We proceed through the data point by point. The basic process of smoothing is very simple.

The FWHM is related to sigma by the formula (matlab format): The width of the kernel at 0.2 (on the Y axis) is the FWHM. Thus, for the standard Gaussian above, the maximum height is ~0.4. The FWHM is the width of the kernel, at half of the maximum of the height of the Gaussian. However, when the Gaussian is used for smoothing, it is usual to describe the width of the Gaussian with another related measure, the Full Width at Half Maximum (FWHM). In the standard statistical way, we have defined the width of the Gaussian shape in terms of sigma.

Here is a standard Gaussian, with a mean of 0 and a sigma (=population standard deviation) of 1. A Gaussian kernel is a kernel with the shape of a Gaussian (normal distribution) curve. The 'kernel' for smoothing, defines the shape of the function that is used to take the average of the neighbouring points. The numbers were generated with matlab, by creating 40 successive random numbers from a normal distribution. Here is a set of data, made out of random numbers, that we will use as a pretend time series, or a single line of data from one plane of an image. The matlab commands are contained in the file The code makes some of the ideas a little clearer, to those with some familiarity with matlab. This page is designed to be read in conjunction with the matlab commands that were used to make the figures. We hope we will succeed in explaining this phrase in the explanation below. There are many different methods of smoothing, but here we discuss smoothing with a Gaussian kernel. Smoothing is sometimes referred to as filtering, because smoothing has the effect of suppressing high frequency signal and enhancing low frequency signal. This (usually) has the effect of blurring the sharp edges in the smoothed data. bar ( x, scale * kernel2_at_pos, alpha = 0.Smoothing is a process by which data points are averaged with their neighbours in a series, such as a time series, or image. bar ( x, scale * kernel1_at_pos, alpha = 0.5, color = 'r' ) plt. sum ( kernel2_at_pos ) scale = 200 # So we can actually see it plt. sum ( kernel1_at_pos ) # Sum to 1 FWHM2 = 60 # The value falls below the half of maximum value after 2 sigma2 = fwhm2sigma ( FWHM2 ) kernel2_at_pos = np. exp ( - ( x - x_position ) ** 2 / ( 2 * sigma1 ** 2 )) kernel1_at_pos = kernel1_at_pos / np. X_position = 9 # Position in array is 6 (0 based) FWHM1 = 8 # The value falls below the half of maximum value after 2 sigma1 = fwhm2sigma ( FWHM1 ) kernel1_at_pos = np.

Gaussian fwhm sigma