FIRWIN

The window method of FIR filter design involves multiplying an ideal impulse response by a window function to produce a practical finite impulse response filter.

This function computes the coefficients of a finite impulse response filter with linear phase. These filters are stable and have a predictable phase response.

Excel Usage

=FIRWIN(numtaps, cutoff, window, pass_zero, scale, fs)

numtaps (int, required): Length of the filter (number of coefficients).
cutoff (list[list], required): Cutoff frequency or frequencies (expressed in same units as fs).
window (str, optional, default: “hamming”): Desired window to use (e.g., ‘hamming’, ‘hann’, ‘blackman’).
pass_zero (bool, optional, default: true): If True, the gain at frequency 0 is 1.
scale (bool, optional, default: true): Set to True to scale the coefficients for unity gain.
fs (float, optional, default: null): The sampling frequency of the signal.

Returns (list[list]): Coefficients of the FIR filter as a 2D array.

Example 1: Simple low-pass

Inputs:

numtaps	cutoff
3	0.1

Excel formula:

=FIRWIN(3, 0.1)

Expected output:

Result
0.0679902	0.86402	0.0679902

Example 2: Band-pass

Inputs:

numtaps	cutoff		pass_zero
11	0.2	0.4	false

Excel formula:

=FIRWIN(11, {0.2,0.4}, FALSE)

Expected output:

Result
-3.70383e-18	-0.0406874	-0.128586	-0.0780689	0.208783	0.395894	0.208783	-0.0780689	-0.128586	-0.0406874	-3.70383e-18

Python Code

Show Code

import numpy as np
from scipy.signal import firwin as scipy_firwin

def firwin(numtaps, cutoff, window='hamming', pass_zero=True, scale=True, fs=None):
    """
    FIR filter design using the window method.

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

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

    Args:
        numtaps (int): Length of the filter (number of coefficients).
        cutoff (list[list]): Cutoff frequency or frequencies (expressed in same units as fs).
        window (str, optional): Desired window to use (e.g., 'hamming', 'hann', 'blackman'). Default is 'hamming'.
        pass_zero (bool, optional): If True, the gain at frequency 0 is 1. Default is True.
        scale (bool, optional): Set to True to scale the coefficients for unity gain. Default is True.
        fs (float, optional): The sampling frequency of the signal. Default is None.

    Returns:
        list[list]: Coefficients of the FIR filter as a 2D array.
    """
    try:
        if isinstance(cutoff, list):
            cutoff_flat = [float(v) for row in cutoff for v in row]
            cutoff_val = cutoff_flat[0] if len(cutoff_flat) == 1 else cutoff_flat
        else:
            cutoff_val = float(cutoff)

        result = scipy_firwin(
            int(numtaps), 
            cutoff_val, 
            window=window, 
            pass_zero=bool(pass_zero), 
            scale=bool(scale), 
            fs=float(fs) if fs is not None else None
        )

        # Return as a 2D list (single row)
        return [result.tolist()]
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

numtaps *

Length of the filter (number of coefficients).

cutoff *

Cutoff frequency or frequencies (expressed in same units as fs).

window

Desired window to use (e.g., 'hamming', 'hann', 'blackman').

pass_zero

If True, the gain at frequency 0 is 1.

scale

Set to True to scale the coefficients for unity gain.

The sampling frequency of the signal.