DSP - FIR Filters, linear phase conditions

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SUMMARY

The discussion centers on the necessity of symmetry or antisymmetry in Finite Impulse Response (FIR) filters to achieve a linear phase response. The key takeaway is that the condition for linear phase is fulfilled when the impulse response is symmetric, which ensures that the output signal is delayed uniformly. Rune seeks a proof for this principle, emphasizing the relationship between the filter's frequency response and the linear phase characteristic, specifically referencing the term \left|H\left(\omega\right)\right|X\left(\omega\right)e^{-j\omega n_{0}}.

PREREQUISITES
  • Understanding of FIR filter design and characteristics
  • Knowledge of linear phase response in signal processing
  • Familiarity with frequency response analysis
  • Basic concepts of symmetry and antisymmetry in mathematical functions
NEXT STEPS
  • Research the mathematical proof of linear phase conditions in FIR filters
  • Study the implications of symmetry in digital signal processing
  • Explore the design of FIR filters using MATLAB or Python
  • Learn about the effects of phase distortion in signal transmission
USEFUL FOR

Signal processing students, audio engineers, and anyone involved in the design and analysis of FIR filters will benefit from this discussion.

Runei
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Hello there

I'd like to know if anyone has a proof of why the condition of symmetry or antisymmetry must be followed by a FIR filter, in order for it to have a linear phase response?

I've been pouring over this for an exam, and my initial question was what constitutes a linear phase response and after a little pouring and talking with myself I finally got that it is because of the \left|H\left(\omega\right)\right|X\left(\omega\right)e^{-j\omega n_{0}} that the x(n) will be delayed by n_0 samples.

Now, however, the only step I need to have rounded this off is a proof to myself that the impulse response of the filter must be symmetric in order for a linear phase response to occur.

Thank you in advance,

Rune
 
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Im just going to bump it once in one last hope :)
 

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