RESAMPLE_POLY

Polyphase resampling changes a signal’s sampling rate by first inserting additional samples, then applying a low-pass FIR filter, and finally keeping every selected output sample. It is often preferred over FFT-based resampling for long signals or lengths with large prime factors.

For an upsampling factor u and downsampling factor d, the resulting sample-rate conversion ratio is:

\frac{f_{s,\text{out}}}{f_{s,\text{in}}} = \frac{u}{d}

The low-pass filter is designed so that spectral images created during upsampling are suppressed before downsampling. Boundary behavior is controlled with the selected padding mode.

Excel Usage

=RESAMPLE_POLY(x, up, down, window, poly_padtype, cval)
  • x (list[list], required): The data to be resampled.
  • up (int, required): The upsampling factor.
  • down (int, required): The downsampling factor.
  • window (str, optional, default: “kaiser”): Desired window to use for the FIR filter (defaults to Kaiser window with beta=5).
  • poly_padtype (str, optional, default: “constant”): The signal extension mode to use at boundaries.
  • cval (float, optional, default: 0): Value to use if padtype is ‘constant’.

Returns (list[list]): A 2D array of the resampled data.

Example 1: Upsample by 2

Inputs:

x up down
1 2 3 2 1

Excel formula:

=RESAMPLE_POLY({1,2,3}, 2, 1)

Expected output:

Result
1.00052 1.29462 2.00103 2.96514 3.00155 1.60706
Example 2: Downsample by 2

Inputs:

x up down
1 2 3 4 5 6 1 2

Excel formula:

=RESAMPLE_POLY({1,2,3,4,5,6}, 1, 2)

Expected output:

Result
1.06167 2.7954 5.46644
Example 3: Resample by a 3-to-2 polyphase ratio

Inputs:

x up down
0 1 0 -1 0 1 3 2

Excel formula:

=RESAMPLE_POLY({0,1,0,-1,0,1}, 3, 2)

Expected output:

Result
2.79341e-17 0.761991 0.925732 3.1772e-17 -0.876403 -0.876403 3.1772e-17 0.925732 0.761991
Example 4: Resample with line boundary extension

Inputs:

x up down poly_padtype
2 3 5 7 11 2 1 line

Excel formula:

=RESAMPLE_POLY({2,3,5,7,11}, 2, 1, "line")

Expected output:

Result
2.00103 2.44091 3.00155 3.98362 5.00259 5.81483 7.00362 8.92601 11.0057 12.392

Python Code

Show Code 
import numpy as np
from scipy.signal import resample_poly as scipy_resample_poly

def resample_poly(x, up, down, window='kaiser', poly_padtype='constant', cval=0):
    """
    Resample x along the matrix using polyphase filtering.

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

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

    Args:
        x (list[list]): The data to be resampled.
        up (int): The upsampling factor.
        down (int): The downsampling factor.
        window (str, optional): Desired window to use for the FIR filter (defaults to Kaiser window with beta=5). Default is 'kaiser'.
        poly_padtype (str, optional): The signal extension mode to use at boundaries. Valid options: Constant, Line, Mean, Median, Maximum, Minimum. Default is 'constant'.
        cval (float, optional): Value to use if padtype is 'constant'. Default is 0.

    Returns:
        list[list]: A 2D array of the resampled data.
    """
    try:
        def to_1d(v):
            if isinstance(v, list):
                return np.array([float(x) for row in v for x in row])
            return np.array([float(v)])

        x_arr = to_1d(x)

        # Preserve SciPy's default Kaiser tuple when users leave the window as the wrapper default.
        win = window
        if win == "kaiser":
            win = ("kaiser", 5.0)

        kwargs = {
            "window": win,
            "padtype": poly_padtype,
        }
        if poly_padtype == "constant":
            kwargs["cval"] = float(cval)

        result = scipy_resample_poly(x_arr, int(up), int(down), **kwargs)

        return [result.tolist()]
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

The data to be resampled.
The upsampling factor.
The downsampling factor.
Desired window to use for the FIR filter (defaults to Kaiser window with beta=5).
The signal extension mode to use at boundaries.
Value to use if padtype is 'constant'.