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.
