User`s guide

Autocorrelation LPC
5-31
5Autocorrelation LPC
Purpose Determine the coefficients of an Nth-order forward linear predictor.
Library Estimation / Linear Prediction
Description The Autocorrelation LPC block determines the coefficients of an N-step
forward linear predictor for the time-series in length-M input vector, u, by
minimizing the prediction error in the least-squares sense. A linear predictor
is an FIR filter that predicts the next value in a sequence from the present and
past inputs. This technique has applications in filter design, speech coding,
spectral analysis, and system identification.
The Autocorrelation LPC block can output the prediction error as polynomial
coefficients, reflection coefficients, or both. It can also output the prediction
error power. The length-M input, u, can be a scalar, 1-D vector, frame- or
sample-based column vector, or a sample-based row vector. Frame-based row
vectors are not valid inputs.
When
Inherit prediction order from input dimensions is selected, the
prediction order, N, is inherited from the input dimensions. Otherwise, the
Prediction order parameter sets the value of N.
When
Output(s) is set to A, port A is enabled. Port A outputs an (N+1)-by-1
column vector, a = [1 a
2
a
3
… a
N+1
]
T
, containing the coefficients of an
Nth-order moving average (MA) linear process that predicts the next value,
û
M+1
, in the input time-series.
When
Output(s) is set to K, port K is enabled. Port K outputs a length-N
column vector whose elements are the prediction error reflection coefficients.
When
Output(s) is set to A and K, both port A and K are enabled, and each port
outputs its respective column vector of prediction coefficients. The outputs at
both port
A and K are always 1-D vectors.
When
Output prediction error power (P) is selected, port P is enabled. The
prediction error power, a scalar, is output at port
P.
u
ˆ
M 1+
a
2
u
M
()– a
3
u
M 1–
()– L– a
N 1+
u
MN– 1+
()–=