EBUR128.cpp

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/**********************************************************************
 
Audacity: A Digital Audio Editor
 
EBUR128.cpp
 
Max Maisel
 
***********************************************************************/
 
#include "EBUR128.h"
#include <cstring>
 
EBUR128::EBUR128(double rate, size_t channels)
   : mChannelCount{ channels }
   , mRate{ rate }
   , mBlockSize( ceil(0.4 * mRate) ) // 400 ms blocks
   , mBlockOverlap( ceil(0.1 * mRate) ) // 100 ms overlap
{
   mLoudnessHist.reinit(HIST_BIN_COUNT, false);
   mBlockRingBuffer.reinit(mBlockSize);
   mWeightingFilter.reinit(mChannelCount, false);
   for(size_t channel = 0; channel < mChannelCount; ++channel)
      mWeightingFilter[channel] = CalcWeightingFilter(mRate);
 
   memset(mLoudnessHist.get(), 0, HIST_BIN_COUNT*sizeof(long int));
   for(size_t channel = 0; channel < mChannelCount; ++channel)
   {
      mWeightingFilter[channel][0].Reset();
      mWeightingFilter[channel][1].Reset();
   }
}
 
// fs: sample rate
// returns array of two Biquads
//
// EBU R128 parameter sampling rate adaption after
// Mansbridge, Stuart, Saoirse Finn, and Joshua D. Reiss.
// "Implementation and Evaluation of Autonomous Multi-track Fader Control."
// Paper presented at the 132nd Audio Engineering Society Convention,
// Budapest, Hungary, 2012."
ArrayOf<Biquad> EBUR128::CalcWeightingFilter(double fs)
{
   ArrayOf<Biquad> pBiquad(size_t(2), true);
 
   //
   // HSF pre filter
   //
   double db =    3.999843853973347;
   double f0 = 1681.974450955533;
   double Q  =    0.7071752369554196;
   double K  = tan(M_PI * f0 / fs);
 
   double Vh = pow(10.0, db / 20.0);
   double Vb = pow(Vh, 0.4996667741545416);
 
   double a0 = 1.0 + K / Q + K * K;
 
   pBiquad[0].fNumerCoeffs[Biquad::B0] = (Vh + Vb * K / Q + K * K) / a0;
   pBiquad[0].fNumerCoeffs[Biquad::B1] =       2.0 * (K * K -  Vh) / a0;
   pBiquad[0].fNumerCoeffs[Biquad::B2] = (Vh - Vb * K / Q + K * K) / a0;
 
   pBiquad[0].fDenomCoeffs[Biquad::A1] =   2.0 * (K * K - 1.0) / a0;
   pBiquad[0].fDenomCoeffs[Biquad::A2] = (1.0 - K / Q + K * K) / a0;
 
   //
   // HPF weighting filter
   //
   f0 = 38.13547087602444;
   Q  =  0.5003270373238773;
   K  = tan(M_PI * f0 / fs);
 
   pBiquad[1].fNumerCoeffs[Biquad::B0] =  1.0;
   pBiquad[1].fNumerCoeffs[Biquad::B1] = -2.0;
   pBiquad[1].fNumerCoeffs[Biquad::B2] =  1.0;
 
   pBiquad[1].fDenomCoeffs[Biquad::A1] = 2.0 * (K * K - 1.0) / (1.0 + K / Q + K * K);
   pBiquad[1].fDenomCoeffs[Biquad::A2] = (1.0 - K / Q + K * K) / (1.0 + K / Q + K * K);
 
   return pBiquad;
}
 
void EBUR128::ProcessSampleFromChannel(float x_in, size_t channel) const
{
   double value;
   value = mWeightingFilter[channel][0].ProcessOne(x_in);
   value = mWeightingFilter[channel][1].ProcessOne(value);
   if(channel == 0)
      mBlockRingBuffer[mBlockRingPos] = value * value;
   else
   {
      // Add the power of additional channels to the power of first channel.
      // As a result, stereo tracks appear about 3 LUFS louder, as specified.
      mBlockRingBuffer[mBlockRingPos] += value * value;
   }
}
 
void EBUR128::NextSample()
{
   ++mBlockRingPos;
   ++mBlockRingSize;
 
   if(mBlockRingPos % mBlockOverlap == 0)
   {
      // A new full block of samples was submitted.
      if(mBlockRingSize >= mBlockSize)
         AddBlockToHistogram(mBlockSize);
   }
   // Close the ring.
   if(mBlockRingPos == mBlockSize)
      mBlockRingPos = 0;
   ++mSampleCount;
}
 
double EBUR128::IntegrativeLoudness()
{
   // EBU R128: z_i = mean square without root
 
   // Calculate Gamma_R from histogram.
   double sum_v;
   long int sum_c;
   HistogramSums(0, sum_v, sum_c);
 
   // Handle incomplete block if no non-zero block was found.
   if(sum_c == 0)
   {
      AddBlockToHistogram(mBlockRingSize);
      HistogramSums(0, sum_v, sum_c);
   }
 
   // Histogram values are simplified log(x^2) immediate values
   // without -0.691 + 10*(...) to safe computing power. This is
   // possible because they will cancel out anyway.
   // The -1 in the line below is the -10 LUFS from the EBU R128
   // specification without the scaling factor of 10.
   double Gamma_R = log10(sum_v/sum_c) - 1;
   size_t idx_R = round((Gamma_R - GAMMA_A) * double(HIST_BIN_COUNT) / -GAMMA_A - 1);
 
   // Apply Gamma_R threshold and calculate gated loudness (extent).
   HistogramSums(idx_R+1, sum_v, sum_c);
   if(sum_c == 0)
      // Silence was processed.
      return 0;
   // LUFS is defined as -0.691 dB + 10*log10(sum(channels))
   return 0.8529037031 * sum_v / sum_c;
}
 
void
EBUR128::HistogramSums(size_t start_idx, double& sum_v, long int& sum_c) const
{
    double val;
    sum_v = 0;
    sum_c = 0;
    for(size_t i = start_idx; i < HIST_BIN_COUNT; ++i)
    {
       val = -GAMMA_A / double(HIST_BIN_COUNT) * (i+1) + GAMMA_A;
       sum_v += pow(10, val) * mLoudnessHist[i];
       sum_c += mLoudnessHist[i];
    }
}
 
void EBUR128::AddBlockToHistogram(size_t validLen)
{
   // Reset mBlockRingSize to full state to avoid overflow.
   // The actual value of mBlockRingSize does not matter
   // since this is only used to detect if blocks are complete (>= mBlockSize).
   mBlockRingSize = mBlockSize;
 
   size_t idx;
   double blockVal = 0;
   for(size_t i = 0; i < validLen; ++i)
      blockVal += mBlockRingBuffer[i];
 
   // Histogram values are simplified log10() immediate values
   // without -0.691 + 10*(...) to safe computing power. This is
   // possible because these constant cancel out anyway during the
   // following processing steps.
   blockVal = log10(blockVal/double(validLen));
   // log(blockVal) is within ]-inf, 1]
   idx = round((blockVal - GAMMA_A) * double(HIST_BIN_COUNT) / -GAMMA_A - 1);
 
   // idx is within ]-inf, HIST_BIN_COUNT-1], discard indices below 0
   // as they are below the EBU R128 absolute threshold anyway.
   if(idx < HIST_BIN_COUNT)
      ++mLoudnessHist[idx];
}