Explore Data Tapering Windows

The Explore Data Tapering Windows option is available from the Fourier Spectrum with Data Window, Fourier Spectra with Data Window Comparison, Fourier Spectra of Segmented Data, and Fourier Spectrum of Unevenly Sampled Data options in the Spectral menu.

Data tapering windows are used to reduce the spectral leakage in Fourier spectra. Since it can be difficult to commit the properties of the various windows to memory, especially when they contain an adjustable parameter, and since they are important in using a windowed FFT effectively, AutoSignal offers this Explore Data Tapering Windows option.

This option plots a discrete FFT in a problem designed to illustrate the frequency widths of each window as well as the rolloff vs. maximum sidelobe tradeoff. You can view as many as four windows simultaneously. Both the time and frequency domain plots are displayed. A numerical display of the three key properties of tapering windows is also given for the first window.

FFT n and Win n

In this posed problem, the data tapering window of length Win n is constructed at the center of a data series of length FFT n. The default values use a data length of 1001 with a window length of 101 in the center of the data stream. The remaining 900 values are 0. An exact n FFT is made to produce the corresponding frequency spectra.

Win Cnt

You can inspect the spectra for up to 4 windows simultaneously.

Window Selection

For each data tapering window up to the count specified, you must select a window, and if it includes an adjustable parameter, you must also set it.

Window 1 Properties

· Mainlobe - the one-sided normalized frequency width from 0 frequency to the first null.

· Sidelobe - the delta in dB between signal at 0 frequency and the highest sidelobe signal. The highest sidelobe is usually, but not always, adjacent.

· Rolloff - This value in dB/octave represents the whole of the decay in the frequency domain, rather than the asymptotic rolloff. A non-linear robust (Lorentzian minimization) log fit is used to determine this value.

Note that these are empirical values derived directly from the frequency spectrum. You should find good agreement with analytic values reported in the literature.

Copy

The Copy Data to Clipboard option copies all of the columns currently selected in the List Data option to the clipboard. Formats include full precision binary (for spreadsheets such as Excel) and ASCII (for pasting into text editors). You can generally find a Paste As option in most applications if you want specific control over the format imported.

Save

The Save Data to Disk option writes all of the columns currently selected in the List Data option to a supported file format. These formats include ASCII, Excel 97, Excel 95, Lotus WK3, Lotus WK1, SPSS, or Systat.

List

The List Data option offers an extended FFT data summary for the first window. The listing uses the AutoSignal text viewer facility. The FFT channel number, frequency, and magnitude are always listed. The Format menu offers the optional selection of the following:

· Add Real,Imag

· Add Amplitude

· Add Wavelength

· Add Phase

· Add dB

· or Add dB Normalized

· Add Power Spectral Density, Sum Squared Amplitude

· or Add Power Spectral Density, Mean Squared Amplitude

· or Add Power Spectral Density, Time-Integral Squared Amplitude