All-Pass Functions
The magnitude response of an all-pass (AP) filter is unity for all frequencies, thus all frequencies are passed without attenuation. The associated phase response, however, is useful for approximating a specified phase characteristic, and the AP group delay function is useful for approximating a specified delay characteristic. Moreover, if we indicate that a parameter α can be adjusted for a specific phase response, it is understood that α can likewise be adjusted for a specific group delay response. Approximating a linear phase by the AP phase corresponds to approximating a constant delay by the AP delay. Theoretically these approximations are not necessarily the same, but in practice the difference is often negligible. The phase (delay) properties of AP filters are so important for achieving a specified phase (delay) response of the electronic system that we devote an entire chapter to them, and we hope to consolidate much of the scattered information on this subject.
All-Pass Functions, Page 1 of 2
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