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Appendix C: Algorithms
TVS600 & TVS600A Command Reference
C–21
Figure C–6: Using a rectangular window to truncate the data from Figure C–5 to a
finite number of points
The frequency domain convolution of H(f) with W(f) has three effects: the filter
edges are no longer abrupt, the pass band transmission is no longer exactly unity,
and the stop band attenuation is no longer infinite. Figures C–7 through C–9
show the original, ideal filter and the resultant filter with three different lengths
of rectangular windows. Note that these plots use a dB scale for the filter.
As more points are used in the filter (corresponding to a longer window) the
transition becomes sharper and sharper. However, in this example, the worst case
attenuation of the filter in the stop band stays fixed at about –21 dB. Examining
Figures C–7 through C–9 carefully, you can see that the peak amplitude of the
ripple in the stop band (i.e., minimum attenuation) remains fixed at about
–21 dB. As more points are used, the filter becomes sharper but this side lobe
remains 21 dB down. For other filter shapes, such as bandpass and notch filters,
the worst case stop band attenuation can be as low as –15 dB. The limitation on
the stop band attenuation is the major drawback of using a rectangular window.