Is there a relationship between amplitude response and phase?

In summary, there is a relationship between the amplitude and phase response of a realizable filter, specifically for a FIR digital filter. The amplitude and phase responses are given as a function of frequency and can be designed independently, as long as the inverse Fourier Transform exists. This supports the understanding that amplitude and phase are independent. Non-causal filters are allowed and the amplitude and phase responses are continuous and absolute integrable.
  • #1
manjuvenamma
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Is there a relationship between amplitude and phase response of a realizable filter? For the purpose of ease, let us consider only a FIR digital filter. I would like to design a FIR digital filter with a given frequency response (amplitude and phase responses given as a function of frequency)? Non-causal filters are allowed. The amplitude and phase responses are continuous and absolute integrable. Theoretically, you can find the filter coefficients by taking the inverse Fourier transform of the frequency response. So long as the Inverse Fourier Transform exists, you can choose amplitude and phase responses arbitrarily and independently. Is this understanding correct?
 
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  • #2
I don't think I'm on your level, but just in case it helps Ill tell you I just did experiments and reading on the fact that (at least with simple harmonic, which I am sure yours isn't so I should probably just stop typing now but what the hell) Amplitutude and frequency-and therefore?Amplitude and phase are independent.
Which seems to support your conclusion, sorry if I wasted your time
 

Related to Is there a relationship between amplitude response and phase?

1. What is amplitude response and phase in relation to a system's response?

Amplitude response is a measure of the magnitude of a system's output in response to a given input. Phase, on the other hand, describes the relationship between the input and the output in terms of time delay. In other words, amplitude response is the strength of the signal while phase is the timing of the signal.

2. How are amplitude response and phase related?

Amplitude response and phase are closely related as they both describe the behavior of a system in response to an input. However, they are not the same and can vary independently. A system's amplitude response can be affected by its phase and vice versa.

3. What is the importance of understanding the relationship between amplitude response and phase?

Understanding the relationship between amplitude response and phase is crucial in many fields, such as signal processing and control systems. It allows us to analyze and predict the behavior of a system and make adjustments to improve its performance.

4. How can amplitude response and phase be measured?

Amplitude response can be measured by inputting a known signal into the system and measuring the output amplitude. Phase can be measured by comparing the input and output signals and calculating the time delay between them.

5. Can the relationship between amplitude response and phase change over time?

Yes, the relationship between amplitude response and phase can change over time. This can be due to various factors such as changes in the system's components or external influences. It is important to monitor and adjust these parameters to maintain the desired performance of the system.

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