Information Theory and Perceptual Audio Coding

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Information Theory and Perceptual Audio Coding

• SC500
• Danny Morris

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Introduction

• Need to compress audio data
• CD audio 1.41/1.52 Mbits/sec
• Lossless Compression not good enough
• Unpredictable
• Not many statistical redundancies
• Psychoacoustics can help
• Variable bit allocation for frequency bands
• Masking properties of the human ear
• Non coding of irrelevant information

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Audio Coding Overview
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Psychoacoustic Model

• Models the ears perceptual properties
• Absolute Hearing Threshold
• Critical Bands
• Noise and Tonal Maskers
• Global Hearing Threshold
• Allows to compress signals by getting rid of
  inaudible information

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Absolute Hearing Threshold
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Critical Bands

• The ear as a signal processing filter
• Transform frequency into position
• Bank of highly overlapping band pass filters
• Asymmetric and nonlinear
• Critical bands
• Due to physics of the cochlea

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Noise and Tonal Masking

• Noise making Tone
• Signal to Mask ratio -5db

• Tone masking Noise
• Signal to Mask ratio 21 - 28 db

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Masking Spreading Function
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Global Masking Threshold
Step 1 Identify Noise and Tonal maskers X
Tonal Masker O Noise Masker
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Global Masking Threshold
Step 2 Apply Tonal and Noise Spreading Functions
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Global Masking Threshold
Step 3 Determine Max of spreading functions and
absolute hearing threshold as Global threshold
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Time to Frequency Analysis

• Converts windowed time to frequency information
  
• Uses critically sampled perfect reconstruction
  filter banks
• Polyphase Quadrature Mirror Filters (PQMF)
• Modified Discrete Cosine Transform (MDCT)

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Bit Allocation

• Minimize the Error as well as the
• SMR SNR in each frequency band
• d(x-x)
• Leads to a bit allocation of

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Perceptual Entropy

• Evaluates the Rate Distortion function where Di
  for each frequency band is not above the global
  masking threshold
• Lower limit on the number of bits required to
  code an audio sample with out perceptual loss

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MPEG-1 layer 1,2,3

• Layer 1 , 2
• 512-tap polyphase quadrature mirror filter (PQMF)
• 32 frequency bands
• Linear Quantization, 12 sample block coding
• Layer 3
• 18 point Modified discrete cosine transform
  (MDCT) after PQMF
• 576 frequency bands
• Non uniform quantization , Huffman coding

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Conclusion

• PE tells us its possible to compress audio to 2.1
  bits per sample
• Audio coding minimizes the mutual information
  between the source and the quantized samples
• Constrained that the distortion cannot produce a
  signal to noise ratio smaller than the signal to
  mask ratio
• Compression is achieved with little to no
  perceptual loss of information