Read macro sharp-t

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The read macro sharp-t is useful to apply a filter multiple times.

The following code shows an implementation of the Moog VCF written by Julius O. Smith in Faust (effect.lib):

moog_vcf(res,fr) = (+ : seq(i,4,pole(p)) : *(unitygain(p))) ~ *(mk)
with {
     p = 1.0 - fr * 2.0 * PI / SR; // good approximation for fr << SR
     unitygain(p) = pow(1.0-p,4.0); // one-pole unity-gain scaling
     mk = -4.0*max(0,min(res,0.999999)); // need mk > -4 for stability
};

In particular, the sequential composition `seq(i,4,pole(p))' defines four pole filters in series. A direct translation in Lisp is

(pole (pole (pole (pole (in p) p) p) p) p)

but it seems an auto-incitement to get the pole position in Moto GP. With the read macro sharp-t, the composition becomes

#4t(pole in p)

It means: "apply the pole filter four times". Often the input of a filter is the first argument, but if it is not the case, a number after sharp-t specifies the position of the input in the list of the arguments starting from zero. Example:

(in-package :scratch)

SCRATCH> (init)

SCRATCH> '#4t1(fname x in y)
(FNAME X (FNAME X (FNAME X (FNAME X IN Y) Y) Y) Y)

A VUG to define the previous VCF is

(define-vug moog-vcf (in res fr)
  (with-samples ((wt (hz->radians fr))
                 (coef (- 1 wt))
                 (unity-gain (* wt wt wt wt))
                 (mk (* -4 (clip res 0.0d0 0.999999d0))))
    (~ (* #4t(pole (+ in it) coef) unity-gain mk))))

Another example: the first-order recursive lowpass filter used in Csound

(define-vug tone (in hp)
  (with-samples ((b (- 2 (cos (hz->radians hp))))
                 (coef (- b (sqrt (the non-negative-sample (- (* b b) 1)))))
                 (g (- 1 coef)))
    (pole (* g in) coef)))

(dsp! tone2-test (amp)
  (with-samples ((hp (expon 50 8000 10 #'free)))
    (stereo #2t(tone (white-noise amp) hp))))

(dsp! tone4-test (amp)
  (with-samples ((hp (expon 50 8000 10 #'free))
                 (b (- 2 (cos (hz->radians hp))))
                 (coef (- b (sqrt (the non-negative-sample (- (* b b) 1)))))
                 (g (expt (the non-negative-sample (- 1 coef)) 4)))
    (stereo #4t(pole (* g (white-noise amp)) coef))))

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