Infinite Impulse Response Filters

Infinite impulse response filters (IIR) are digital filters with impulse responses that can theoretically be infinite in length (duration). The general difference equation characterizing IIR filters is

,(1)

where Nb is the number of forward coefficients (bj) and Na is the number of reverse coefficients (ak).

In most IIR filter designs (and in all of the LabVIEW IIR filters), coefficient a0 is 1. The output sample at the present sample index i is the sum of scaled present and past inputs (xi and xi – j when 0) and scaled past outputs (yi – k). Because of this, IIR filters are also known as recursive filters or autoregressive moving-average (ARMA) filters.

The response of the general IIR filter to an impulse (x0 = 1 and xi = 0 for all i 0) is called the impulse response of the filter. The impulse response of the filter described by Equation (1) is indeed of infinite length for nonzero coefficients. In practical filter applications, however, the impulse response of stable IIR filters decays to near zero in a finite number of samples.

IIR filters in LabVIEW contain the following properties:

You can eliminate this transient response on successive calls by enabling state memory. To enable state memory, set the init/cont control of the VI to TRUE (continuous filtering).

The number of elements in the filtered sequence equals the number of elements in the input sequence.

The filter retains the internal filter state values when the filtering completes.

The advantage of digital IIR filters over finite impulse response (FIR) filters is that IIR filters usually require fewer coefficients to perform similar filtering operations. Thus, IIR filters execute much faster and do not require extra memory, because they execute in place.

The disadvantage of IIR filters is that the phase response is nonlinear. If the application does not require phase information, such as signal monitoring, IIR filters may be appropriate. You should use FIR filters for those applications requiring linear phase responses.