matrixing

Matrixing is an electronic operation that combines two or more input signals into a smaller number of output signals using linear mixing equations. Each output is a weighted sum of the inputs, with the weights (called matrix coefficients) determined by the application. The process is performed by analog circuits (resistor networks, operational amplifiers) or digital algorithms, and is reversible if the original coefficient values are known.

The classic consumer application is stereo matrix encoding. A four-channel quadraphonic signal (left front, right front, left rear, right rear) can be encoded into two stereo channels through matrixing, allowing quadraphonic content to be played on standard stereo equipment. The rear channels modulate the stereo signal with out-of-phase information that a decoder can extract. The Dolby Surround system used this principle to embed surround information into stereo without requiring additional wiring or channels.

Technical operation and variants

In analog matrixing, resistors set the gain of each input path, and summing amplifiers combine them. A simple stereo example might generate a center channel as (Left + Right) / 2 and a side channel as (Left - Right) / 2. In digital form, matrixing is a matrix multiplication: each output sample is computed as a dot product of input samples and fixed coefficients. The number of coefficients and their arrangement determine how much information is preserved and whether the transformation can be inverted.

Matrixing differs from simple mixing (which adds signals) because it applies specific phase and amplitude relationships to separate signal components or decorrelate channels. When matrixing fails, outputs become unintelligible or lose spatial information. Incorrect coefficients in a decoder can cause phase cancellation, where the reconstructed surround channels sound thin or collapse to mono. Temperature drift in analog resistor networks can also shift coefficients over time.

The term comes from the mathematical matrix, the rectangular array of numbers describing the linear transformation. Matrixing remains embedded in modern surround formats: Dolby Pro Logic and Pro Logic II use adaptive matrix decoding to extract surround and center information from stereo or 5.1 signals. Professional audio consoles include matrix outputs for generating monitor mixes from a master mix using fixed or variable coefficients.