1d filter implementation

I wanna implement this function, f=t^2*exp(-t^2), the exponential part is a gaussian filter and I should finetune mean and variance based on my data, now my question is when gaussian filter is multiplying by a polynomial function how should I convert it to filter?my confusion here is the sigma and varinance of the f function, and how to sode it.

Answer 1

[Sai Pavan]

Hi,

I understand that you are trying to implement a 1D gaussian filter multiplied by an exponential function.

Please follow the below workflow to implement the custom 1D filter:

• Create a function handle for the polynomial part, f(t) using the @(t) notation.
• Create the Gaussian filter using the “normpdf” function and determine the mean (mu) and variance (sigma^2) values that best fit your data as these values control the shape and position of the Gaussian filter.
• Multiply the polynomial function f(t) with the Gaussian filter

Please refer to the below code snippet that illustrates the implementation of custom 1D gaussian filter:

f = @(t) t.^2 .* exp(-t.^2); % Define the function f(t) = t^2 * exp(-t^2)
mu = 0; % Mean of the Gaussian filter  
sigma = 1; % Variance of the Gaussian filter
gaussianFilter = @(t) normpdf(t, mu, sigma); % Define the Gaussian filter 
filteredFunction = @(t) f(t) .* gaussianFilter(t); % Combine the polynomial and Gaussian filter 

Please refer to the below documentation to learn more about the “normpdf” function:

https://www.mathworks.com/help/stats/normpdf.html

Hope it helps.

Regards,

Sai Pavan