Recent applications of bandpass filtering Page: 6 of 15
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Recent Applications of Bandpass Filtering
1 Hz Displacement Source; Peak SNR=2: alpha=50 1 Hz Displacement Source; Peak SNR=10: alpha=50
E 10-1 10-
signal.am N signal.am
10-2 - Herrmann-S 10-2 - Herrmann-S
- Herrmann-N - Herrmann-N
A Parseval-S A Parseval-S
A Parseval-N A Parseval-N
102 I 1111111 I I102
Q Herrmann-SNR o Herrmann-SNR
A Parseval-SNR A Parseval-SNR
Z 101 - 101
2 4 6 8 2 4 6 8 0 101
10- 100 101 10- 100 101
Frequency (hz) Frequency (hz)
Figure 1. Comparison of scaling factors. Both Herrmann scaling and one derived from
Parseval's theorem work well in the case for which the maximum SNR is 10. In the case for
which the maximum SNR was specified as 2, however, Herrmann scaling does not work as well.
In both SNR cases, Herrmann scaling grossly underestimates the noise spectrum. As explained
in the text, this is to be expected. Gaussian filters were used in this example.
1.2 Alpha = 20
1.0 Figure 2. Bandpass comparisons. The comb
filter shown is the same order as the bandpass
-, filter but consists of a low-pass followed by a
high-pass filter; both filters have the same
0.8 corner frequency. For the Gaussian filter, the
parameter a was chosen so that its maximum
errors would be comparable to the errors of the
0.6- -comb filter. As shown, this requirement results
in the Gaussian filter having approximately the
same low-frequency decay as the comb filter.
O 5 10 15 20
M. D. Denny
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Denny, M D. Recent applications of bandpass filtering, report, March 15, 1999; California. (https://digital.library.unt.edu/ark:/67531/metadc784805/m1/6/: accessed May 20, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.