Frequency bins
The FFT algorithm takes a discrete source waveform, defined over N
points, and computes N complex Fourier coefficients, which are
interpreted as harmonic components of the input signal.
For a real source waveform (imaginary part equals 0), there are only N/2
independent harmonic components.
The FFT corresponds to analyzing the input signal with a bank of N/2
filters, all having the same shape and width, and centered at N/2
discrete frequencies. Each filter collects the signal energy falling
into the immediate neighborhood of its center frequency, and thus it can
be said that there are N/2 "frequency bins".
The distance, in Hz, between the center frequencies of the bins is
always
af = I/T
where T is the duration of the time domain record in seconds.
The width of a bin is equal to Af.
The width of the main lobe of the filter centered at each bin depends on
the window function used. With the Rectangular window, the width at
-3.92 dB is 1.0 bins. Other windows have wider main lobes (consult
Table 11.3).
Frequency Range
The range of frequencies computed and displayed in the 9400A is from 0
Hz at the left hand edge of the screen to the Nyquist frequency at 5 or
6.25 divisions.
Frequency Resolution
In a narrow sense, the frequency resolution is equal to the bin width,
af. That is, if the input signal changes its frequency by af, the
corresponding spectrum peak will be displaced by ~f. For smaller changes
of frequency, only the shape of the peak will change.
However, the effective frequency resolution (i.e. the ability to
actually resolve two signals having close frequencies) is further
limited by the use of window functions. The ENBW value of all windows
other than the rectangular is greater than ~f, i.e. greater than the bin
width. Table 11.3 lists the ENBW value for the windows implemented.
11-17
Fast Fourier Waveform Processing
Option (WP02, V 2.06FT)
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