How implement the convolution between f(t) and Delta(t-t0)

[nicozuo]

how to implement convolution

Hello, my friends,

We all know that the convolution between a signal f(t) and the
Delta function D(t - t0) is to shift f(t) with t0 away. But, how could
we validate this property? Namely, how do we implement the
convolution between a signal f(t) and the Delta function D(t - t0),
where t0 is a shift constant.

I think, we can implement it in frequency space, but I don't know
how bu sample exp(-j w t0), which is the Fourier transform of Delta(t-t0).

Any suggestions would be appreciated!

Thank you,

Nico

 

[bulx]

delta shift convolution

if matlab is acceptable "validation"...see how changing the postion of the impulse shifts the ouptut by different amounts..

t = -5:5
x= randn (1, length(t));

hold off;
plot(x,'g');
hold on;
d = zeros (1,length(t));
d(2) = 1;
plot(conv (x,d),'b');

d = zeros (1,length(t));
d(6) = 1;
plot(conv (x,d),'r');
hold off


-b

 

[nicozuo]

Re: How implement the convolution between f(t) and Delta(t-t

if matlab is acceptable "validation"...see how changing the postion of the impulse shifts the ouptut by different amounts..

t = -5:5
x= randn (1, length(t));

hold off;
plot(x,'g');
hold on;
d = zeros (1,length(t));
d(2) = 1;
plot(conv (x,d),'b');

d = zeros (1,length(t));
d(6) = 1;
plot(conv (x,d),'r');
hold off


-b

Thank you for your reply.

I just got the answer this moring.
A reasonable interval for sampling Delta(t - t0) is 2*pi/N, where N denotes
the length of the signal f(t). It is effetive regardless of the sign of t0.

Thank you,

Nico