Determine coefficients of Nth-order forward linear predictors
DSP System Toolbox / Estimation / Linear Prediction
The Autocorrelation LPC block determines the coefficients of an N-step forward linear predictor for the time-series in each length-M input channel, 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 for each channel as polynomial coefficients, reflection coefficients, or both. The block can also output the prediction error power for each channel.
Input 1 — Input array
unoriented vector | column vector | matrix
Specify the input u as an unoriented vector, column vector, or a matrix. Row vectors are not valid inputs. The block treats all M-by-N matrix inputs as N channels of length M.
A — Polynomial coefficients
column vector | matrix
Polynomial coefficients generated when you set the Output(s)
K. For each input channel, port A outputs an
(N+1)-by-1 column vector a =
containing the coefficients of an
average (MA) linear process that predicts the next value,
ûM+1, in the input
To enable port A, set Output(s) to
K — Reflection coefficients
column vector | matrix
Reflection coefficients generated when Output(s)
is set to
K. For each input channel, port K outputs a
length-N column vector whose elements are the
prediction error reflection coefficients.
To enable port K, set Output(s) to
P — Prediction error power
Prediction error power output at port P as a vector whose length is the number of input channels.
To enable port P, select the Output prediction error power (P) parameter.
Output(s) — Type of prediction coefficients
A and K (default) |
Specify the type of prediction coefficients output by the block. The block
can output polynomial coefficients (
K), or both (
When you set Output(s) to
A and K, the
block enables port A and K and each port outputs its respective set of
prediction coefficients for each channel.
Output prediction error power (P) — Output prediction error power
off (default) |
Select this parameter to enable the output port
which outputs the output prediction error power.
Inherit prediction order from input dimensions — Inherit prediction order from input dimensions
off (default) |
Select this parameter to inherit the prediction order N from the input dimensions.
Prediction order (N) — Prediction order
1 (default) | scalar
Specify the prediction order N. Note that N must be a scalar with a value less than the length of the input channels or the block produces an error.
This parameter appears only when you do not select the Inherit prediction order from input dimensions parameter.
The Autocorrelation LPC block computes the least squares solution to
where indicates the 2-norm and
Solving the least squares problem via the normal equations
leads to the system of equations
where r = [r1r2r3 ... rn+1]T is an autocorrelation estimate for u computed using the Autocorrelation block, and * indicates the complex conjugate transpose. The normal equations are solved in O(n2) operations by the Levinson-Durbin block.
Note that the solution to the LPC problem is very closely related to the Yule-Walker AR method of spectral estimation. In that context, the normal equations above are referred to as the Yule-Walker AR equations.
 Haykin, S. Adaptive Filter Theory. 3rd ed. Englewood Cliffs, NJ: Prentice Hall, 1996.
 Ljung, L. System Identification: Theory for the User. Englewood Cliffs, NJ: Prentice Hall, 1987. Pgs. 278-280.
 Proakis, J. and D. Manolakis. Digital Signal Processing. 3rd ed. Englewood Cliffs, NJ: Prentice-Hall, 1996.
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