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Appendix C: Algorithms
TVS600 & TVS600A Command Reference
C–23
Figure C–9: Using many more points in the Lowpass filter results in a quicker
transition but a minimum attenuation of 21 dB
When the filter response is truncated with a rectangular window the minimum
attenuation in the stop band is at best 21 dB. In order to achieve greater
attenuation in the stop band a non–rectangular window must be applied to the
filter data.
There are many choices for non–rectangular windows. Common windows
include Bartlett, Hamming, Hanning, and Blackman. The filter in the waveform
analyzer employs a Kaiser window. This window was chosen because it offers a
range of possible window shapes, and thus different stop band attenuations. For a
window that is M+1 points long, the Kaiser window is defined as follows:
w[n] +
ȧ
ȧ
ȧ
ȧ
ȥ
ȡ
Ȣ
I
0
ƪ
b
ǒ
1–
ƪ
(n–Mń2)
Mń2
ƫ
2
Ǔ
1ń2
ƫ
I
0
ƪ
b
ƫ
0 v n v M
ȧ
ȧ
ȧ
ȧ
Ȧ
ȣ
Ȥ
0 otherwise
I
0
represents the zero order modified Bessel function of the first kind. b is a
parameter that ranges from 0 to infinity. The larger the value of b, the more the
window tapers at the edges. When b=0 the Kaiser window reduces to a rectangu-
lar window. Figure C–10 shows three Kaiser windows with 200 points in the
window and a b of 1, 5 and 20.
Kaiser Window