Is there a relationship between amplitude response and phase?

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SUMMARY

The discussion confirms that there is indeed a relationship between amplitude response and phase response in the context of FIR (Finite Impulse Response) digital filters. It establishes that one can design a FIR filter with a specified frequency response, where both amplitude and phase responses can be chosen independently, provided the inverse Fourier transform exists. The participants agree that for realizable filters, especially non-causal ones, the amplitude and phase can be manipulated without direct dependency on each other, supporting the theoretical framework of filter design.

PREREQUISITES
  • Understanding of FIR (Finite Impulse Response) digital filters
  • Knowledge of Fourier transforms, specifically inverse Fourier transforms
  • Familiarity with frequency response concepts in signal processing
  • Basic principles of filter design and realizability
NEXT STEPS
  • Study the design techniques for FIR digital filters using MATLAB or Python
  • Explore the implications of non-causal filters in signal processing
  • Learn about the properties of Fourier transforms and their applications in filter design
  • Investigate the relationship between amplitude and phase response in other filter types, such as IIR (Infinite Impulse Response) filters
USEFUL FOR

Signal processing engineers, audio engineers, and anyone involved in digital filter design and analysis will benefit from this discussion.

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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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
 

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