Time shift and scale a conv()

I have a problem where I am finding z = conv(y(t),y(t)).

I want to test whether z(2t-1) = {y(t)*y(2t-1)} or {y(2t-1)*y(2t-1)}

I know how to prove this mathematically, but i must also print and compare the graphs. However I do not know how to time scale/delay z to create z(2t-1) since the conv() function does not have an apparent place to affect the time inputs.

Any help would be appreciated!

[Paul]

Is there a source that shows a time scaling property of the convolution? That is if

z(t) = y(t)*y(t) * means convolution

then

z(2t) = ??

Or alternatively,

?? = y(2t)*y(t)

?? = y(2t)*y(2t)

Is there a known form for ?? in any of the above?

Answer 1

[vidyesh]

Hi Turner,

I understand that you want to know how to time scale or delay a signal in MATLAB.

To achieve time scaling or delay of a signal in MATLAB, we need to manipulate the time axis rather than the signal itself, as the magnitude of the signal remains unchanged.

The code snippet below demonstrates how to introduce a delay in the signal and how to calculate the time range for convolution of two signals:

t = 0:10; 
t_z = linspace(t(1) + t(1), t(end) + t(end), numel(t) + numel(t) - 1); % Time range for conv(y(t), y(t)) 
y = [0 1 1 1 zeros(1,7)]; % Sample signal 
z = conv(y,y); 

% Plotting y(t) and y(t-2) 
figure 
stem(t+2, y, 'Marker', 'x') 
hold on 
stem(t, y) 
hold off
% Plotting y(t) and z(t) = conv(y(t), y(t)) 
figure 
stem(t, y, 'Marker', 'x') 
hold on 
stem(t_z, z); 
hold off

Refer to the following documentation to learn more about convolution.

• https://www.mathworks.com/help/matlab/ref/conv.html

Hope this answer helps.