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Appendix C: Algorithms
TVS600 & TVS600A Command Reference
C–19
Digital Filter Algorithms
This section describes how the digital filter of the waveform analyzer operates.
The commands in the CALCulate:FILTer subsystem control the digital filter.
The filter functions in the waveform analyzer instrument allow lowpass,
highpass, bandpass and notch filters to be applied to any acquired set of data. A
perfect filter would have unity transmission (with linear phase response) in the
pass band, infinite attenuation in the stop band and abruptly change from pass to
stop band. The transfer function for an ideal bandpass filter is depicted in
Figure C–4.
Figure C–4: Transfer function H(f) for an ideal bandpass filter
When you use a filter in the waveform analyzer, the frequency response of the
desired filter is inverse Fourier transformed to calculate the response of the filter
for a time domain impulse and this impulse response is convolved with the
waveform data as shown in the following equation:
h(t) + T
–1
{
H(f)
}
output wfm + (input wfm)*h(t)
These equations are mathematically correct, however, it is impossible to
implement them. For any ideal filter, which has abrupt changes in the transfer
function, the impulse response extends for all time. Clearly an infinitely long
impulse response cannot be convolved with the waveform data.
An Ideal Filter