Speech characteristics and linear predictive coder

Characteristics of speech signal

• Bandwidth: most energy and intelligibility lie in about 300–3400 Hz (telephone band).
• Non-uniform amplitude distribution: small amplitudes are much more likely than large ones (Laplacian-like pdf), so non-uniform quantization helps.
• Short-term stationarity: speech is quasi-stationary over 10–30 ms, so it can be analysed in frames.
• Voiced and unvoiced sounds: voiced sounds (vowels) are quasi-periodic with a pitch of roughly 80–350 Hz; unvoiced sounds (s, f, sh) are noise-like.
• Formants: the vocal tract resonances give spectral peaks (formants) that carry most information.
• High correlation between adjacent samples and pitch periods, so speech is predictable.
• Silence: about 40–60% of a conversation is pauses, used by voice activity detection.
• Non-flat spectrum: energy falls at higher frequencies.

Linear predictive coder (LPC)

LPC is a vocoder that models the vocal tract as an all-pole digital filter and sends only the filter parameters plus the excitation type, instead of the waveform. Each sample is predicted as a linear combination of the previous p samples:

ŝ(n) = Σₖ₌₁ᵖ aₖ · s(n − k)

The coefficients aₖ are chosen to minimise the mean square prediction error e(n) = s(n) − ŝ(n) over a frame, by solving the normal (Yule–Walker) equations with the Levinson–Durbin algorithm.

 Encoder (transmitter)
 speech -> [A/D] -> [frame 20 ms] -+-> [LPC analysis:
                                   |    a1..ap, gain G]
                                   +-> [pitch / V-UV
                                        detector]
            -> quantize & multiplex -> bit stream

 Decoder (receiver)
  [pulse train @ pitch]--+
                         +-[V/UV switch]-(×G)-+
  [white noise gen.]-----+                    |
                                              v
             speech <- [D/A] <- [all-pole filter 1/A(z)]

Operation

1. Speech is sampled (8 kHz) and divided into frames of about 20 ms.
2. LPC analysis finds about 10 predictor coefficients (vocal-tract filter) and the gain G for each frame.
3. A pitch detector decides voiced/unvoiced and measures the pitch period.
4. Coefficients, gain, pitch and V/UV flag are quantized and transmitted; e.g. LPC-10 sends 54 bits per 22.5 ms frame = 2.4 kbps.
5. At the receiver, the excitation is a periodic pulse train (voiced) or white noise (unvoiced), scaled by G.
6. The excitation drives the all-pole synthesis filter H(z) = G / (1 − Σ aₖz⁻ᵏ) to rebuild speech.

Merits: very low bit rate (2.4–4.8 kbps). Drawback: synthetic, "robotic" quality. Improved versions (multi-pulse, RELP, CELP, RPE-LTP in GSM) send a better excitation signal.