How to write a sigma calculation
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doyoun Kim
el 25 de Mayo de 2018
Comentada: doyoun Kim
el 27 de Mayo de 2018
I'm trying to plot a Dtft,
the question is number 2 in the picture.
This is how I wrote
x=ones(1,9);
N=length(x);
n=-4:N-5;
q=@(omega)exp(-1i.*omega.*n);
wn=linspace(-2,2,9);
plot(wn,real(q(wn)), '-b', wn, imag(q(wn)), '-r');
grid
there is no problems, but the graph isn't pretty.
My thought is to change omega's length somehow or is there a better way?
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Abraham Boayue
el 26 de Mayo de 2018
Editada: Abraham Boayue
el 26 de Mayo de 2018
In part two of the problem, you will have to use the definition of the DTFT to compute X(omega). The resultant function is just a periodic version of X(jw) from part one of the problem. See the following code below.
%%Part 1
clear variables
close all
N= 200;
T = 2;
t = -2:4/(N-1):2;
x = rectpuls(t,T);
f= -2:4/(N-1):2;
X = T*sin(pi*f*T)./(pi*f*T);
figure
subplot(121)
plot(t,x,'linewidth',2,'color','b')
grid;
a = title('x(t)');
set(a,'fontsize',14);
a = ylabel('x');
set(a,'Fontsize',14);
a = xlabel('t');
set(a,'Fontsize',14);
subplot(122)
plot(f,abs(X)/(max(X)),'linewidth',2,'color','m')
a = title('|X(jw)|');
set(a,'fontsize',14);
a = ylabel('X');
set(a,'Fontsize',14);
a = xlabel('f');
set(a,'Fontsize',14);
grid
%%Part 2
M = 1000;
N = 7;
n = 0:N-1;
xn = ones(1,N);
w = 8*pi;
omega = -w:2*w/(M-1):w;
Xn= exp(-1i.*omega.*(N-1)./2).*(sin(omega*N/2)./sin(omega/2)); %define DTFT function
Mag = abs(Xn)/max(Xn); %compute magnitude
Phase = angle(Xn); %compute phase
figure
subplot(3,1,1)
stem(n,xn,'linewidth',2,'color','b');
a = title('x(n)');
set(a,'fontsize',14);
a = ylabel('xn');
set(a,'Fontsize',14);
a = xlabel('n');
set(a,'Fontsize',14);
grid
subplot(3,1,2)
plot(omega/pi,real(Mag),'linewidth',2,'color','k');
a = title('|X(\omega)|');
set(a,'fontsize',14);
a = ylabel('X');
set(a,'Fontsize',14);
a = xlabel('f');
set(a,'Fontsize',14);
grid
subplot(3,1,3)
plot(omega./pi,Phase,'linewidth',2,'color','k');
a = title('<X(\omega)');
set(a,'fontsize',14);
a = ylabel('X');
set(a,'Fontsize',14);
a = xlabel('f');
set(a,'Fontsize',14);
grid
3 comentarios
Abraham Boayue
el 26 de Mayo de 2018
Editada: Abraham Boayue
el 26 de Mayo de 2018
fs = 4;
fo = 10;
f = -fo:2*fo/(M-1):fo; % -10<f<10
omega = 2*pi*f/fs;
fn = omega/2*pi; % You can plot the function vs the normalized frequency f/fs % if you wish
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