18.2.2 Algorithms (FFT Filters)

The Fourier transform of the input signal is first computed. Then the transformed data is processed in the frequency domain. Finally, the altered frequencies are converted back to signal in time domain with inverse Fourier transform.

Different types of filters apply different processing on the transform data, resulting in different filtering effects.

For low-pass, high-pass, band-pass, band-block filter or parabolic low-pass, transformed data is multiplied with a window determined by the filter type, as shown in the below table.

Low Pass
Algorithm FFT Filters1.gif
High Pass
Algorithm FFT Filters2.gif
Band Pass
Algorithm FFT Filters3.gif
Band Block
Algorithm FFT Filters4.gif
Low Pass Parabolic
Algorithm FFT Filters5.gif

Let f_{c1}\,\! be the pass frequency and f_{c2}\,\! be the stop frequency. The window function can be expressed by:

w(f)=\begin{cases}1,f\leq f_{c1}\\1-\frac{(f-f_{c1})^2}{(f_{c2}-f_{c1})^2},f_{c1}<f<f_{c2}\\0,f\geq f_{c2}\end{cases}

Note that the Keep DC Offset option can affect the window used for multiplying the transformed data. If this check box is selected, the first point of the window will be set to 1.

If the threshold filter is used, the power of every frequency component is examined after the Fourier transformed is performed on the input signal. If the power of a component is not greater than the threshold, this component will be discarded. Otherwise, it is preserved. After examining all frequency components, inverse Fourier transform is performed on the altered frequencies.

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