 Filtering Frequency Domain Noise - Maple Help

Filtering Frequency Domain Noise Introduction

This application filters out certain frequencies from the frequency domain representation of an experimental data set.

 > $\mathrm{restart}$
 > $\mathrm{with}\left(\mathrm{SignalProcessing}\right):$$\phantom{\rule[-0.0ex]{0.0em}{0.0ex}}\phantom{\rule[-0.0ex]{0.0em}{0.0ex}}\mathrm{with}\left(\mathrm{plots}\right):$ Experimental Data

This data table contains 1024 experimental data points, assigned to the variable 'data'.

From the following plot, there appears to be an underlying trend in the data.

 >  Frequency Domain Representation

If the data is examined in the frequency domain, the resulting power spectrum shows two dominant frequencies, as well as many low power frequencies.

 > $\mathrm{data_fft}:=\mathrm{FFT}\left(\mathrm{data}\right):$
 > $\mathrm{data_fft_ps}≔\mathrm{sqrt}~\left(\mathrm{PowerSpectrum}\left(\mathrm{data_fft}\right)\right):$
 >  Filtering Noise in the Frequency Domain

Frequencies below a specific threshold can be removed with a custom filter. The Explore command can be used to show how the changing the frequency option of the low pass filter changes the resulting filtered signal.

 >     Comparison of Original and Filtered Data Set

By comparing the original signal plot with the filtered data, the underlying trend is more clearly visible.

 >
 > $\mathrm{display}\left(\mathrm{OriginalDataPlot},\mathrm{filteredDataPlot}\right)$ 