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

  • Thread starter kolycholy
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In summary, the conversation discusses evaluating the expression (G(jw).H(jw))*K(jw). The suggested methods are to either multiply the two frequency functions G(jw) and H(jw) and convolve that with K(jw) using the convolution formula, or to multiply the two frequency functions and transform the result and K(jw) back to time using the Inverse Fourier Transform. It is noted that convolution in the time domain is the same as multiplication in the frequency domain, and vice versa.
  • #1
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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  • #2
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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  • #3


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.
 

1. What is G(jw), H(jw), and K(jw)?

G(jw), H(jw), and K(jw) are all transfer functions in the frequency domain. They represent the relationship between the input and output of a system at different frequencies.

2. How do you evaluate the expression (G(jw).H(jw))*K(jw)?

To evaluate this expression, you first need to calculate the individual values of G(jw), H(jw), and K(jw) at the specific frequency, w. Then, multiply G(jw) and H(jw) together, and finally multiply the result with K(jw).

3. What does the result of (G(jw).H(jw))*K(jw) represent?

The result of this expression represents the overall transfer function of the system. It shows how the input signal is modified by the system at a specific frequency.

4. How can this expression be used in practical applications?

This expression can be used to analyze and design systems in various engineering fields, such as electrical engineering, control systems, and signal processing. It can help to understand the behavior of a system at different frequencies and make adjustments to achieve desired performance.

5. What factors can affect the evaluation of (G(jw).H(jw))*K(jw)?

The evaluation of this expression can be affected by the accuracy of the transfer functions, the frequency range used, and any external disturbances that may affect the system. It is important to have precise and reliable transfer functions for a more accurate evaluation.

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