Allpassphase -
Where ( a ) is the coefficient determining the cutoff frequency. The magnitude ( |H(z)| = 1 ) for all ( z ), but the phase ( \angle H(z) ) shifts from 0 to -180 degrees (or 0 to -360 degrees for second-order filters). To understand allpassphase, you must understand group delay —the derivative of phase with respect to frequency. Group delay measures the time delay each frequency component experiences as it passes through a system.
[ a = \frac\tan(\pi \cdot fc / fs) - 1\tan(\pi \cdot fc / fs) + 1 ] allpassphase
Introduction: The Phase You Never Hear, But Always Feel In the world of digital signal processing (DSP), most discussions revolve around amplitude—how loud a sound is, how steep a filter cuts, or how much gain an amplifier provides. Yet, lurking beneath the surface is an equally powerful, often misunderstood phenomenon: phase . Specifically, when engineers discuss the peculiar behavior of phase without altering magnitude, they are venturing into the domain of the allpass filter and its associated allpassphase . Where ( a ) is the coefficient determining
import numpy as np def allpass_first_order(x, a): y = np.zeros_like(x) y_prev = 0 x_prev = 0 for n in range(len(x)): y[n] = a * x[n] + x_prev - a * y_prev x_prev = x[n] y_prev = y[n] return y Group delay measures the time delay each frequency
The coefficient a is related to cutoff frequency fc and sample rate fs by: