Filter Design Toolbox

Prediction

Predicting signals may seem to be an impossible task, without some limiting assumptions. Assume that the signal is either steady or slowly varying over time, and periodic over time as well.

Figure 3-6: Predicting Future Values of a Periodic Signal

Accepting these assumptions, the adaptive filter must predict the future values of the desired signal based on past values. When s(k) is periodic and the filter is long enough to remember previous values, this structure with the delay in the input signal, can perform the prediction. You might use this structure to remove a periodic signal from stochastic noise signals.

Finally, notice that most systems of interest contain elements of more than one of the four adaptive filter structures. Carefully reviewing the real structure may be required to determine what the adaptive filter is adapting to. Also, for clarity in the figures, the analog-to-digital (A/D) and digital-to-analog (D/A) components do not appear. Since the adaptive filters are assumed to be digital in nature, and many of the problems produce analog data, converting the input signals to and from the analog domain is probably necessary.

Noise Cancellation (or Interference Cancellation)

Adaptive Filters in the Filter Design Toolbox