How do you evaluate the following: (G(jw).H(jw))*K(jw)?

[kolycholy]

so i need to figure out how do you evaluate the following:
(G(jw).H(jw))*K(jw)
note
note: i would like you to assume that the dot means multiplication and the star sign means convolution

 

[Ouabache]

Why not multiply the two frequency functions G(jw) and H(jw) and convolve that with K(jw) using the convolution formula

Or, multiply the two frequency functions G(jw) and H(jw) and transform the resultant and K(jw) back to time (using the Inverse Fourier Transform) Did you learn that convolution in the time domain is the same as multiplication in the frequency domain? Well the dual is also true; convolution in frequency becomes multiplication in time.