Linear Prediction. Linear Prediction (Introduction) :. The object of linear prediction is to estimate the output sequence from a linear combination of input samples, past output samples or both : The factors a(i) and b(j) are called predictor coefficients.
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Linear Prediction
σ
1-A(z)
Pitch
Gain
s(n)
Speech
Signal
DT
Impulse
generator
G(z)
Glottal
Filter
Voiced
U(n)
Voiced
Volume
velocity
H(z)
Vocal tract
Filter
R(z)
LP
Filter
V
U
Uncorrelated
Noise
generator
Unvoiced
Gain
Pitch
Gain
estimate
DT
Impulse
generator
Voiced
s(n)
Speech
Signal
All-Pole
Filter
(AR)
V
U
White
Noise
generator
Unvoiced
H(z)
Convert this to equality by including an excitation term:
The prediction error:
Error transfer function:
We seek to minimize the mean squared error signal:
(*)
Terms of short-term covariance:
With this notation, we can write (*) as:
A set of P equations, P unknowns
The minimum mean-squared error can be expressed as:
w(m): a window zero outside 0≤m≤N-1
The mean squared error is:
And:
The resulting covariance matrix is symmetric, but not Toeplitz,
and can be solved efficiently by a set of techniques called
Cholesky decomposition
Preemphasis: typically a first-order FIR,
To spectrally flatten the signal
Most widely the following filter is used:
Frame Blocking:
N number of samples in the analysis frame
M number of samples shift between frames
P LPC analysis order
Q dimension of LPC derived cepstral vector
K number of frames over which cepstral time derivatives are computed
N
300 (45 msec)
240 (30 msec)
300 (30 msec)
M
100 (15 msec)
80 (10 msec)
100 (10 msec)
p
8
10
10
Q
12
12
12
K
3
3
3