Moving-Averaging-Filter

The moving-averaging-filter is easy-to-understand, and implement. While effective on Time Domain, it is the worst filter in Frequency Domain. The basic equation of the moving-average-filter is:

$$y(n) = \frac{1}{M} \sum_{j=0}^{M-1} x[n+j]$$

On the other hand, the Frequency Response is given by:

$$H(w) = \frac{1}{M} \sum_{k=0}^{M-1} e^{-jwk} = \frac{1 - e^{-jwM}}{1 - e^{-jw}}$$

where M is the window size of the filter.

This implementation allows to explore how Time and Frequency Responses of the moving- averaging-filter vary according to its window size. Code is implemented with integration of C and MATLAB in mind, thus a MEX function can be created in MATLAB as follows:

• Using the command mex -R2018a Averaging_filter.c.

Then, an input signal can be simulated and the passed to the MEX function created.

• Use the .mex function with the command: [filtered_data, frequency_response] = Average_filter(input signal, 15, 500) , where 15 is the window size of the averaging-filter and 500 is the size of the Frequency Response.

• When plotting, remember to use the absolute value (command $abs()$ in MATLAB) when passing the frequency_response to $plot()$.

Note: In order to successfully run this program it is necessary to have MATLAB Coder installed, as well as the MinGW-w64 C/C++ compiler.