# convolution and frequncy response

I have a sinusiodal signal x in time domain.I have done the convlotion as followings using matlab: y=conv(x,x) and y=conv(x,fliplr(x)). Observing the result by Matlab, both of the above signal giving the same result in frequency domain. Why do you think is that?

P.S: FLIPLR(X) returns X with row preserved and columns flipped in the left/right direction.

X = 1 2 3     becomes  3 2 1
4 5 6              6 5 4


Convolution in the time domain means you are multiplying their frequency transforms. This is one of the many properties of the Fourier Transform.

Now, when you flip a signal X[n], you can also write it down as x[n1], where n1 = -n. If you look at the time scaling property, try replacing 'a' by -1. You'll observe that the F(W) will now become F(-W).

Since F(-W) is exactly the same as F(W), your result does not change.