Sub-band coding

Sub-band coding (SBC) is a frequency-domain speech coding method in which the speech band is split into several frequency sub-bands by a filter bank, and each sub-band is coded separately with a number of bits matched to its perceptual importance and energy.

Idea: speech energy and its importance to the ear are not uniform over 0–4 kHz. Low bands (with pitch and the first formants) get more bits; high bands get fewer. Quantization noise is also kept within each band, so it is masked by the speech in that band.

 TRANSMITTER
         +-[BPF1]-[↓D]-[ADPCM, n1 bits]-+
 s(n) ---+-[BPF2]-[↓D]-[ADPCM, n2 bits]-+-[MUX]-> channel
         +-[BPFk]-[↓D]-[ADPCM, nk bits]-+

 RECEIVER
            +-[decode1]-[↑D]-[BPF1]-+
 ch->[DEMUX]+-[decode2]-[↑D]-[BPF2]-+-(Σ)-> s^(n)
            +-[decodek]-[↑D]-[BPFk]-+
   (↓D: decimate, ↑D: interpolate)

Transmitter

1. Speech sampled at 8 kHz is passed through a bank of k band-pass filters (often quadrature mirror filters, QMF), e.g. 4–8 bands.
2. Each band output is decimated (down-sampled) to its Nyquist rate, so the total sample rate stays 8 kHz.
3. Each sub-band is encoded, usually with ADPCM, using a bit allocation nᵢ based on band energy and perception (e.g. 4–5 bits in low bands, 2 bits in high bands).
4. Coded bits of all bands are multiplexed and transmitted.

Receiver

1. The bit stream is demultiplexed into the sub-band streams.
2. Each stream is decoded, interpolated (up-sampled) and passed through the matching synthesis filter.
3. The band outputs are added to reconstruct the speech. QMF filters cancel the aliasing created by decimation.

Advantages: noise in each band is controlled separately; bits are allocated to what the ear hears; good quality at 16–32 kbps (ITU G.722 wideband audio uses two-band SBC with ADPCM at 64 kbps). Disadvantage: filter bank adds delay and complexity.