GAUSSIAN_FILTER1D

The 1-D Gaussian filter is a linear filter that smoothes a signal by convolving it with a Gaussian function. This process effectively removes high-frequency noise from the signal while preserving its overall shape and characteristics.

The Gaussian kernel is defined as:

G(x) = \frac{1}{\sqrt{2\pi}\sigma} e^{-\frac{x^2}{2\sigma^2}}

where \sigma is the standard deviation that determines the width of the filter. Larger \sigma values result in more smoothing.

Excel Usage

=GAUSSIAN_FILTER1D(input_data, sigma, axis, order, gaussian_mode, cval, truncate)

input_data (list[list], required): The input array (Excel range).
sigma (float, required): Standard deviation for Gaussian kernel (determines smoothing width).
axis (int, optional, default: -1): The axis along which to calculate.
order (int, optional, default: 0): Order of the derivative (0 for smoothing).
gaussian_mode (str, optional, default: “reflect”): Extension mode for padded signal.
cval (float, optional, default: 0): Value to fill past edges if mode is ‘constant’.
truncate (float, optional, default: 4): Truncate the filter at this many standard deviations.

Returns (list[list]): The smoothed signal as a 2D array.

Example 1: Simple smoothing

Inputs:

input_data					sigma
1	2	3	4	5	1

Excel formula:

=GAUSSIAN_FILTER1D({1,2,3,4,5}, 1)

Expected output:

Result
1.42704	2.06782	3	3.93218	4.57296

Example 2: Higher sigma smoothing

Inputs:

input_data					sigma
1	2	3	4	5	4

Excel formula:

=GAUSSIAN_FILTER1D({1,2,3,4,5}, 4)

Expected output:

Result
2.91948	2.95024	3	3.04976	3.08052

Python Code

Show Code

import numpy as np
from scipy.ndimage import gaussian_filter1d as scipy_gaussian

def gaussian_filter1d(input_data, sigma, axis=-1, order=0, gaussian_mode='reflect', cval=0, truncate=4):
    """
    1-D Gaussian filter for signal denoising and smoothing.

    See: https://docs.scipy.org/doc/scipy/reference/generated/scipy.ndimage.gaussian_filter1d.html

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

    Args:
        input_data (list[list]): The input array (Excel range).
        sigma (float): Standard deviation for Gaussian kernel (determines smoothing width).
        axis (int, optional): The axis along which to calculate. Default is -1.
        order (int, optional): Order of the derivative (0 for smoothing). Default is 0.
        gaussian_mode (str, optional): Extension mode for padded signal. Valid options: Reflect, Constant, Nearest, Mirror, Wrap. Default is 'reflect'.
        cval (float, optional): Value to fill past edges if mode is 'constant'. Default is 0.
        truncate (float, optional): Truncate the filter at this many standard deviations. Default is 4.

    Returns:
        list[list]: The smoothed signal as a 2D array.
    """
    try:
        def to2d(x):
            return [[x]] if not isinstance(x, list) else x

        data = np.array(to2d(input_data), dtype=float)

        result = scipy_gaussian(
            data, 
            sigma=float(sigma), 
            axis=int(axis), 
            order=int(order), 
            mode=gaussian_mode, 
            cval=float(cval), 
            truncate=float(truncate)
        )

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

Online Calculator

input_data *

The input array (Excel range).

sigma *

Standard deviation for Gaussian kernel (determines smoothing width).

axis

The axis along which to calculate.

order

Order of the derivative (0 for smoothing).

gaussian_mode

Extension mode for padded signal.

cval

Value to fill past edges if mode is 'constant'.

truncate

Truncate the filter at this many standard deviations.