Fourier effect of time shift + convolution

[azay]

Ok, I know the Fourier effect of a time shift is a multiplication with an exponential:

x(t-t0) → exp(-j2∏f*t0)X(f)

Now say Y(f) is the Fourier transform of y(t).

What I am wondering what is the difference in the Fourier space when convolving Y(f) with either X(f) or exp(-j2∏f*t0)X(f) respectively? (and why)

 

[algebrat]

If you want me to improve your intuition of the Fourier transform and convolution, that would be very hard.

but if you want to know physically what's the difference between convolving with e^(...)X, isn't it just in correspondence with normal multiplication of x(t-t_0) and y? Multiplying two signals should just multiply there amplitude at each moment in time.

The Fourier transform is weird, it's all referring to functions of frequency, not time. Convolution is maybe just a funny way to add up all the frequency contributions.