latc2tf

R2026b

Convert lattice filter coefficients to transfer function form

Syntax

[b,a] = latc2tf(k,v)

[b,a] = latc2tf(k,iirOption)

b = latc2tf(k,firOption)

Description

[b,a] = latc2tf(k,v) returns the transfer function coefficients b and a corresponding to the IIR lattice-ladder filter specified by lattice coefficients k and ladder coefficients v.

[b,a] = latc2tf(k,iirOption) specifies the option to generate an all-pole IIR filter transfer function or an allpass IIR filter transfer function.

b = latc2tf(k,firOption) specifies the option to generate a minimum-phase FIR filter, a maximum-phase FIR filter, or a general FIR filter.

Examples

Generate Maximum-Phase FIR Filter from Lattice Coefficients

Convert lattice coefficients to transfer function form. Specify the filter option as "max" to generate a maximum-phase FIR filter.

k = [1/6 1/1.4];
b = latc2tf(k,"max")

b = 1×3

    0.7143    0.2857    1.0000

Confirm that the generated filter is maximum-phase.

ismaxphase(b)

ans = logical
   1

Input Arguments

k — Lattice coefficients

vector

Lattice coefficients, specified as a vector.

Data Types: single | double

v — Ladder coefficients

vector

Ladder coefficients, specified as a vector.

Data Types: single | double

iirOption — IIR filter option

"allpole" | "allpass"

IIR filter option, specified as one of these:

• "allpole" — Obtain an all-pole filter transfer function from the associated all-pole IIR lattice filter coefficients k.

• "allpass" — Obtain an allpass filter transfer function from the associated allpass IIR lattice filter coefficients k.

Data Types: char | string

firOption — FIR filter option

"min" | "max" | "FIR"

FIR filter option, specified as one of these:

• "min" — Obtain a minimum-phase FIR filter from the associated minimum-phase FIR lattice filter coefficients k.

• "max" — Obtain a maximum-phase FIR filter from the associated maximum-phase FIR lattice filter coefficients k.

• "FIR" — Obtain a general FIR filter from the associated lattice filter coefficients k. This option is equivalent to not specifying iirOption or firOption.

Data Types: char | string

Output Arguments

b, a — Transfer function coefficients

row vectors

Transfer function coefficients, returned as row vectors.

Depending on the filter implementation, latc2tf uses the rc2poly and rlevinson functions to convert k = [k₁ k₂ ⋯ k_n] and v = [v₁ v₂ ⋯ v_n+1] into transfer function coefficients, b = [b₀ b₁ ⋯ b_n] and a = [a₀ a₁ ⋯ a_n]. . The transfer function is expressed in terms of b and a 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, where a₀ = 1

References

[1] Proakis, John G., and Dimitris G. Manolakis. Digital Signal Processing: Principles, Algorithms, and Applications. 3rd Edition. Upper Saddle River, NJ: Prentice-Hall, 1996.

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

Extended Capabilities

Thread-Based Environment

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

The latc2tf 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 latc2tf in thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.