One-Liner IIR Filters (1st order)

Type : IIR 1-pole
References : Posted by chris at ariescode dot com
Notes :
Here is a collection of one liner IIR filters.
Each filter has been transformed into a single C++ expression.

The filter parameter is f or g, and the state variable that needs to be kept around between interations is s.

- Christian
Code :
    101 Leaky Integrator

        a0 = 1
        b1 = 1 - f

        out = s += in - f * s;


    102 Basic Lowpass (all-pole)

        A first order lowpass filter, by finite difference appoximation (differentials --> differences).

        a0 = f
    b1 = 1 - f

        out = s += f * ( in - s );


    103 Lowpass with inverted control

    Same as above, except for different filter parameter is now inverted.
        In this case, g equals the location of the pole.

        a0 = g - 1
    b1 = g

        out = s = in + g * ( s - in );


    104 Lowpass with zero at Nyquist

        A first order lowpass filter, by via the conformal map of the z-plane (0..infinity --> 0..Nyquist).

        a0 = f
        a1 = f
        b1 = 1 - 2 * f

    s = temp + ( out = s + ( temp = f * ( in - s ) ) );


    105 Basic Highpass (DC-blocker)

        Input complement to basic lowpass, yields a finite difference highpass filter.

        a0 = 1 - f
        a1 = f - 1
        b1 = 1 - f

        out = in - ( s += f * ( in - s ) );


    106 Highpass with forced unity gain at Nyquist

        Input complement to filter 104, yields a conformal map highpass filter.

        a0 = 1 - f
        a1 = f - 1
        b1 = 1 - 2 * f

        out = in + temp - ( s += 2 * ( temp = f * ( in - s ) ) );


    107 Basic Allpass

        This corresponds to a first order allpass filter,
        where g is the location of the pole in the range -1..1.

        a0 = -g
        a1 = 1
        b1 = g

    s = in + g * ( out = s - g * in );





Comments
from : tomfbrady1[AT]gmail[DOT]com
comment : Great help, although could you advise as to where the parameters a0, a1 and b1 are used for the high pass filter 105? Thanks