latcfilt

Lattice and lattice-ladder filter implementation

Syntax

[f,g] = latcfilt(k,x)

[f,g] = latcfilt(k,v,x)

[f,g] = latcfilt(k,1,x)

[f,g,zf] = latcfilt(___,"ic",zi)

[f,g,zf] = latcfilt(___,dim)

Description

[f,g] = latcfilt(k,x) filters input signal x with the FIR lattice coefficients specified by k and returns the forward lattice filter result f and backward filter result g.

[f,g] = latcfilt(k,v,x) filters input signal x with the IIR lattice coefficients specified by k and ladder coefficients specified by v. Both k and v must be vectors, while x can be a matrix.

[f,g] = latcfilt(k,1,x) filters input signal x with the IIR lattice coefficients specified by k and returns the all-pole lattice filter result f and the allpass filter result g.

[f,g,zf] = latcfilt(___,"ic",zi) specifies the initial conditions of the lattice states zi and returns the final conditions of the lattice states zf.

[f,g,zf] = latcfilt(___,dim) filters x along the dimension dim.

Examples

FIR Lattice Filter

Generate a signal with 512 samples of white Gaussian noise.

x = randn(512,1);

Filter the data with an FIR lattice filter. Specify the reflection coefficients so that the lattice filter is equivalent to a 3rd-order moving average filter.

[f,g] = latcfilt([1/2 1],x);

Plot the maximum- and minimum-phase outputs of the lattice filter in separate plots

subplot(2,1,1)
plot(f)
title('Maximum-Phase Output')

subplot(2,1,2)
plot(g)
title('Minimum-Phase Output')

Input Arguments

k — Lattice coefficients

vector | matrix

Lattice coefficients, specified as a vector or matrix. If $$\left|k\right|\le 1$$, f corresponds to the minimum-phase output, and g corresponds to the maximum-phase output.

When filtering data, lattice coefficients can be used to represent

• FIR filters

• All-pole IIR filters

• Allpass IIR filters

• General IIR filters

Data Types: double

x — Input signal

vector | matrix

Input signal, specified as a vector or matrix.

Data Types: double

v — Ladder coefficients

vector

Ladder coefficients, specified as a vector.

Data Types: double

zi — Initial conditions

vector | matrix

Initial conditions of the lattice states, specified as a vector or matrix. If zi is a vector, then it must have the same length as k. If zi is a matrix, then each column must have a length equal to the length of k.

Data Types: double

dim — Dimension

positive integer scalar

Dimension along which to operate, specified as a positive integer scalar. To specify a dim value, the FIR lattice coefficients k must be a vector and you must specify all previous input parameters in order. Use the empty vector [ ] for any parameters you do not want to specify.

Data Types: double

Output Arguments

f — Forward lattice filter

vector | matrix

Forward lattice filter, returned as a vector or matrix.

If k and x are vectors, f is a vector. Matrix arguments are permitted under these rules:

• If x is a matrix and k is a vector, the function processes each column of x through the lattice filter specified by k.

• If x is a vector and k is a matrix, the function uses each column of k to filter x and returns a matrix.

• If x and k are both matrices with the same number of columns, then the function uses the ith column of k to filter the ith column of x and returns a matrix.

g — Backward lattice filter

vector | matrix

Backward lattice filter, returned as a vector or matrix.

zf — Final conditions

vector | matrix

Final conditions of the lattice states, returned as a vector or matrix. If zf is a vector, then it has the same length as k. If zf is a matrix, then each column has a length equal to the length of k. zf returns the final conditions in columns, regardless of the shape of x.

Version History

Introduced before R2006a