Filtering in the Time and Frequency Domains
This book stands as the most comprehensive treatment of filtering techniques, devices and concepts as well as pertinent mathematical relationships.
TABLE OF CONTENTS Filtering in the Time and Frequency Domains
Chapter 5: 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 ? can be adjusted for a specific phase response, it is understood that ? 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.
5.1 APPLICATIONS OF ALL-PASS FILTERS
5.1.1 Delay Equalization
The most common and oldest use of AP filters is to reduce delay distortion in a transmission channel. The group delay of a transmission channel, whose bandwidth is essentially dictated by a selective BP filter, should ideally be constant to ensure distortionless pulse propagation for radar, television, telegraph, and high-speed data communication systems. Unfortunately the passband delay associated with these filters (which are usually minimum phase) is nonconstant, and signal frequencies in the channel are delayed by different amounts of time. The resulting signal degradation is...
Copyright Herman J. Blinchikoff 2001 under license agreement with Books24x7
