Waveform/voice coding and GSM codec

Waveform coding and voice (source) coding techniques

Waveform coders try to reproduce the time waveform of speech sample by sample. They work for any signal (speech, music, tones), are robust, but need higher bit rates (16–64 kbps).

• Time domain: PCM (64 kbps, μ/A-law companding), DPCM, ADPCM (32 kbps), delta modulation and CVSD.
• Frequency domain: sub-band coding and adaptive transform coding, which give more bits to the important bands.

Voice coders (vocoders / source coders) do not copy the waveform. They model speech production (excitation + vocal tract filter) and send only model parameters: spectral shape, pitch, voiced/unvoiced flag and gain. Bit rates are very low (1.2–4.8 kbps) but quality is synthetic.

• Types: channel, formant, cepstrum, voice-excited and linear predictive (LPC) vocoders.

Hybrid coders (multi-pulse LPC, RELP, CELP, RPE-LTP) combine both: LPC model plus a coded excitation chosen by analysis-by-synthesis, giving good quality at 4–16 kbps. These are used in cellular systems.

Characteristics of speech

• Band 300–3400 Hz; non-uniform amplitude pdf; strong sample correlation.
• Non-flat spectrum with formants; voiced (pitch 80–350 Hz) and unvoiced sounds.
• Quasi-stationary over 10–30 ms; about 40–60% silence.

GSM CODEC

GSM full-rate uses the RPE-LTP (Regular Pulse Excited – Long Term Prediction) coder at 13 kbps (260 bits per 20 ms frame).

 speech 8 kHz, 13-bit
   |
 [Pre-processing] (offset removal, pre-emphasis)
   |
 [STP: LPC analysis, 8 coefficients] --> LAR (36 bits)
   |
 [Short-term analysis filter] -> residual
   |
 [LTP: pitch lag & gain] --------------> (4 x 9 bits)
   |
 [RPE grid selection & coding] --------> (4 x 47 bits)
   |
 MUX: 36 + 36 + 188 = 260 bits / 20 ms = 13 kbps

The decoder reverses this: RPE decoding → LTP synthesis → short-term LPC synthesis filter → post-processing → speech.