tf2latc

R2026b

Convert transfer function filter coefficients to lattice filter form

Syntax

[k,v] = tf2latc(b,a)

[k,v] = tf2latc(b0,a)

k = tf2latc(1,a)

k = tf2latc(b)

k = tf2latc(b,phase)

Description

[k,v] = tf2latc(b,a) returns the lattice coefficients k and the ladder coefficients v for an IIR lattice-ladder filter, normalized by a(1). The function errors if one or more of the lattice coefficients are exactly equal to 1.

[k,v] = tf2latc(b0,a) returns the ladder coefficients where only the first element in v is nonzero. b0 is a scalar.

k = tf2latc(1,a) returns the lattice coefficients k for an IIR all-pole (autoregression) lattice filter.

k = tf2latc(b) returns the lattice coefficients k for an FIR (moving average) lattice filter, normalized by b(1).

k = tf2latc(b,phase) specifies the type of FIR (moving average) lattice filter as minimum-phase or maximum-phase.

Examples

Convert All-Pole IIR Filter to Lattice Coefficients

Convert an all-pole IIR filter to lattice coefficients.

a = [1 13/24 5/8 1/3];
k = tf2latc(1,a)

k = 3×1

    0.2500
    0.5000
    0.3333

Input Arguments

b, a — Transfer function coefficients

vectors

Transfer function coefficients, specified as vectors.

The transfer function is expressed in terms of b = [b₀ b₁ ⋯ b_n] and a = [a₀ a₁ ⋯ a_n] as one of these:

• H(z) = b₀ + b₁z^–1 + ⋯ + b_nz^–n for FIR filters

• $$H(z)=\frac{b_0+b_1{z}^{-1}+\cdots +b_n{z}^{-n}}{a_0+a_1{z}^{-1}+\cdots +a_n{z}^{-n}}$$ for IIR filters

Data Types: single | double

b0 — Transfer function numerator coefficient

scalar

Transfer function numerator coefficient, specified as a scalar.

The transfer function is expressed in terms of b₀ and a = [a₀ a₁ ⋯ a_n] is

$$H(z)=\frac{b_0}{a_1+a_2{z}^{-1}+\cdots +a_{n+1}{z}^{-n}}$$.

Data Types: single | double

phase — Type of FIR (moving average) filter

"max" | "min"

Type of FIR (moving average) filter, specified as one of these:

• "max" — Implement a maximum-phase filter from the associated transfer function coefficients b.

• "min" — Implement a minimum-phase filter from the associated transfer function coefficients b.

Data Types: char | string

Output Arguments

k, v — Lattice and ladder coefficients

column vectors

Lattice and ladder coefficients, returned as column vectors.

Depending on the filter implementation, tf2latc uses the poly2rc and rlevinson functions to convert the transfer function coefficients into lattice or lattice-ladder coefficients. The result comprises these vectors:

• k = [k₁; k₂; ⋯; k_n], which contains lattice coefficients

• v = [v₁; v₂; ⋯; v_n+1], which contains ladder coefficients

References

[1] Mitra, Sanjit K. Digital Signal Processing: A Computer-Based Approach. 2nd ed. New York: McGraw-Hill Higher Education, 2001.

[2] Hayes, Monson H. Statistical Digital Signal Processing and Modeling. New York: John Wiley & Sons, 1996.

Extended Capabilities

Thread-Based Environment

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

The tf2latc 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 tf2latc in thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.