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 RLS Algorithm.

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.BlockLMSFilter`	Compute output, error, and weights using block least mean squares (LMS) adaptive algorithm
`dsp.LMSFilter`	Compute output, error, and weights of least mean squares (LMS) adaptive filter
`dsp.RLSFilter`	Compute output, error and coefficients using recursive least squares (RLS) algorithm
`dsp.AffineProjectionFilter`	Compute output, error and coefficients using affine projection (AP) Algorithm
`dsp.AdaptiveLatticeFilter`	Adaptive lattice filter
`dsp.FastTransversalFilter`	Fast transversal least-squares FIR adaptive filter
`dsp.FilteredXLMSFilter`	Filtered XLMS filter
`dsp.FrequencyDomainAdaptiveFilter`	Compute output, error, and coefficients using frequency-domain FIR adaptive filter

Blocks

Block LMS Filter	Compute output, error, and weights using LMS adaptive algorithm
Fast Block LMS Filter	Compute output, error, and weights using least mean squares (LMS) adaptive algorithm
Frequency-Domain Adaptive Filter	Compute output, error, and coefficients using frequency domain FIR adaptive filter
Kalman Filter	Predict or estimate states of dynamic systems
LMS Filter	Compute output, error, and weights using least mean squares (LMS) adaptive algorithm
LMS Update	Estimate weights of least mean squares (LMS) adaptive filter
RLS Filter	Compute 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 and NLMS Algorithms
Introduces adaptive filters through a signal enhancement application.
Noise Cancellation Using Sign-Data LMS Algorithm
Perform noise cancellation using sign-data LMS algorithm.
System Identification Using RLS Adaptive Filtering
This example shows how to use a recursive least-squares (RLS) filter to identify an unknown system modeled with a lowpass FIR filter.
Inverse System Identification Using RLS Algorithm
Perform inverse system identification using dsp.RLSFilter.
Compare RLS and LMS Adaptive Filter Algorithms
Comparison of RLS and LMS adaptive filter algorithms.
Adapt Multiple Filters Using LMS Update Block
Adapt multiple filters independently using the same LMS Update block. Use the Adapt port of the LMS Update block to selectively enable or disable the filters from being adapted.
Model Adaptive Linear Combiner using LMS Update Block
Use LMS Update block as an adaptive linear combiner.
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 that support variable-sized signals in DSP System Toolbox.

Related Information

Active Noise Control: From Modeling to Real-Time Prototyping

Featured Examples

Adaptive Line Enhancer (ALE)

Apply adaptive filters to signal separation using a structure called an adaptive line enhancer (ALE). In adaptive line enhancement, a measured signal x(n) contains two signals, an unknown signal of interest v(n), and a nearly-periodic noise signal eta(n).

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Adaptive Noise Cancellation Using RLS Adaptive Filtering

Use an RLS filter to extract useful information from a noisy signal. The information bearing signal is a sine wave that is corrupted by additive white Gaussian noise.

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Acoustic Noise Cancellation (LMS)

Use the least mean square (LMS) algorithm to subtract noise from an input signal. The example uses a preconfigured Simulink® model. The LMS Filter block in the dspanc model models an adaptive filter that uses the reference signal at its Input port and the desired signal at the Desired port to automatically match the filter response. The LMS Filter block subtracts the filtered noise from the original signal. As the filter converges, the resultant error signal contains only the original signal.

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Active Noise Control with Simulink Real-Time

Design a real-time active noise control system using a Speedgoat® Simulink® Real-Time™ target.

(Audio Toolbox)

Adaptive Filter Convergence

Compares the rate of convergence for adaptive filters using different LMS algorithms.

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Noise Canceler (RLS)

Subtract noise from an input signal using the Recursive Least Squares (RLS) algorithm. The RLS adaptive filter uses the reference signal on the Input port and the desired signal on the Desired port to automatically match the filter response in the Noise Filter block. As it converges to the correct filter, the filtered noise should be completely subtracted from the "Signal+Noise" signal, and the "Error Signal" should contain only the original signal.

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Time-Delay Channel Estimation Through Adaptive Filtering

Adaptively estimate the time delay for a noisy input signal using the LMS adaptive FIR algorithm.

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