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Notes on Digital Signal Processing: Practical Recipes for Design, Analysis and Implementation by C. Britton Rorabaugh

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Note 34. Periodicities in Linear-Phase FIR Responses

Most filter design tools generate a filter’s frequency response in magnitude-phase form. When working with linear-phase filters, it is sometimes convenient to view the filters’ responses in amplitude-phase form. This note explores some of the issues that arise in converting a magnitude-phase form into an amplitude-phase form.

The magnitude-phase response can be converted into the amplitude-phase response using Recipe 34.1. However, when this is done for Type 2 or Type 4 linear-phase FIR filters, the resulting normalized-frequency amplitude response is periodic in 4π. This result appears to contradict the fact that the normalized-frequency response for any digital filter should be periodic ...

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