Filter Design Toolbox

Overview of Adaptive Filters and Applications

Adaptive filters self learn. As the signal into the filter continues, the adaptive filter coefficients adjust themselves to achieve the desired result, such as identifying an unknown filter or cancelling noise in the input signal. In Figure 3-1, the shaded box represents the adaptive filter, comprising the adaptive filter and the adaptive RLS algorithm. For the general adaptive algorithm block diagram, look at Figure 3-2.

Figure 3-1: Block Diagram That Defines the Inputs and Output of a Generic RLS Adaptive Filter

Figure 3-2: Block Diagram Defining General Adaptive Filter Algorithm Inputs and Outputs

An adaptive FIR or IIR filter designs itself based on the characteristics of the input signal to the filter and a signal which represent the desired behavior of the filter on its input. Designing the filter does not require any other frequency response information or specification. To define the self learning process the filter uses, you select the adaptive algorithm used to reduce the error between the output signal y(k) and the desired signal d(k). When the LMS performance criteria for e(k) has achieved its minimum value through the iterations of the adapting algorithm, the adaptive filter is finished and its coefficients have converged to a solution. Now the output from the adaptive filter matches closely the desired signal d(k). When you change the input data characteristics, sometimes called the filter environment, the filter adapts to the new environment by generating a new set of coefficients for the new data. Notice that when e(k) goes to zero and remains there you achieve perfect adaptation; the ideal result but not likely in the real world.

The adaptive filter functions in this toolbox implement the shaded portion of Figure 3-1, replacing the adaptive algorithm with an appropriate technique. Therefore, to use one of the functions you provide the input signal or signals and the initial values for the filter. A later section in this User's Guide, Adaptive Filters in the Filter Design Toolbox offers details about the algorithms available and the inputs required to use them in MATLAB.

Designing Adaptive Filters

Choosing an Adaptive Filter