Filter
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Appendix C: Algorithms
TVS600 & TVS600A Command Reference
C–31
drop off above a cutoff frequency. Instead, the filter response drops rapidly in the
transition region and then flattens out somewhat in the stop band. In the
transition region, the roll off cannot be well approximated as a constant roll off
per decade of frequency (such as 40 dB/decade).
The Kaiser window filter technique does not provide a constant dB/decade roll
off in the transition region. In fact, in the transition region, the Kaiser window
technique only specifies that the transfer function will decrease from the pass
band level to the stop band attenuation. What the Kaiser window does guarantee
is the specifications in the pass band and stop band:
Passband Ripple v 20log
10
ƪ
1 ) 10
–SREJ
20
ƫ
f v LPAS –
ǒ
TWID
4 @ TINT
Ǔ
Stopband Rejection w SREJ f v LPAS )
ǒ
TWID
4 @ TINT
Ǔ
Similar specifications are achieved for highpass, bandpass and notch filters. For
notch filters, be sure that (STOP– START) is greater than TWIDHZ or else no
guarantee is made about the attenuation in any portion of the notch region.
Group Delay. The digital filters have linear phase in the pass band. The group
delay, which is the derivative of the phase, is therefore constant in the pass band.
Practically speaking, this means that if you have a signal which is made up of
many frequency components, the relative phase of these frequency components
are preserved in the filter.
There are two main causes of errors from the digital filter code. One of the
sources of error is a filter specification that generates too many filter coefficients.
The other class of errors is from cutoff frequencies that violate certain
constraints.
Too Many Filter Coefficients. If the stop band attenuation SREJ and/or the relative
filter transition width TWID is set to too high, then the number of points
required by the filter may exceed 10% of the acquired record length. Since the
digital filter implementation limits the number of coefficients to 10% of the
record length, waveform analyzer reports an error, and performs no filtering.
Suppose, for example, you acquire a record with 1024 points at 1 GSample/se-
cond acquisition rate. You set the lowpass filter to a cutoff frequency of
200 MHz, a stop band attenuation, SREJ, of 80 dB and relative filter transition
width, TWID, of 0.05. Such a filter requires 219 points, which is more than
102 points (10% of the data record), and the following error is reported:
2100,CalculateN questionable; digital filter error - filter
specs require too many coefficients"
Error Conditions