Brick Wall Digital Filters and Phase Deviations
Over the years controversy has raged back and forth on whether brick wall filters used in digital audio (namely for CD playback systems) exhibit phase shifts in the audio band (20Hz to 20kHz). Audio critics, pundits and assorted experts have gone back and forth on this issue with out much resolution as I can gather. Some companies have put out their so-called solutions to this problem. It is my desire that this article will put this issue to rest once and for all.
The predominant type of digital filter used in audio is called an FIR (Finite Impulse Response) filter. The stated frequency response in most data books is a flat frequency response to 20.0 kHz and anywhere from -6db to -12db down at 22.05 kHz. The frequency 1 / 2*Ts (where fs = 1 / 2*Ts, fs = sampling frequency, Ts = sampling period) known today as the Nyquist frequency and the Shannon sampling frequency , corresponds to the highest frequency at which a signal can contain energy and remain compatible with the Sampling Theorem. High-quality sampling systems ensure that no aliasing occurs by deleteriously lowpass filtering the signal (cutoff frequency being slightly lower than the Nyquist frequency) before sampling. At 24 kHz a typical high performance digital filter for this application is typically greater than -100db down. As we can see from these numbers, that's a really stiff slope, and most of us with some analog electronics or speaker crossover background would immediately say this filter must have a phase shift. But digital filters of this type are different from analog filters in one major respect. The FIR filters that are used in digital audio have "uniform group delay". Now if we think about that for a minute we start to realize that if a filter has uniform group delay, than there can be no phase shift in the pass band (The pass band is where the frequency response is flat). For more information on FIR filters, their uniform phase response and lack of "phase distortion" touted by many self proclaimed audio experts, read this FIR Filter Supplemental .
Since words are generally meaningless to most people it's appropriate and necessary to support this fact with some oscilloscope photos to illustrate things more clearly.
The following tests come from the Philips test CD, Audio Signals disc 1. This disc contains close to 100 different signals for testing CD players and outboard DAC's.
The description of the test is as follows: "Tracks 74 & 75; A 1 kHz sine wave is recorded on one channel (black trace) while the frequency on the other channel is 20 kHz (green trace). These sine waves are coherent, whereby both have zero crossings at the same moment. This can be monitored by displaying both signals simultaneously on the same oscilloscope screen. If the player exhibits no phase difference between the two channels, the up going as well as the down going zero crossing of the 1 kHz signal should coincide with the up going zero crossing of the 20 kHz signal"
The scope photo shown above has the right channel in black with our 1kHz sine wave and the left channel in green with our 20kHz sine wave. If you look carefully the zero crossover points line up exactly, and if you wish to count you will find for every cycle of our 1kHz sine wave you will find 20 cycles of the 20kHz sine wave.