UPFIRDN

This function combines three multirate operations into one efficient polyphase routine: insert samples during upsampling, apply an FIR filter, and then retain samples according to the downsampling factor. It is a core building block for interpolation, decimation, and rational sample-rate conversion.

If the interpolation factor is u and the decimation factor is d, the output sampling rate satisfies:

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

Compared with explicitly inserting zeros, filtering, and decimating in separate passes, the polyphase implementation reduces redundant work and is therefore more efficient for many signal-processing pipelines.

Excel Usage

=UPFIRDN(h, x, up, down, upfirdn_mode, cval)
  • h (list[list], required): 1-D FIR filter coefficients (Excel range).
  • x (list[list], required): Input signal array.
  • up (int, optional, default: 1): Upsampling rate.
  • down (int, optional, default: 1): Downsampling rate.
  • upfirdn_mode (str, optional, default: “constant”): The signal extension mode to use.
  • cval (float, optional, default: 0): The constant value to use when mode is ‘constant’.

Returns (list[list]): A 2D array of the output signal.

Example 1: Simple FIR filter

Inputs:

h x
1 1 1 1 1 1

Excel formula:

=UPFIRDN({1,1,1}, {1,1,1})

Expected output:

Result
1 2 3 2 1
Example 2: Upsample with zeros

Inputs:

h x up
1 1 2 3 3

Excel formula:

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

Expected output:

Result
1 0 0 2 0 0 3
Example 3: FIR filter with decimation by 3

Inputs:

h x down
1 0 1 2 3 4 5 6 7 8 9 3

Excel formula:

=UPFIRDN({1}, {0,1,2,3,4,5,6,7,8,9}, 3)

Expected output:

Result
0 3 6 9
Example 4: Linear boundary extension during interpolation

Inputs:

h x up upfirdn_mode
0.5 1 0.5 1 2 3 2 line

Excel formula:

=UPFIRDN({0.5,1,0.5}, {1,2,3}, 2, "line")

Expected output:

Result
0.5 1 1.5 2 2.5 3 3.5

Python Code

Show Code 
import numpy as np
from scipy.signal import upfirdn as scipy_upfirdn

def upfirdn(h, x, up=1, down=1, upfirdn_mode='constant', cval=0):
    """
    Upsample, FIR filter, and downsample.

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

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

    Args:
        h (list[list]): 1-D FIR filter coefficients (Excel range).
        x (list[list]): Input signal array.
        up (int, optional): Upsampling rate. Default is 1.
        down (int, optional): Downsampling rate. Default is 1.
        upfirdn_mode (str, optional): The signal extension mode to use. Valid options: Constant, Symmetric, Reflect, Anti-Reflect, Anti-Symmetric, Edge, Wrap, Smooth, Line. Default is 'constant'.
        cval (float, optional): The constant value to use when mode is 'constant'. Default is 0.

    Returns:
        list[list]: A 2D array of the output signal.
    """
    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)])

        h_arr = to_1d(h)
        x_arr = to_1d(x)

        result = scipy_upfirdn(
            h_arr, 
            x_arr, 
            up=int(up), 
            down=int(down), 
            mode=upfirdn_mode, 
            cval=float(cval)
        )

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

Online Calculator

1-D FIR filter coefficients (Excel range).
Input signal array.
Upsampling rate.
Downsampling rate.
The signal extension mode to use.
The constant value to use when mode is 'constant'.