Wigner Distribution

The Wigner distribution was advocated in quantum mechanics by E. Wigner.  It is similar in characteristics to the power spectrum extended for an unsteady signal.  With conventional FFT, the time resolution and frequency resolution are complementary (higher frequency resolution results in longer sampling time) making it difficult to obtain an instantaneous spectrum of the unsteady signal with a favorable resolution.  With the Wigner distribution, on the contrary, the time resolution and frequency resolution are not directly subject to complementary restrictions, making it possible to obtain favorable time-frequency resolution of the power spectrum on the frequency-time plane. However, the Wigner distribution has not been practical because it requires a greater number of calculation points than FFT.  The CF-6400 FFT analyzer can perform Wigner distribution analysis in a comparatively short time by means of a built-in high-speed DSP.


Window (Time Window)

The FFT operation is performed for sampled numerical data within a certain interval (for example, 1,024 or 2,048 points). The operation to cut out a certain portion of a waveform in this manner is referred to as cutting out a waveform with a window (time window) or applying a window. The Fourier transform itself is defined in terms of infinite data. This also applies to discrete Fourier transform (DFT). The FFT analyzer analyzes signals on the premise that, when the waveform is cut out with a window, the waveform in this section is repeated infinite times.At this time, if the analysis data length (time length) is integer times the period of each frequency, the waveform presumed by the FFT analyzer is identical to the actual input waveform, making it possible to obtain a single line spectrum.

However, if the analysis data length is not integer times the period (the frequency resolution not applied, and the front end of a frame does not connect to the tail end), the waveform obtained by FFT is distorted and side lobes appear because the power is not concentrated in the spectrum. Theoretically, data with infinite length is required to obtain a single line spectrum. Since the FFT analyzer processes signals using data within a limited section, a leakage error occurs. The processing for minimizing this leakage error is referred to as window processing. When a peak-shaped function with which both ends of the frame reaches zero is applied, the front and tail ends of the frame are connected, resulting in smaller error. This kind of function is referred to as the window function, and the processing for synchronization of the analysis signal using the window function is referred to as window processing. As a result, the shape of the spectrum becomes similar to that of the line spectrum.

A typical window is the Hanning window; other types of windows are used that best suit the analysis signal.


Zooming Function

In usual FFT analysis, the range from 0 to the frequency range is analyzed for the number of lines (for example, 800 lines).  In some cases, you may want to analyze the range from f1 to f2 for 800 lines.  In this case, data is analyzed by means of the digital zoom processing which takes time because the number of data sampling points is required for each zoom magnification.