Digital Signal Processing Reference
In-Depth Information
2DIFF
nnn
F
m.m
x
2DIFF
Second-Order Differentiator
nnn
Number of filter coefficients (i.e., filter length)
F
Normalized frequency
m.m
Cut-off frequency value
x = a, b
a - Differentiator designed from a unity gain filter
b - Differentiator designed using Fourier coefficients and Gaussian window
6.7.2
Filter Coefficients Table
The filter coefficients are listed for all differentiators except for those of lengths
255 and 511; this has been done chiefly for space reasons. All filters are archived
in the accompanying CD to full precision in comma separated variable (CSV)
format. The coefficients have all been multiplied by 2
9
, and should be
renormalized by this value when used in full-precision filtering.
6.8 OVERVIEW AND SUMMARY
The main driver for designing band-limited differentiators has been the
management of noise amplification. Not much emphasis has been placed on edge
transition width or on attenuation in the rejection band, although first-order
differentiators are typically -100 dB. In this regard, two options have been given
for second-order differentiators, in particular, Types a and b. These have been
summarized in Table 6.1.
An overview of all first- and second-order differentiators designed and
presented in this chapter is given in Table 6.2. A total of 53 differentiators is
provided consisting of 25 first-order, 8 band-pass, and 20 second-order filters.
They have been designed with the widest range of applications and conditions in
mind; however there may be situations when these filters will no longer be
applicable. In such cases, the user may need to find alternative differentiator
solutions.
