Lattice phase equaliser

A lattice phase equaliser is an all-pass network designed to compensate for phase distortion while leaving a signal’s amplitude response substantially unchanged.

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All-pass filter: A filter with constant magnitude response and frequency-dependent phase or delay. The equaliser is built from all-pass sections to change phase without materially changing amplitude.
Phase distortion: A change in relative phase among frequency components that alters a signal’s waveform or timing. This is the distortion the lattice equaliser is intended to compensate.
Complex frequency: A frequency variable that combines oscillation rate with exponential growth or decay in system analysis. It provides the variable used to describe and design all-pass transfer functions.
Amplitude equalization: Adjustment of a system’s frequency-dependent gain to compensate for level variations. Unlike amplitude equalization, the lattice phase equaliser aims to preserve the magnitude response.
Lattice filter: A recursive digital or analog filter structured as cascaded two-port lattice sections. Its lattice architecture provides the section structure used to realize the equaliser.
Audio crossover: A circuit or filter network that divides an audio signal into frequency bands for separate loudspeaker drivers. Phase alignment between crossover bands can be improved without changing their intended level curves.
Transfer function: A mathematical representation of a system’s output-to-input relation, usually expressed in a transform domain. The equaliser’s magnitude and phase are both derived from its transfer function.
Minimum-phase system: A stable causal system whose inverse is also stable and causal, with the least phase lag for a given magnitude response. A lattice all-pass stage can add phase without changing magnitude, unlike minimum-phase magnitude shaping.
Group delay: The negative derivative of a system’s phase response with respect to angular frequency. Equalisation targets unwanted variation in this frequency-dependent delay.
Television transmission: The transmission of moving images and associated sound through broadcast or cable systems. Phase correction can reduce waveform distortion in transmission paths carrying wideband video signals.