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Fast Fourier Transforms
Reference
3Ć46
Zoom always uses either sin(x)/x or linear interpolation when expanding
displayed waveforms. To select the interpolation method: press DISPLAY ➞
Setting (main) ➞ Display (popĆup) ➞ Filter (main) ➞ Sin(x)/x or Linear
(side), or if your oscilloscope does not have color, press DISPLAY ➞ FilĆ
ter (main) ➞ Sin(x)/x or Linear (side)
If the source waveform record length is 500 points, the FFT will use 2X Zoom
to increase the 250 point FFT frequency domain record to 500 points. ThereĆ
fore, FFT math waveforms of 500 point waveforms are always zoomed 2X or
more with interpolation. Waveforms with other record lengths can be
zoomed or not and can have minimum Zooms of 1X or less.
Sin(x)/x interpolation may distort the magnitude and phase displays of the
FFT depending on which window was used. You can easily check the efĆ
fects of the interpolation by switching between sin(x)/x and linear interpolaĆ
tion and observing the difference in measurement results on the display. If
significant differences occur, use linear interpolation.
Undersampling (Aliasing)
Aliasing occurs when the oscilloscope acquires a source waveform with
frequency components outside of the frequency range for the current samĆ
ple rate. In the FFT waveform, the actual higher frequency components are
undersampled, and therefore, they appear as lower frequency aliases that
fold back" around the Nyquist point (see Figure 3Ć26).
The greatest frequency that can be input into any sampler without aliasing is
½ the sample frequency. Since source waveforms often have a fundamental
frequency that does not alias but have harmonic frequencies that do, you
should have methods for recognizing and dealing with aliases:
H Be aware that a source waveform with fast edge transition times creates
many high frequency harmonics. These harmonics typically decrease in
amplitude as their frequency increases.
H Sample the source signal at rates that are at least 2X that of the highest
frequency component having significant amplitude.
H Filter the input to bandwidth limit it to frequencies below that of the
Nyquist frequency.
H Recognize and ignore the aliased frequencies.
If you think you have aliased frequencies in your FFT, select the source
channel and adjust the horizontal scale to increase the sample rate. Since
you increase the Nyquist frequency as you increase the sample rate, the
alias signals should appear at their proper frequency.