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.

 

[ravenprp]

To evaluate the expression (G(jw).H(jw))*K(jw), we can follow these steps:

1. First, we need to understand the meaning of each term in the expression. In this case, G(jw), H(jw), and K(jw) are all functions of the frequency variable w.

2. Next, we need to evaluate each of these functions at a specific value of w. This will give us numerical values for G(jw), H(jw), and K(jw).

3. Once we have the numerical values for each function, we can multiply G(jw) and H(jw) together, and then convolve the resulting product with K(jw).

4. The resulting value from the convolution will be the final evaluation of the expression (G(jw).H(jw))*K(jw).

5. It is important to note that the dot in this expression represents multiplication, while the star sign represents convolution. Multiplication is a simple arithmetic operation, while convolution is a mathematical operation used to combine two functions to produce a third function.

Overall, to evaluate the expression (G(jw).H(jw))*K(jw), we need to understand the functions involved, evaluate them at a specific value of w, and then perform the appropriate mathematical operations (multiplication and convolution) to get the final result.