Audio Coding

Audio codecs exploit the expected signal type.

• Speech
• Music
• Fax and modem signals

Speech codecs can perform poorly on music.

Sampling

The Nyquist condition requires a sampling frequency greater than twice the highest input frequency for ideal reconstruction of a band-limited signal.

$f_s > 2f_{\max}$

• $f_s$: sampling frequency
• $f_{\max}$: highest input frequency

Pulse Code Modulation

Pulse code modulation (PCM) samples and quantises the waveform directly.

G.711 telephony uses 8,000 samples per second with 8 bits per sample.

$8{,}000 \times 8 = 64{,}000\ \text{bps} = 64\ \text{kbps}$

• $\mu$-law
  Maps 14-bit samples to 8 bits. Used in North America and Japan.
• A-law
  Maps 13-bit samples to 8 bits. Used in Europe.

Differential PCM

Differential pulse code modulation (DPCM) encodes the difference between an actual sample and its predicted value.

$e_n = x_n - \hat{x}_n$

• $e_n$: prediction error
• $x_n$: actual sample
• $\hat{x}_n$: predicted sample

Encoder and decoder use the same predictor.

Adaptive DPCM (ADPCM) adapts prediction and quantisation to changing waveform characteristics.

G.721 uses 4-bit differences at 8,000 samples per second, producing 32 kbps.

Linear Predictive Coding

Linear predictive coding (LPC) models speech using an excitation source and a vocal-tract filter.

• Excitation source
  Periodic excitation for voiced speech or noise-like excitation for unvoiced speech.
• Vocal-tract filter
  Shapes the excitation through acoustic resonance.
• Formants
  Resonance peaks in the speech frequency spectrum.

Encoding analyses short speech segments of approximately 20 ms.

• Estimate linear-prediction coefficients describing the filter.
• Separate the filter contribution from the residual excitation.
• Determine whether excitation is voiced or unvoiced.
• Estimate pitch for voiced speech.

The decoder reconstructs speech by passing the reconstructed excitation through the synthesis filter.

Code-Excited Linear Prediction

Code-excited linear prediction (CELP) uses codebook entries to represent the excitation of a linear-prediction speech model.

The encoder sends references to a shared excitation codebook alongside filter parameters.

Examples:

• Speex