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A low-pass filter with weights

Frequency response:

Input specification:

;; This example introduces ``weights.''  In example 1, the ripple in
;; the passband and in the stopband were the same.  We now trade a
;; smaller passband ripple for a larger stopband ripple.

;; parameters as in example-1.scm
(title "A simple filter II")
(verbose #t)
(cosine-symmetry)
(filter-length 10)
(sampling-frequency 60)

;; Like in example-1, we specify the frequency reponse.  The passband
;; is from 0 to 10 Hz, and H(f) should be 1 in this band.  Now the
;; constraint has weight 0.2, however.  The weight is a measure of how
;; much H(f) can deviate from the constraint.  Since the stopband
;; constraint has a default weight 1, the passband ripple will be one
;; fifth of the stopband ripple.

(limit-= (band 0 10) 1 .2)   ; .2 is the weight
(limit-= (band 20 30) 0)     ; no weight specified ==> weight = 1

(output-file "example-2.coef")
(plot-file "example-2.plot")
(go)