National Instruments NI Spectral Measurements Toolkit - Manual (Page 12)

NI Spectral Measurements Toolkit User Guide 12 ni.com
Continuous Zoom FFT
Continuous zoom FFT is a technique for quickly analyzing data as it
arrives. A decimation process reduces the sample rate in real time. After the
process acquires all the data and decimates it in time T, a relatively small
FFT remains. The term continuous refers to beginning the process while
data arrives. With a standard FFT, you must wait until all the data arrives
before beginning calculations.
The continuous zoom FFT first shifts the spectral region of interest into
the baseband. The technique then applies a lowpass antialias filter and
decimates, or downsamples, the data by a factor of M. The zoom factor of
M yields a new effective sample rate, f
s
/M. The antialias filter has a cutoff
frequency of f
s
/(2
× M) because the Nyquist frequency has decreased by
a factor of M.
After lowpass filtering, the continuous zoom FFT performs an FFT on the
reduced sample rate data to produce the zoom spectrum. This technique is
destructive because the original data changes as a result of the filtering and
decimation. If you store the data and batch process it later, you lose the
primary benefit of the technique, which is its real-time capability. Figure 3
shows the basic steps of frequency shifting, decimation, and FFT.
Figure 3. Continuous Zoom FFT Diagram
Although it might seem possible to reduce the sample rate, f
s
, to improve
frequency resolution, this method does not work. You cannot acquire the
data with a lower sample rate to increase resolution because the Nyquist
sampling theorem applies. In the original acquisition, you must sample at
least twice as fast as the highest frequency of your desired zoom region to
obtain the frequency information you need. You cannot reduce the sample
rate until after frequency shifting occurs if you want to improve the
frequency resolution of the zoom region. The continuous zoom FFT shifts a
high-frequency signal into the baseband before adjusting the sample rate.
x(n) f
s
f
s
/M
Fixed Size
FFT
Zoom Processor
Lowpass Filter
Decimate by M
Modulation