Discrete Systems—Moving Average Systems
The digital filters have the decisive advantage of being easy to implement in a signal processing chain, easily modifiable, and able to vary over time to adapt to the evolutions of the signals to be processed (adaptive filtering, Kalman filtering). We show that the function z n is an eigenfunction of a time-invariant digital system. The impulse response, the transfer function and the frequency response are defined. The z-plane plays the role played by the Laplace plane for analog systems. A discrete convolution of the input signal by the impulse response provides the output signal. We study some examples of moving average filters and show how we can interpret geometrically the variation of the system’s frequency response. The advantages of the Moving Average Filters are that they have a finite impulse response length. A disadvantage of MA filters is that they are not very selective.