IIRDESIGN

The iirdesign function provides a high-level interface to design IIR filters by specifying the desired passband and stopband characteristics, rather than the filter order directly.

It constructs an analog or digital IIR filter of minimum order for a given basic type (Butterworth, Chebyshev I, Chebyshev II, or Elliptic).

Excel Usage

=IIRDESIGN(wp, ws, gpass, gstop, analog, ftype, filter_output_form, fs)
  • wp (list[list], required): Passband edge frequencies.
  • ws (list[list], required): Stopband edge frequencies.
  • gpass (float, required): The maximum loss in the passband (dB).
  • gstop (float, required): The minimum attenuation in the stopband (dB).
  • analog (bool, optional, default: false): When True, return an analog filter.
  • ftype (str, optional, default: “ellip”): The type of IIR filter.
  • filter_output_form (str, optional, default: “ba”): Type of output representation.
  • fs (float, optional, default: null): The sampling frequency of the digital system.

Returns (list[list]): Filter coefficients or representation as a 2D array.

Example 1: Low-pass (b, a)

Inputs:

wp ws gpass gstop
0.2 0.3 1 40

Excel formula:

=IIRDESIGN(0.2, 0.3, 1, 40)

Expected output:

Result
0.0196744 -0.017137 0.0332899 -0.017137 0.0196744
1 -3.03301 3.8118 -2.2911 0.555357
Example 2: Band-pass (SOS)

Inputs:

wp ws gpass gstop filter_output_form
0.2 0.4 0.1 0.5 1 60 sos

Excel formula:

=IIRDESIGN({0.2,0.4}, {0.1,0.5}, 1, 60, "sos")

Expected output:

Result
0.00366595 0 -0.00366595 1 -1.11784 0.808699
1 0.44536 1 1 -0.77776 0.846087
1 -1.86313 1 1 -1.43271 0.887093
1 -0.106599 1 1 -0.605994 0.9492
1 -1.76647 1 1 -1.59091 0.968224

Python Code

Show Code 
import numpy as np
from scipy.signal import iirdesign as scipy_iirdesign

def iirdesign(wp, ws, gpass, gstop, analog=False, ftype='ellip', filter_output_form='ba', fs=None):
    """
    Complete IIR digital and analog filter design from passband and stopband specs.

    See: https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.iirdesign.html

    This example function is provided as-is without any representation of accuracy.

    Args:
        wp (list[list]): Passband edge frequencies.
        ws (list[list]): Stopband edge frequencies.
        gpass (float): The maximum loss in the passband (dB).
        gstop (float): The minimum attenuation in the stopband (dB).
        analog (bool, optional): When True, return an analog filter. Default is False.
        ftype (str, optional): The type of IIR filter. Valid options: Butterworth, Chebyshev I, Chebyshev II, Cauer/Elliptic. Default is 'ellip'.
        filter_output_form (str, optional): Type of output representation. Valid options: Numerator/Denominator, Pole-Zero, Second-Order Sections. Default is 'ba'.
        fs (float, optional): The sampling frequency of the digital system. Default is None.

    Returns:
        list[list]: Filter coefficients or representation as a 2D array.
    """
    try:
        def to_val(v):
            if isinstance(v, list):
                flat = [float(x) for row in v for x in row]
                return flat[0] if len(flat) == 1 else flat
            return float(v)

        wp_val = to_val(wp)
        ws_val = to_val(ws)

        result = scipy_iirdesign(
            wp_val, 
            ws_val, 
            float(gpass), 
            float(gstop), 
            analog=bool(analog), 
            ftype=ftype, 
            output=filter_output_form, 
            fs=float(fs) if fs is not None else None
        )

        if filter_output_form == 'ba':
            b, a = result
            max_len = max(len(b), len(a))
            return [b.tolist() + [""] * (max_len - len(b)), a.tolist() + [""] * (max_len - len(a))]
        elif filter_output_form == 'zpk':
            z, p, k = result
            max_len = max(len(z), len(p), 1)
            return [z.tolist() + [""] * (max_len - len(z)), p.tolist() + [""] * (max_len - len(p)), [float(k)] + [""] * (max_len - 1)]
        else: # sos
            return result.tolist()
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Passband edge frequencies.
Stopband edge frequencies.
The maximum loss in the passband (dB).
The minimum attenuation in the stopband (dB).
When True, return an analog filter.
The type of IIR filter.
Type of output representation.
The sampling frequency of the digital system.