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.