Mid-Side recording decodes to stereo via matrix multiplication: L = M+S, R = M-S

Mid-Side (MS) recording uses two microphones: a central omnidirectional (M) and a perpendicular bidirectional (S). The bidirectional mic produces a positive signal from the left and an inverted signal from the right. Decoding to stereo is a simple 2×2 matrix: Left = M + S (constructive interference from the left) and Right = M − S (constructive interference from the right). A central source puts S near zero, so both channels reproduce M equally — phantom center. A source hard left gives a large positive S, boosting L and cancelling R. MS is the conceptual foundation of first-order Ambisonics: Ambisonics is simply MS recording extended into three dimensions, adding a Z (vertical) bidirectional axis alongside X and Y.

Examples

M=1, S=0 (centered source): L=1, R=1 → phantom center. M=1, S=0.7 (45° left source): L=1.7, R=0.3 → image pans left. Decode expression: [sig_M + sig_S, sig_M - sig_S].

Assessment

Given M=0.8 and S=−0.6 (right-of-center source), calculate L and R, then state where the phantom image appears. Also explain why the Z channel is zero in a horizontal-plane 2D stereo decoder.