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

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To evaluate (G(jw).H(jw))*K(jw), one approach is to multiply the frequency functions G(jw) and H(jw), then convolve the result with K(jw) using the convolution formula. Alternatively, the two frequency functions can be multiplied, and the resultant along with K(jw) can be transformed back to the time domain using the Inverse Fourier Transform. It's important to note that convolution in the time domain corresponds to multiplication in the frequency domain, and vice versa. Understanding these relationships is crucial for accurate evaluation. This discussion highlights key methods for analyzing frequency domain expressions.
kolycholy
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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
 
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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.
 
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