Filters Preserving Phase

In this chapter, linear phase and zero phase filters are defined and discussed.

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Subsections

• Linear-Phase Filters
• Zero-Phase Filters
  • -Phase Filters
  • Phase in the Stopband
  • Example Zero-Phase Filter Design
  • Elementary Zero-Phase Filter Examples
  
  
• Odd Impulse Reponses
• Symmetric Linear-Phase Filters
  • Simple Linear-Phase Filter Examples
  • Software for Linear-Phase Filter Design
  
  
• Antisymmetric Linear-Phase Filters
• Forward-Backward Filtering
• Phase Distortion at Passband Edges

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Previous: Pole-Zero Analysis Problems
Next: Linear-Phase Filters (Symmetric Impulse Responses)

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About the Author: Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.

I am a beginner of DSP. And these days I am confusing with the zero phase filtering in STFT as every segment after using the window will be zero padded and shifted to fulfill the zero phase. What's the advantage to realize the zero phase? As the purpose is to reconstruct the original signal using the inverse STFT, is the zero phase useful and key to get the original signal?Thank you!
Looking forward to your reply!

If all you are doing is performing the STFT and reconstructing the original signal by an inverse STFT, then the phase (or even type) of the window doesn't matter. All that matters in that (degenerate) case is that the windows overlap and add to a constant at the chosen hop size R.

Thank you for your answer.
I am still not totally understand what happens in the degenerate case if I don't add zeros and shift the window. Can you tell me the difference in detail?
If the original signal need be reconstructed, is the hop size R of some window is fixed?

Well, I wrote down what I know in pretty good detail in this book! You might want to start with the previous book Mathematics of the DFT. You seem to be weak on basic Fourier theorems, so I would recommend getting to the point that you can prove all the main theorems for the DFT case.