Multiply freq response by w ?

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In summary, the conversation discusses the effect of multiplying the frequency response by "w" on a periodic signal with a frequency domain representation of X(w). The question is about the corresponding change in x(t) and the suggested approach is to write out the complex Fourier transform and see the effect of taking a derivative with respect to t. The person asking the question expresses difficulty with this approach and hopes for a general procedure.
  • #1
anjana.rafta
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multiply freq response by "w" ??

hi all,
i am not able to proced to this problem
lets say there is a signal x(t), which has freq domain representatiojn of X(w)
lets say signal is periodic with T = 1
now in freq domian X(w) is multiplied with "w" for 0<w<2

then what would be corresponding change in x(t)??
i tried to do inverse ifft, but that's giving me ans = 0.

how should i go about it? not exact solution but in general procedure?

Thanks
 
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  • #2


You receive the derivative of the function. Just write out the complex Fourier transform and see what a derivative with respect to t does to the terms in the integral.
 
  • #3


thanks!

:frown: <-- me
 

1. What is the purpose of multiplying frequency response by w?

Multiplying the frequency response by w is a common mathematical operation used in signal processing and control systems. It allows us to analyze how a system responds to different frequencies of input signals, which is important for understanding the behavior of the system and designing appropriate control strategies.

2. How does multiplying frequency response by w affect the system's behavior?

The multiplication by w amplifies the high frequency components of the frequency response while attenuating the low frequency components. This means that the system will respond more strongly to high frequency inputs and less strongly to low frequency inputs.

3. Can multiplying frequency response by w change the stability of a system?

Yes, multiplying frequency response by w can change the stability of a system. If the frequency response is multiplied by a value greater than 1, the system's stability may be compromised. However, if the multiplication is less than 1, it can improve the system's stability.

4. Is there a specific reason for using w when multiplying frequency response?

Yes, w (or omega) is a commonly used variable in frequency domain analysis. It represents the frequency of the input signal and is used to express the frequency response of a system. Multiplying the frequency response by w allows us to analyze the system's behavior at different frequencies.

5. Are there any limitations to multiplying frequency response by w?

One limitation is that it assumes a linear system, meaning that the output is proportional to the input. Additionally, multiplying frequency response by w only tells us about the system's response to sinusoidal inputs and does not provide information about its behavior for other types of inputs.

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