This example introduces point constraints. Even though a frequency response can only be approximated over a whole band, it is usually possible to specify an exact value of H(f) for a single frequency f, or for a finite set of frequencies. In this example, we design the same filter as in Example 2, but in addition, we specify that H(0) = 1 and H(25) = 0 exactly. These constraints are useful whenever we have noise at a known frequency (in our case, 25Hz) that we want to eliminate completely. The following specification file describes this design.
(title "A simple filter III")
(verbose #t)
(cosine-symmetry)
(filter-length 10)
(sampling-frequency 60)
(limit-= (band 0 10) 1 .2)
(limit-= (band 20 30) 0)
;; We now constrain H(0) to be exactly 1. We accomplish this effect
;; by setting weight = 0, and specifying the constraint for a point,
;; not for a band.
(limit-= 0 1 0)
;; another point constraint at 25 Hz. H(25) = 0.
(limit-= 25 0 0)
(output-file "example-3.coef")
(plot-file "example-3.plot")
(go)
A graph of the frequency response follows.
A point constraint is specified as in the command (limit-= 25 0
0). Note that we specify a single frequency 25 instead of a
band. gmeteor interprets this single frequency as the band
(band 25 25). Second, we set the weight to 0, so that the
constraint cannot be violated. (See Example 2, for a discussion
about weights.) With this change, we have |H(25)| = 0 exactly,
while in Example 2, we had |H(25)| = 0.008.