Contents

1 Intro

• Input: a sequence of 16-bit PCM samples.
• Output: a sequence of MPEG Audio frames (frame = header + code-stream) which can be streamed.
  audio   +-----------+       +--------------+         +----------+  
  channel | Time      |       | Quantization |         |          | MPEG audio  
  ---+--->| frequency |---+-->| and          |-------> | Framming |------->  
     |    | mapping   |   |   | coding       |         |          |  
     |    +-----------+   |   +--------------+         +----------+  
     |                    |           ^  
     |                    |           |  
     |                    |   +--------------+  
     |                    +-->| Phycho-      |  
     |                        | acustic      |  
     +----------------------->| model        |  
                              +--------------+

• The MPEG audio bitstream definition is normative. Most guidance about encoding is informative. Thus, two MPEG-compliant bitstreams that encode the same audio material at the same rate but on different encoders may sound very different. On the other hand, a given MPEG bitstream decoded on different decoders will result in essentially the same output.

2 Layer I

• 4:1 compression (384 kbps).
• CBR (Constant Bit-Rate).

2.1 Encoder

1. Split $s\left[n\right]$ into blocks of $12\times 32=384$ samples. For each block:
   1. Analyze the block using a 32-band equally-spaced (analysis) filter bank, producing $12$ coeffs/subband (the coeffs are downsampled (subsampled, decimated) by factor of $32$). $342$ time-domain samples are transformed into $32$ subbands with $12$ coeffs. Notice that in a subband, each coeff can be considered as a sample of such subband.
   2. Scale each block of $12$ coeffs to ensure that the entire range of the selected quantizer will be used. Output the *scalefactor*.
   3. Using the FFT, compute the ATH for the block (considering the masking effects).
   4. Let $R^{\ast }$ the bit-rate selected by the user. While the generated bit-rate $R\le R^{\ast }$:
      1. Decrement the quantization step ${\Delta }_b$ for each subband $b$, proportionally to the ATH in $b$. Compute $R$. The bit-rate is controlled be switching between quantizers with different number of bits.
   5. Output ${\left\{{\Delta }_b\right\}}_{b=1}^{32}$ and the quantization indexes.

2.2 Decoder

1. For each input frame:
   1. "Dequantize" the coeffs of each subband.
   2. Descale the coeffs to their original dynamic range.
   3. Apply the 32-band synthesis filters bank.

3 Loss information analysis

• Aliasing in the 32-band analysis filter bank.
     ^ Amplitude  
     |     _______     _______     ____....__     _______  
     |    /       \   /       \   /          \   /       \  
     |   /         \ /         \ /            \ /         \  
     |  / subband 0 X subband 1 X              X  sub. 31  \  
     +-/-----------/-\---------/-\-----....---/-\-----------\-> frequency

• Quantization.

4 Layer II

• Backward compatibile with MP1.
• 8:1 compression (174 kbps).
• CBR (Constant Bit-Rate).
• Increases block-size to $3\times 12\times 32=1152$ samples.

5 Layer III

• “Rescued” by Napster.
• Backward compatibile with MP1 and MP2.
• CBR and VBR (Variable Bit-Rate). In this last case, users usually select the average bit-rate.
• Typically, virtually lossless at 128 kbps for most human beings.
• Improved subband analysis by means of the MDCT (using 32 subbands, the low-frequency ones contains more than un bark, which generates a poor frequency resolution in the ATH computation).

5.1 Encoder

1. Split $s\left[n\right]$ into blocks of $36\times 32=1152$ samples. For each block:
   1. Performs FFT of the block to compute the ATH and windows sequence.
   2. Analyze the block using a 32-band equally-spaced (analysis) filter bank, producing $36$ coeffs/subband.
   3. For each subband:
      1. Analyze transients. If detected, use a sequece of start/short*3/stop windows. Otherwise, use a long window.
         
      2. Compute MDCT. This produces $36$ (long), $30$ (start/stop) or $12$ coeffs/subband (short). This step produces $18$ coeffs/subband (long), $15$ coeffs/subband (start/stop) and $6$ coeffs/subband (short).
      3. Apply scalefactors to optimize quantization.
   4. Distortion control loop: keep (as much as possible) the quantization error below the ATH.
      1. Rate control loop: Let $R^{\ast }$ the bit-rate selected by the user. While the generated bit-rate $R\le R^{\ast }$:
         1. Decrement the quantization step ${\Delta }_b$ for each subband $b$, proportionally to the ATH in $b$. Compute $R$ after encoding the quantizer indexes with (static) Huffman coding. As in previous layers, a quantizer is selected from a list of predefined logaritmic quantizers.

5.2

1. For each input frame:
   1. Decode the Huffman codes.
   2. “Dequantize” the coeffs of each subband.
   3. Descale the coeffs to their original dynamic range.
   4. Apply inverse MDCT.
   5. Apply the 32-band synthesis filters bank.

References