phase jumps in dtft

hey what causes the phase jumps in angle plot? whats the problem ? its not like that theorically it just happens in matlab

this is the code:

% Plotting the spectrum of a discrete-time rectangular pulse

n=-20:20;

w=-2.5*pi:.01:2.5*pi;

x1=zeros(size(n));

x1(n>=-2 & n<=2)=1;

% x1(19:23)=1;

X=dtft(n,x1,w);

subplot(3,1,1)

stem(n,x1,'linewidth',3);

set(gca,'fontsize',24)

axis([-20 20 0 1.2])

xlabel('n')

ylabel('x[n]')

subplot(3,1,2)

plot(w/pi,abs(X),'linewidth',3);

set(gca,'fontsize',24)

xlabel('\omega (\times\pi rad)')

ylabel('|X(e^{j\omega})|')

subplot(3,1,3)

plot(w/pi,angle(X),'linewidth',1);

set(gca,'fontsize',24)

xlabel('\omega (\times\pi rad)')

ylabel('\angle X(e^{j\omega})')

Answer 1

[Paul]

n=-20:20;
w=-2.5*pi:.01:2.5*pi;
x1=zeros(size(n));
x1(n>=-2 & n<=2)=1;
% x1(19:23)=1;

Matlab doesn't have a function dtft.

which -all dtft

'dtft' not found.

try
X=dtft(n,x1,w);
catch ME
    ME.message
end

ans = 'Undefined function 'dtft' for input arguments of type 'double'.'

Here's one way to generate the DTFT over the frequency range

X = freqz(x1,1,w).*exp(-1j*w*n(1));

Yes, the angle jumps around.

subplot(211);
plot(w,abs(X))
subplot(212);
plot(w,angle(X))

That's because the DTFT as computed by freqz returns very, very, very small imaginary part, presumably due to round off, which causes the phase to be either very close to zero, very close to pi, over very close to -pi

figure
subplot(211),plot(w,real(X))
subplot(212),plot(w,imag(X))