k; % [0, pi] axis divided into 501 points. w0 = pi/2; figure(1); n = -50:50; h = (0.9).^(abs(n)); H = dtft(h,n,w); subplot(3,2,1); plot(w/pi,abs(H)); xlabel('frequency in pi units'); ylabel('|H|'); title('Magnitude Response'); subplot(3,2,2); plot(w/pi,angle(H)/pi); xlabel('frequency in pi units'); ylabel('\Theta'); title('Phase Response'); h = sinc(0.2*n).*((stepseq(-20,-50,50)-stepseq(20,-50,50))); H = dtft(h,n,w); subplot(3,2,3); plot(w/pi,abs(H)); xlabel('frequency in pi units'); ylabel('|H|'); title('Magnitude Response'); subplot(3,2,4); plot(w/pi,angle(H)/pi); xlabel('frequency in pi units'); ylabel('\Theta'); title('Phase Response'); h = sinc(0.2*n).*((stepseq(0,-50,50)-stepseq(40,-50,50))); H = dtft(h,n,w); subplot(3,2,5); plot(w/pi,abs(H)); xlabel('frequency in pi units'); ylabel('|H|'); title('Magnitude Response'); subplot(3,2,6); plot(w/pi,angle(H)/pi); xlabel('frequency in pi units'); ylabel('\Theta'); title('Phase Response');

figure(2); h = ((0.5).^n+(0.4).^n).*stepseq(0,-50,50); H = dtft(h,n,w); subplot(3,2,1); plot(w/pi,abs(H),'k'); xlabel('frequency in pi units'); ylabel('|H|'); title('Magnitude Response'); subplot(3,2,2); plot(w/pi,angle(H)/pi,'k'); xlabel('frequency in pi units'); ylabel('\Theta'); title('Phase Response'); h = (0.5).^(abs(n)).*cos(0.1*pi*n); H = dtft(h,n,w); subplot(3,2,3); plot(w/pi,abs(H),'k'); xlabel('frequency in pi units'); ylabel('|H|'); title('Magnitude Response'); subplot(3,2,4); plot(w/pi,angle(H)/pi,'k'); xlabel('frequency in pi units'); ylabel('\Theta'); title('Phase Response');

% P3.13 colordef white; clear; clc; M = 250; k = -M:M; w = (pi/M)*k; % [0, pi] axis divided into 501 points. w0 = pi/2; figure(1); alpha=20; wc=0.5*pi; n = 0:40; h = sin(wc*(n-alpha))./(pi*(n-alpha)); h(21) = 1/exp(1); subplot(3,1,1); plot(n,h,'k'); xlabel('n'); ylabel('h(n)'); title('Truncated Impulse Response'); H = dtft(h,n,w); subplot(3,1,2); plot(w/pi,abs(H),'k'); xlabel('frequency in pi units'); ylabel('|H|'); title('Magnitude Response'); subplot(3,1,3); plot(w/pi,angle(H)/pi,'k'); xlabel('frequency in pi units'); ylabel('\Theta'); title('Phase Response');

% P3.15 function [H]=freqresp(b,a,w) % Frequency response function from difference equation % [H] = freqresp(b,a,w) % H = frequency response array evaluated a w frequencies % b = numerator coefficient array % a = denominator coefficient array (a(1)=1) % w = frequency location array m = 0:length(b)-1; l = 0:length(a)-1; num = b*exp(-j*m'*w); den = a*exp(-j*l'*w); H = num./den;

% P3.19 % Señal Analógica Dt=0.0005; t=-.5:Dt:0.5; xa=3*cos(20*pi*t); subplot(2,2,1); plot(t,xa,'k'); xlabel('Frequency'); ylabel('Amplitude'); title('Analog Input Signal x_a(t)'); % Señal en tiempo discreto Ts=0.01; n=-50:1:50; nTs=n*Ts; x=3*cos(20*pi*nTs); subplot(2,2,3); stem(n,x,'k'); xlabel('Frequency'); ylabel('Amplitude'); title('Discrete Input Signal x(n)'); % x(n)*h(n) h=((0.5).^n).*stepseq(0,-50,50); [y,n]=conv_m(x,n,h,n); subplot(2,2,2); stem(n,y,'k'); xlabel('Frequency'); ylabel('Amplitude'); title('Discrete Output Signal y(n)'); % Señal de salida reconstruida ya(t) Dt=0.0005; t=-0.50:Dt:0.50; Ts=0.01; Fs=1/Ts; nTs=n*Ts; ya=y*sinc(Fs*(ones(length(n),1)*t-nTs'*ones(1,length(t)))); subplot(2,2,4); plot(t,ya,'k'); xlabel('Frequency'); ylabel('Amplitude'); title('Analog Output Signal y_a(t)');

figure(2); % Señal Analógica Dt=0.0005; t=-.5:Dt:0.5; xa=3*[t>=0]; subplot(2,2,1); plot(t,xa,'k'); xlabel('Frequency'); ylabel('Amplitude'); title('Señal analogica de entrada xa(t)'); % Señal en tiempo discreto Ts=0.01; n=-50:1:50;nTs=n*Ts; x=3*[nTs>=0]; subplot(2,2,3); stem(n,x,'k'); xlabel('Frequency'); ylabel('Amplitude'); title('Señal discretizada de entrada x(n)'); % x(n)*h(n) h = ((0.5).^n).*stepseq(0,-50,50); [y,n]=conv_m(x,n,h,n); subplot(2,2,2); stem(n,y,'k'); xlabel('Frequency'); ylabel('Amplitude'); title('Señal discretizada de salida y(n)'); % Señal de salida reconstruida ya(t) Dt=0.0005; t=-0.50:Dt:0.50; Ts=0.01; Fs=1/Ts;nTs=n*Ts; ya=y*sinc(Fs*(ones(length(n),1)*t-nTs'*ones(1,length(t)))); subplot(2,2,4); plot(t,ya,'k'); xlabel('Frequency'); ylabel('Amplitude'); title('Analog Output Signal y_a(t)');