non-recursive filters

Finite Impulse Response

FIR

Infinite Impulse Response

IIR

system operating on discrete-time signals. As we saw in chapter 1, such a system

is completely described by its impulse response or by its (rational) transfer

function. Even though the adjective digital refers to the fact that parameters

and signals are quantized, we will not be too concerned about the effects of

quantization, that have been briefly introduced in sec. 1.6. In this chapter, we

will face the problem of designing impulse responses or transfer functions that

satisfy some specifications in the time or frequency domain.

function have the denominator. Since the filters of the first family admit a

realization where the output is a linear combination of a finite number of input

samples, they are sometimes called non-recursive filters

number of non-null samples, thus calling them Finite Impulse Response (FIR)

filters. On the other hand, the filters of the second family admit only recursive

realizations, thus meaning that the output signal is always computed by using

previous samples of itself. The impulse response of these filters is infinitely long,

thus justifying their name as Infinite Impulse Response (IIR) filters.

samples of the input signal. In our examples we will treat causal filters, therefore

we will not process input samples coming later than the time instant of the

output sample that we are producing.