Matrix decoder

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Matrix decoder is an audio technology where a finite number of discrete audio channels (e.g., 2) are decoded into a larger number of channels on play back (e.g., 5). The channels are generally, but not always, arranged for transmission or recording by an encoder, and decoded for playback by a decoder.

The notation for matrix encoding consists of the number of discrete audio channels separated by a colon from the number of decoded channels. For example, two discrete channels decoded to four-channels would be notated:

2:4

Five discrete channels decoded to six channels would be notated:

5:6

Many matrix encoders take advantage of the Haas effect, as well as audio cues inherent in the source channels.

The various encoding matrixes are described below.

Encoding Matrix Left Front Right Front Left Back Right Back
Left Total 1.0 0.0 j0.7 k0.7
Right Total 0.0 1.0 k0.7 j0.7

j = +90^\circ phase-shift, k = -90^\circ phase-shift

Encoding Matrix Left Front Right Front Left Back Right Back
Left Total 0.92 0.38 j0.92 j0.38
Right Total 0.38 0.92 k0.38 k0.92

j = +90^\circ phase-shift, k = -90^\circ phase-shift

Encoding Matrix W (pressure signal) X (front-back information) Y (left-right information)
Left Total 0.470 + k0.171 0.093 + j0.255 +0.328
Right Total 0.470 + j0.171 0.093 + k0.255 -0.328

j = +90^\circ phase-shift, k = -90^\circ phase-shift

Encoding Matrix Left Right Center Surround
Left Total 1 0 \sqrt{2} j\sqrt{2}
Right Total 0 1 \sqrt{2} k\sqrt{2}

j = +90^\circ phase-shift, k = -90^\circ phase-shift

The encoding matix is the same as for Dolby Surround; only the Pro Logic decoder differs.

Encoding Matrix Left Right Center Surround
Left Total 1 0 \sqrt{\frac{1}{2}} j\sqrt{\frac{1}{2}}
Right Total 0 1 \sqrt{\frac{1}{2}} k\sqrt{\frac{1}{2}}

j = +90^\circ phase-shift, k = -90^\circ phase-shift

Encoding Matrix Left Right Center Rear Left Rear Right
Left Total 1 0 \sqrt{\frac{1}{2}} j\sqrt{\frac{2}{3}} j\sqrt{\frac{1}{3}}
Right Total 0 1 \sqrt{\frac{1}{2}} k\sqrt{\frac{1}{3}} k\sqrt{\frac{2}{3}}

j = +90^\circ phase-shift, k = -90^\circ phase-shift


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