Frequency and impulse response

In summary, to find the frequency response of a discrete system with input x(t) and output y(t), you need to take the Fourier transform of y(t) and divide it by the Fourier transform of x(t). For the impulse response, the input convolved with the impulse response will give the output. To calculate the impulse response, you can take the inverse Fourier transform of the frequency response. This information should help with your assignment.
  • #1
TheTopGun
16
0
Hi, I have a discrete system with input x(t) and output y(t).

Using the formula frequency response H(f) = y(f)/x(f) in the Fourier domain.

Does this mean to find the frequency response I have to take the Fourier Transform of

y(t) to get y(f) and divide it by the Fourier transform of x(t) , x(f) ?also, for the impulse response: input convolved with impulse response = output.

How do I go about calculating the impulse response given I know the input, output and frequency response.

Just looking for some clarification and guidance before I dive into this assignment.

Thanks.
 
Last edited:
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  • #2
Think I got it...I can go from the freq response to impulse response by taking the inverse Fourier transform of the freq response.
 

Related to Frequency and impulse response

1. What is the difference between frequency response and impulse response?

Frequency response is a measure of how a system responds to different frequencies, while impulse response is a measure of how a system responds to an instantaneous input or impulse.

2. How is frequency response related to the transfer function of a system?

The frequency response of a system is the magnitude and phase relationship between the input and output signals, and it can be obtained by taking the Fourier transform of the impulse response. The transfer function, on the other hand, is the ratio of the output to the input signals in the frequency domain.

3. What is the significance of the frequency response in signal processing?

The frequency response provides important information about how a system affects different frequency components of a signal. It is used to analyze and design filters, equalizers, and other signal processing systems.

4. Can the frequency response of a system change over time?

Yes, the frequency response of a system can change over time due to factors such as aging of components, temperature changes, and environmental conditions. This can result in a degraded performance of the system.

5. How can the impulse response of a system be measured?

The impulse response can be measured by exciting the system with an impulse input and recording the resulting output. This can be done using specialized equipment or by using mathematical techniques such as deconvolution on input-output data.

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