Adaptive Filters

LMS, RLS, frequency domain filters, affine projection filter, adaptive lattice filter

DSP System Toolbox™ offers several variations of the LMS and RLS adaptive finite impulse response (FIR) filter algorithms. While these algorithms differ in detail, they share a common operational approach, which is to minimize the error difference between the adaptive filter output and the desired signal. The mean square error (MSE) is the most commonly used metric to quantify this error. Adaptive filters are widely used in multiple applications including acoustic noise cancellation, echo cancellation, beam forming, system identification, bio medical signal enhancement, equalization of communication channels, etc. For examples illustrating some of these applications, see System Identification of FIR Filter Using LMS Algorithm, Noise Cancellation Using Sign-Data LMS Algorithm, and Inverse System Identification Using dsp.RLSFilter.

When the inputs are colored, the affine projection adaptive filter algorithms offered by dsp.AffineProjectionFilter object significantly improve the convergence speed over the LMS variations. For increased computational cost, adaptive lattice filter algorithm offered by dsp.AdaptiveLatticeFilter object can provide a better convergence over the LMS and RLS counterparts. You can also implement an adaptive FIR filter in the frequency domain using the dsp.FrequencyDomainAdaptiveFilter object.

The convergence performance is determined by the trajectory of the actual MSE, determined by msesim, and how it converges with the predicted MSE, determined by msepred.

Objects

dsp.BlockLMSFilterCompute output, error, and weights using block LMS adaptive algorithm
dsp.LMSFilterCompute output, error, and weights of LMS adaptive filter
dsp.RLSFilterCompute output, error and coefficients using recursive least squares (RLS) algorithm
dsp.AffineProjectionFilterCompute output, error and coefficients using affine projection (AP) Algorithm
dsp.AdaptiveLatticeFilterAdaptive lattice filter
dsp.FastTransversalFilterFast transversal least-squares FIR adaptive filter
dsp.FilteredXLMSFilterFiltered XLMS filter
dsp.FrequencyDomainAdaptiveFilterCompute output, error, and coefficients using frequency-domain FIR adaptive filter
dsp.KalmanFilterEstimate system measurements and states using Kalman filter

Blocks

Block LMS FilterCompute output, error, and weights using LMS adaptive algorithm
Fast Block LMS FilterCompute output, error, and weights using LMS adaptive algorithm
Frequency-Domain Adaptive FilterCompute output, error, and coefficients using frequency domain FIR adaptive filter
Kalman FilterPredict or estimate states of dynamic systems
LMS FilterCompute output, error, and weights using LMS adaptive algorithm
LMS UpdateEstimate weights of LMS adaptive filter
RLS FilterCompute filtered output, filter error, and filter weights for given input and desired signal using RLS adaptive filter algorithm

Topics

Overview of Adaptive Filters and Applications

General discussion on how adaptive filters work, list of adaptive filter algorithms in DSP System Toolbox, convergence performance, and details on few common applications.

System Identification of FIR Filter Using LMS Algorithm

Identify an unknown system using LMS algorithm.

System Identification of FIR Filter Using Normalized LMS Algorithm

Identify an unknown system using normalized LMS algorithm.

Compare Convergence Performance between LMS Algorithm and Normalized LMS Algorithm

Compare the speed with which the adaptive filter algorithms converge.

Signal Enhancement Using LMS Algorithm and Normalized LMS Algorithm

Introduces adaptive filters through a signal enhancement application.

Noise Cancellation Using Sign-Data LMS Algorithm

Perform noise cancellation using sign-data LMS algorithm.

Compare RLS and LMS Adaptive Filter Algorithms

Comparison of RLS and LMS adaptive filter algorithms.

Inverse System Identification Using dsp.RLSFilter

Perform inverse system identification using dsp.RLSFilter.

Remove Low Frequency Noise in Simulink Using Normalized LMS Adaptive Filter

Design a normalized LMS adaptive filter and use it to remove low frequency noise in Simulink®.

Noise Cancellation in Simulink Using Normalized LMS Adaptive Filter

Remove colored noise generated from an acoustic environment, using a normalized LMS adaptive filter.

Variable-Size Signal Support DSP System Objects

List of System objects which support variable-sized signals in DSP System Toolbox.

Featured Examples