latcfilt

R2026b

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,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,dim) specifies the initial lattice-state conditions zi and the dimension dim along which to process x for any of the previous syntaxes. Use zf to return the final lattice-state conditions.

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

tiledlayout("flow")
nexttile
plot(f)
title('Maximum-Phase Output')
nexttile
plot(g)
title('Minimum-Phase Output')

Input Arguments

k — Lattice coefficients

vector | matrix

Lattice coefficients, specified as a vector or matrix.

• If you do not specify v, you can specify k as a matrix with the same number of columns as x. In this case, the function filters the ith column of x using a lattice filter whose coefficients come from the ith column of k.

• If $$\left|k\right|\le 1$$, then 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: single | double
Complex Number Support: Yes

x — Input signal

vector | matrix | N-D array

Input signal, specified as one of these:

• Vector — Single-channel input signal.

• Matrix — Multichannel input signal with as many channels as columns in x.

• N-D array — Multidimensional array. In this case, also specify k as a vector and specify dim.

Data Types: single | double
Complex Number Support: Yes

v — Ladder coefficients

[] | vector

Ladder coefficients, specified as a vector.

The length of v must be less than or equal to length(k)+1. If v has fewer than length(k)+1elements, then latcfilt pads v with zeros to until it reaches that length.

Data Types: single | double
Complex Number Support: Yes

zi — Initial conditions of lattice states

scalar | vector | matrix

Initial conditions of the lattice states, specified as one of these:

• Scalar — The function sets the initial condition of each lattice state to zi.

• Vector — zi must have the same length as k. This length represents the filter order or the number of lattice stages.

• Matrix — Each column of zi must have the same length as k. The number of columns of zi must be equal to max(width(k),numel(x)/height(x)).

Data Types: single | double
Complex Number Support: Yes

dim — Dimension to operate along

positive integer scalar

Dimension along which to operate, specified as a positive integer scalar.

• By default, the function operates along the first array dimension of x with size greater than 1.

• To specify dim, the FIR lattice coefficients k must be a vector and you must specify all previous input arguments in order. To skip input arguments, use the empty vector [].

Data Types: double

Output Arguments

f — Forward lattice filter

vector | matrix | N-D array

Forward lattice filter, returned as a vector, matrix, or N-D array.

If k and x are vectors, f is a vector of the same size as x. 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 | N-D array

Backward lattice filter, returned as a vector, matrix, or N-D array of the same size as f.

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.

More About

Lattice and Lattice-Ladder Filters

The lattice and lattice-ladder filters are modular structures interconnected in sections that enable a filter implementation based on reflection coefficients instead of transfer-function polynomial coefficients. Compared to direct-form structures, lattice and lattice-ladder filters offer better quantization robustness in high-order polynomials, enable adjusting the filter order by adding or removing sections, and are more suitable for fixed-point implementations and adaptive filtering.

Assume a filter with n sections. The filter has an input signal x and the output signals f and g. You can implement lattice and lattice-ladder filters in these ways:

• Lattice structure for FIR filters with lattice coefficients k = [k ₁ k ₂ ⋯ k _n ]. The lattice structure implements a moving average (MA) filter, where the outputs depend on past inputs. The output f corresponds to the forward lattice filter, and the output g corresponds to the backward lattice filter.

• Lattice structure for all-pole and allpass IIR filters with lattice coefficients k = [k ₁ k ₂ ⋯ k _n ]. The lattice structure implements an autoregressive (AR) filter, where the outputs depend on past outputs. The output f corresponds to the all-pole lattice filter, while the output g corresponds to the allpass lattice filter.

• Lattice-ladder structure for pole-zero IIR Filters with lattice coefficients k = [k ₁ k ₂ ⋯ k _n ] and ladder coefficients v = [v ₁ v ₂ ⋯ v _n+1 ]. The lattice portion accounts for the poles and implements an AR filter, while the ladder portion accounts for the zeros and implement an MA filter. Together, the lattice-ladder structure implement a generalized (ARMA) IIR filter. The output f corresponds to the forward lattice-ladder filter, while the output g corresponds to the backwards lattice-ladder filter.

Algorithms

Assume a filter with reflection coefficients k = [k₁ k₂ ⋯ k_n] and v = [v₁ v₂ ⋯ v_n+1]. Depending on the filter impulse response, the latcfilt function uses the lattice or lattice-ladder structure to implement the filter. To learn more about these structures, see Lattice and Lattice-Ladder Filters.

The filter has n initial states, which are located at the inputs of each z^-1 delay block in the filter implementation diagram.

• When you specify zi as a scalar, latcfilt initializes the filter states by setting ζ₁ = ζ₂ = ⋯ =ζ_n = zi.

• When you specify zi as a vector, latcfilt initializes the filter states by setting ζ_r = zi(r) for r = 1, 2, …, n.

• When you specify zi as a matrix, then the state initialization repeats for each column of x.

For each sample of x across the first array dimension whose size is greater than 1 or across the dimension dim, the latcfilt function computes f and g from the lattice or lattice-ladder structure, updates the filter states, and repeats this operation until it finishes filtering the last sample of x.

The filter has n final states, which are located at the outputs of each z^-1 delay block in the filter implementation diagram.

• When you specify to return zf, latcfilt gathers the states computed during the filtering of the last sample of x, and stores these final states in zf as zf(r) = ζ_r, for r = 1, 2, …, n.

• The filtering operation repeats for each column of x and latcfilt returns the final states in a new column of zf.

Extended Capabilities

Thread-Based Environment

Run code in the background using MATLAB® backgroundPool or accelerate code with Parallel Computing Toolbox™ ThreadPool.

The latcfilt function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.

Version History

Introduced before R2006a

R2026b: Use thread-based environments

You can use latcfilt in thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.