iir1

Create and/or apply an IIR filter.

Usage 1

iir1(f1, f2 {, m, rp, rs, inv, type})

f1, f2: the lower and upper cutoff frequency; both values must be specified as relative frequencies (f / sampling-rate); 0 <= f1 < f2 <= 0.5

m: the filter order (default=5)
rp: the desired passband ripple in dB; 0 < rp (default=0.5)
rs: the desired stopband damping level in dB; 0 < rs (default=40)
inv: invert filter response (0=no, 1=yes); if this value is set to 1, the filter frequency response is inverted and f1/f2 are the boundaries of the stopband

type: the type of the filter

type=1

... Butterworth filter

type=2

... Chebyshev filter

type=3

... elliptic filter (this is the default)

Result: The function computes the filter coefficients for the IIR defined by the arguments and returns a matrix c with 2 columns. The first column (c[*,0]) contains the denominator coefficients (poles) and the second (c[*,1]) the nominator coefficients (zeros). The matrix c can be used to apply the filter to a signal (see Usage 3).

Usage 2

iir1(f1, f2, m, rp, rs, inv, type, x)

Result: The function computes the filter coefficients for the IIR defined by the arguments and applies it to the signal x. The result has the same type as the input signal x and containes the filtered signal.

Usage 3

iir1(c, z, x{, s})

c

IIR filter coefficients (see Usage 1)

z

the filter state (delay); must be a matrix with the same dimensions as c

notes:

The matrix should be initialized with zeros (e.g.: #z := eval init($#c[!nrow],$#c[!ncol],0))
The values of z are changed (z must be a reference to a table item

x

the signal sample (scalar) or the signal vector to be filtered

s

the downsampling factor; must be an integer in the range 0<s<ncol(x) (default=1)

note:

If s>1, only the filter output values y[0], y[s], y[2s], ... are stored in the result.
If s>1, nrow(x) should be a multiple of s.

Result: The filtered signal (sample or vector). The argument (reference) z is updated with the new filter state.

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