Slight update to the UHJ coefficients
The extended precision of the encoder's 0.6512*X term was guesswork, with no real basis for it. Switch back to the original value until something better actually comes up. Also updates the decoder to account for the change in the encoder.
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Chris Robinson
parent
bd254c5426
commit
a73b64ce3c
@ -28,7 +28,7 @@ const PhaseShifterT<UhjFilterBase::sFilterDelay*2> PShift{};
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*
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* Left = (S + D)/2.0
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* Right = (S - D)/2.0
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* T = j(-0.1432*W + 0.6511746*X) - 0.7071068*Y
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* T = j(-0.1432*W + 0.6512*X) - 0.7071068*Y
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* Q = 0.9772*Z
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*
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* where j is a wide-band +90 degree phase shift. 3-channel UHJ excludes Q,
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@ -95,9 +95,9 @@ void UhjEncoder::encode(float *LeftOut, float *RightOut, const FloatBufferLine *
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* S = Left + Right
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* D = Left - Right
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*
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* W = 0.981530*S + 0.197484*j(0.828347*D + 0.767835*T)
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* X = 0.418504*S - j(0.828347*D + 0.767835*T)
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* Y = 0.795954*D - 0.676406*T + j(0.186626*S)
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* W = 0.981532*S + 0.197484*j(0.828331*D + 0.767820*T)
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* X = 0.418496*S - j(0.828331*D + 0.767820*T)
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* Y = 0.795968*D - 0.676392*T + j(0.186633*S)
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* Z = 1.023332*Q
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*
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* where j is a +90 degree phase shift. 3-channel UHJ excludes Q, while 2-
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@ -130,19 +130,19 @@ void UhjDecoder::decode(const al::span<BufferLine> samples, const size_t offset,
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float *RESTRICT xoutput{samples[1].data() + offset};
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float *RESTRICT youtput{samples[2].data() + offset};
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/* Precompute j(0.828347*D + 0.767835*T) and store in xoutput. */
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/* Precompute j(0.828331*D + 0.767820*T) and store in xoutput. */
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auto tmpiter = std::copy(mDTHistory.cbegin(), mDTHistory.cend(), mTemp.begin());
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std::transform(mD.cbegin(), mD.cbegin()+samplesToDo+sFilterDelay, mT.cbegin(), tmpiter,
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[](const float d, const float t) noexcept { return 0.828347f*d + 0.767835f*t; });
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[](const float d, const float t) noexcept { return 0.828331f*d + 0.767820f*t; });
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std::copy_n(mTemp.cbegin()+forwardSamples, mDTHistory.size(), mDTHistory.begin());
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PShift.process({xoutput, samplesToDo}, mTemp.data());
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/* W = 0.981530*S + 0.197484*j(0.828347*D + 0.767835*T) */
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/* W = 0.981532*S + 0.197484*j(0.828331*D + 0.767820*T) */
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for(size_t i{0};i < samplesToDo;++i)
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woutput[i] = 0.981530f*mS[i] + 0.197484f*xoutput[i];
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/* X = 0.418504*S - j(0.828347*D + 0.767835*T) */
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woutput[i] = 0.981532f*mS[i] + 0.197484f*xoutput[i];
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/* X = 0.418496*S - j(0.828331*D + 0.767820*T) */
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for(size_t i{0};i < samplesToDo;++i)
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xoutput[i] = 0.418504f*mS[i] - xoutput[i];
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xoutput[i] = 0.418496f*mS[i] - xoutput[i];
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/* Precompute j*S and store in youtput. */
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tmpiter = std::copy(mSHistory.cbegin(), mSHistory.cend(), mTemp.begin());
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@ -150,9 +150,9 @@ void UhjDecoder::decode(const al::span<BufferLine> samples, const size_t offset,
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std::copy_n(mTemp.cbegin()+forwardSamples, mSHistory.size(), mSHistory.begin());
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PShift.process({youtput, samplesToDo}, mTemp.data());
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/* Y = 0.795954*D - 0.676406*T + j(0.186626*S) */
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/* Y = 0.795968*D - 0.676392*T + j(0.186633*S) */
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for(size_t i{0};i < samplesToDo;++i)
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youtput[i] = 0.795954f*mD[i] - 0.676406f*mT[i] + 0.186626f*youtput[i];
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youtput[i] = 0.795968f*mD[i] - 0.676392f*mT[i] + 0.186633f*youtput[i];
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if(samples.size() > 3)
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{
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@ -141,9 +141,9 @@ const PhaseShifterT<UhjDecoder::sFilterDelay*2> PShift{};
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* S = Left + Right
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* D = Left - Right
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*
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* W = 0.981530*S + 0.197484*j(0.828347*D + 0.767835*T)
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* X = 0.418504*S - j(0.828347*D + 0.767835*T)
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* Y = 0.795954*D - 0.676406*T + j(0.186626*S)
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* W = 0.981532*S + 0.197484*j(0.828331*D + 0.767820*T)
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* X = 0.418496*S - j(0.828331*D + 0.767820*T)
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* Y = 0.795968*D - 0.676392*T + j(0.186633*S)
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* Z = 1.023332*Q
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*
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* where j is a +90 degree phase shift. 3-channel UHJ excludes Q, while 2-
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@ -162,49 +162,49 @@ const PhaseShifterT<UhjDecoder::sFilterDelay*2> PShift{};
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* Gerzon's original paper for deriving Sigma (S) or Delta (D) from the L and R
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* signals. As proof, taking Y for example:
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*
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* Y = 0.795954*D - 0.676406*T + j(0.186626*S)
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* Y = 0.795968*D - 0.676392*T + j(0.186633*S)
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*
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* * Plug in the encoding parameters, using ? as a placeholder for whether S
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* and D should receive an extra 0.5 factor
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* Y = 0.795954*(j(-0.3420201*W + 0.5098604*X) + 0.6554516*Y)*? -
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* 0.676406*(j(-0.1432*W + 0.6511746*X) - 0.7071068*Y) +
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* 0.186626*j(0.9396926*W + 0.1855740*X)*?
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* Y = 0.795968*(j(-0.3420201*W + 0.5098604*X) + 0.6554516*Y)*? -
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* 0.676392*(j(-0.1432*W + 0.6512*X) - 0.7071068*Y) +
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* 0.186633*j(0.9396926*W + 0.1855740*X)*?
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*
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* * Move common factors in
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* Y = (j(-0.3420201*0.795954*?*W + 0.5098604*0.795954*?*X) + 0.6554516*0.795954*?*Y) -
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* (j(-0.1432*0.676406*W + 0.6511746*0.676406*X) - 0.7071068*0.676406*Y) +
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* j(0.9396926*0.186626*?*W + 0.1855740*0.186626*?*X)
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* Y = (j(-0.3420201*0.795968*?*W + 0.5098604*0.795968*?*X) + 0.6554516*0.795968*?*Y) -
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* (j(-0.1432*0.676392*W + 0.6512*0.676392*X) - 0.7071068*0.676392*Y) +
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* j(0.9396926*0.186633*?*W + 0.1855740*0.186633*?*X)
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*
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* * Clean up extraneous groupings
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* Y = j(-0.3420201*0.795954*?*W + 0.5098604*0.795954*?*X) + 0.6554516*0.795954*?*Y -
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* j(-0.1432*0.676406*W + 0.6511746*0.676406*X) + 0.7071068*0.676406*Y +
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* j*(0.9396926*0.186626*?*W + 0.1855740*0.186626*?*X)
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* Y = j(-0.3420201*0.795968*?*W + 0.5098604*0.795968*?*X) + 0.6554516*0.795968*?*Y -
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* j(-0.1432*0.676392*W + 0.6512*0.676392*X) + 0.7071068*0.676392*Y +
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* j*(0.9396926*0.186633*?*W + 0.1855740*0.186633*?*X)
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*
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* * Move phase shifts together and combine them
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* Y = j(-0.3420201*0.795954*?*W + 0.5098604*0.795954*?*X - -0.1432*0.676406*W -
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* 0.6511746*0.676406*X + 0.9396926*0.186626*?*W + 0.1855740*0.186626*?*X) +
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* 0.6554516*0.795954*?*Y + 0.7071068*0.676406*Y
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* Y = j(-0.3420201*0.795968*?*W + 0.5098604*0.795968*?*X - -0.1432*0.676392*W -
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* 0.6512*0.676392*X + 0.9396926*0.186633*?*W + 0.1855740*0.186633*?*X) +
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* 0.6554516*0.795968*?*Y + 0.7071068*0.676392*Y
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*
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* * Reorder terms
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* Y = j(-0.3420201*0.795954*?*W + 0.1432*0.676406*W + 0.9396926*0.186626*?*W +
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* 0.5098604*0.795954*?*X + -0.6511746*0.676406*X + 0.1855740*0.186626*?*X) +
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* 0.7071068*0.676406*Y + 0.6554516*0.795954*?*Y
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* Y = j(-0.3420201*0.795968*?*W + 0.1432*0.676392*W + 0.9396926*0.186633*?*W +
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* 0.5098604*0.795968*?*X + -0.6512*0.676392*X + 0.1855740*0.186633*?*X) +
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* 0.7071068*0.676392*Y + 0.6554516*0.795968*?*Y
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*
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* * Move common factors out
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* Y = j((-0.3420201*0.795954*? + 0.1432*0.676406 + 0.9396926*0.186626*?)*W +
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* ( 0.5098604*0.795954*? + -0.6511746*0.676406 + 0.1855740*0.186626*?)*X) +
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* (0.7071068*0.676406 + 0.6554516*0.795954*?)*Y
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* Y = j((-0.3420201*0.795968*? + 0.1432*0.676392 + 0.9396926*0.186633*?)*W +
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* ( 0.5098604*0.795968*? + -0.6512*0.676392 + 0.1855740*0.186633*?)*X) +
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* (0.7071068*0.676392 + 0.6554516*0.795968*?)*Y
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*
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* * Result w/ 0.5 factor:
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* -0.3420201*0.795954*0.5 + 0.1432*0.676406 + 0.9396926*0.186626*0.5 = 0.04843*W
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* 0.5098604*0.795954*0.5 + -0.6511746*0.676406 + 0.1855740*0.186626*0.5 = -0.22023*X
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* 0.7071068*0.676406 + 0.6554516*0.795954*0.5 = 0.73915*Y
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* -> Y = j(0.04843*W + -0.22023*X) + 0.73915*Y
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* -0.3420201*0.795968*0.5 + 0.1432*0.676392 + 0.9396926*0.186633*0.5 = 0.04843*W
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* 0.5098604*0.795968*0.5 + -0.6512*0.676392 + 0.1855740*0.186633*0.5 = -0.22023*X
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* 0.7071068*0.676392 + 0.6554516*0.795968*0.5 = 0.73914*Y
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* -> Y = j(0.04843*W + -0.22023*X) + 0.73914*Y
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*
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* * Result w/o 0.5 factor:
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* -0.3420201*0.795954 + 0.1432*0.676406 + 0.9396926*0.186626 = 0.00000*W
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* 0.5098604*0.795954 + -0.6511746*0.676406 + 0.1855740*0.186626 = 0.00000*X
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* 0.7071068*0.676406 + 0.6554516*0.795954 = 1.00000*Y
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* -0.3420201*0.795968 + 0.1432*0.676392 + 0.9396926*0.186633 = 0.00000*W
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* 0.5098604*0.795968 + -0.6512*0.676392 + 0.1855740*0.186633 = 0.00000*X
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* 0.7071068*0.676392 + 0.6554516*0.795968 = 1.00000*Y
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* -> Y = j(0.00000*W + 0.00000*X) + 1.00000*Y
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*
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* Not halving produces a result matching the original input.
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@ -252,8 +252,8 @@ void UhjDecoder::decode(const float *RESTRICT InSamples, const size_t InChannels
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for(size_t i{0};i < SamplesToDo;++i)
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{
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/* W = 0.981530*S + 0.197484*j(0.828347*D + 0.767835*T) */
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woutput[i] = 0.981530f*mS[i] + 0.197484f*xoutput[i];
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/* W = 0.981532*S + 0.197484*j(0.828347*D + 0.767835*T) */
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woutput[i] = 0.981532f*mS[i] + 0.197484f*xoutput[i];
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/* X = 0.418504*S - j(0.828347*D + 0.767835*T) */
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xoutput[i] = 0.418504f*mS[i] - xoutput[i];
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}
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@ -266,8 +266,8 @@ void UhjDecoder::decode(const float *RESTRICT InSamples, const size_t InChannels
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for(size_t i{0};i < SamplesToDo;++i)
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{
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/* Y = 0.795954*D - 0.676406*T + j(0.186626*S) */
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youtput[i] = 0.795954f*mD[i] - 0.676406f*mT[i] + 0.186626f*youtput[i];
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/* Y = 0.795968*D - 0.676392*T + j(0.186633*S) */
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youtput[i] = 0.795968f*mD[i] - 0.676392f*mT[i] + 0.186633f*youtput[i];
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}
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if(OutSamples.size() > 3)
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@ -89,7 +89,7 @@ const PhaseShifterT<UhjEncoder::sFilterDelay*2> PShift{};
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*
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* Left = (S + D)/2.0
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* Right = (S - D)/2.0
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* T = j(-0.1432*W + 0.6511746*X) - 0.7071068*Y
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* T = j(-0.1432*W + 0.6512*X) - 0.7071068*Y
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* Q = 0.9772*Z
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*
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* where j is a wide-band +90 degree phase shift. T is excluded from 2-channel
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