![Linear Predictive Coding (LPC) LPC
• Introduced in the 1960s • coefficients (‘a’s) correspond to those of a vocal
• nth signal sample is represented as a linear tract filter and the error signal (‘e’) corresponds to
combination of the previous p samples, plus a a source signal
residual representing the prediction error: • Source signal will approximate either a voiced
signal (which looks like a series of impulses) or a
x(n) = a1x(n-1) + a2x(n-2) + … + apx(n-p) + e(n)
white noise source
• So, LPC involves “exciting” a source signal with a
• If the error (‘e’) is small enough, we can just
transmit the coefficients (‘a’s) vocal tract filter
Impulses and Filters LPC – Autocorrelation
• Minimise the error signal by choosing optimal
coefficients (‘a’s)
• Use the autocorrelation criteria (aka root mean
squared criterion):
for 1<=j<=p,
where R is the autocorrelation of x(n) defined as
R(i) = E[x(n)x(n-i)]
LPC – Solving the autocorrelation
LPC
formula
• In matrix form the equation can be written as • Used in:
R*a=r
– GSM (Groupe Speciale Mobile) (Residual
where the autocorrelation matrix R is a symmetric Toeplitz Pulse Excited-LPC) (13kbps)
matrix with elements ri,j = R(i - j), vector r is the
autocorrelation vector rj = R(j), and vector a is the – LD-CELP (Low-Delay Code Excited Linear
parameter vector of ai Prediction) (G.728) (16kbps)
• An algorithm by N. Levinson (proposed in 1947) and – CS-ACELP (Conjugate Structure-Algebraic
modified by J. Durbin (in 1959) recursively calculates the CELP) (G.729) (8kbps)
solution to the Toeplitz matrix.
• GSM coder uses an integer version of the Schur recursion – MP-MLQ (Multi Pulse – Maximum Likelihood
(1917) Quantisation) (G.723.1) (6.3kbps)…
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Z24 4 Speech Compression
- 1. Speech Compression Uncompressed audio data rates • Recommended Reading: J. Harrington and S. • Voice: 8000samples/sec, 8bits/sample, Cassidy, “Techniques in Speech Acoustics”, mono Kluwer, 1999 = 64000bits/sec (64kbps) • Contents • CD: 44100samples/sec, 16bits/sample, – Uncompressed audio data rates stereo – ADPCM – SB-ADPCM =1411200bits/sec (~1.5Mbps) – LPC ADPCM (Adaptive Differential PCM) ADPCM • Uses the statistical properties of human speech (=> not Measured Transmitted compatible with fax/modem signals) value value • Makes a prediction about the size of the next sample, based Adaptive on previous info quantiser - • Transmitter then sends only the difference between real value and predicted value Predictor • Receiver uses the same prediction algorithm, together with the differences to reconstruct the speech data • Enables the data rate to be reduced to 32kbps • Used on international telephone links • Specified in G.721, G.722, G.723, G.726, G.727 SB-APDCM (Sub-band ADPCM) SB-ADPCM • Given 64kbps: ADPCM could produce Upper sub-band ADPCM encoder better than toll voice quality (eg radio) Input 4-7KHz 16kbps MUX • Sub-bands are 0-4kHz (given 48kbps), 4- filters 7kHz (given 16kbps) Lower sub-band ADPCM encoder • Low band contains more audio energy, high 50Hz-4KHz 48kbps band contains intelligibility info. • Standardised in G.722 Analogue Digital signal signal in out 1
- 2. Linear Predictive Coding (LPC) LPC • Introduced in the 1960s • coefficients (‘a’s) correspond to those of a vocal • nth signal sample is represented as a linear tract filter and the error signal (‘e’) corresponds to combination of the previous p samples, plus a a source signal residual representing the prediction error: • Source signal will approximate either a voiced signal (which looks like a series of impulses) or a x(n) = a1x(n-1) + a2x(n-2) + … + apx(n-p) + e(n) white noise source • So, LPC involves “exciting” a source signal with a • If the error (‘e’) is small enough, we can just transmit the coefficients (‘a’s) vocal tract filter Impulses and Filters LPC – Autocorrelation • Minimise the error signal by choosing optimal coefficients (‘a’s) • Use the autocorrelation criteria (aka root mean squared criterion): for 1<=j<=p, where R is the autocorrelation of x(n) defined as R(i) = E[x(n)x(n-i)] LPC – Solving the autocorrelation LPC formula • In matrix form the equation can be written as • Used in: R*a=r – GSM (Groupe Speciale Mobile) (Residual where the autocorrelation matrix R is a symmetric Toeplitz Pulse Excited-LPC) (13kbps) matrix with elements ri,j = R(i - j), vector r is the autocorrelation vector rj = R(j), and vector a is the – LD-CELP (Low-Delay Code Excited Linear parameter vector of ai Prediction) (G.728) (16kbps) • An algorithm by N. Levinson (proposed in 1947) and – CS-ACELP (Conjugate Structure-Algebraic modified by J. Durbin (in 1959) recursively calculates the CELP) (G.729) (8kbps) solution to the Toeplitz matrix. • GSM coder uses an integer version of the Schur recursion – MP-MLQ (Multi Pulse – Maximum Likelihood (1917) Quantisation) (G.723.1) (6.3kbps)… 2