Signal Processing Commands These DFT parameters are related by the equation,
Fmax = (N/2) x delta f (in Hz) 3. Shannon's (Nyquist) Sampling Criterion Shannon's Sampling Criterion says that to calculate an accurate DFT over the span (f = 0 to Fmax), •
The time waveform must be sampled at least at a rate of twice Fmax.
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This is called the Nyquist sampling rate.
Therefore, Fmax and the time domain sampling rate are related by the equation,
2 x Fmax = 1 / delta t (in Hz) Fmax = (1/2) x (Nyquist sampling rate)
(in Hz)
Fundamental Sampling Rule The following equation is derived from the three equations above.
delta f = 1/T
(in Hz)
This equation says that the resolution (delta f) of the DFT equals the length of the time domain sampling window (T). Sampling Rate and Frequency Resolution To increase the frequency resolution in a DFT (reduce delta f), the time domain signal must be sampled over a longer time period (T). NOTE: Increasing the time domain sampling rate does not increase the frequency resolution (delta f). Anti-Aliasing Filter When an analog (continuous) signal is sampled, higher frequencies in the signal will fold back and appear as lower frequencies in the DFT. These aliased high frequency components are not part of the lower frequency spectrum of the original signal. •
To insure that no frequencies higher than the Nyquist frequency are contained in a DFT, higher frequencies must be removed from the time waveform before it is sampled.
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Frequencies higher than the Nyquist sampling frequency are removed using an analog low pass anti-aliasing filter.
Passing a time domain signal through an anti-aliasing filter before sampling insures that all high frequency components are removed from the frequency span (0 to Fmax) of the DFT. •
All anti-aliasing filters have a finite roll off frequency band.
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If the cutoff frequency (start of the filter roll off) is set to 80% of Fmax, (or 40% of the sampling frequency), then 80% of a frequency span (0 to Fmax) will be alias-free.
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Most FFT analyzers have anti-aliasing filters with a cutoff frequency set to 80% of Fmax, or 40% of the sampling frequency.
Transform | FFT Applies the Fast Fourier Transform (FFT) algorithm to all time domain Traces in a Data Block to transform them into their frequency domain spectrum (DFT).
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