Specifications

68 Shaping sound
osc~ 670
clip~ -0.9 0.9
*~ 0.06
rpole~ 0.999
*~ 10000
pd grapha
A
pd grapha
B
fig 6.20: Inte-
gration
Inte grating a square wave gives us a triangle wave. If a constant
signal value is given to an integrator its output will move up or
down at a constant rate. In fact this is the basis of a phasor, so
a filter can be seen as the most fundamental signal generator as
well as a way to shape signals, thus we have come full circle and
can see the words of the great master “It’s all the same thing”.
A square wave is produced by the method shown in Fig. 6.7,
first amplifying a cosinusoidal wave by a larg e value and then
clipping it. As the square wave alternates be tween +1.0 and
−1.0 the integrator output first slopes up at a constant rate,
and then down at a constant rate. A scaling factor is added
to place the resulting triangle wave within the bounds of the
graph. Exper iment with integrating a cosinusoidal wave. What
happens? The integral of cos(x) is sin(x), or in other words we
have shifted cos(x) by 90
◦
. If the same operation is applied
again, to a sine wave, we get back to a cosine wave out of
phase with the first one, a shift of 180
◦
. In other words the integral of sin(x) is
−cos(x). This can b e more properly written as a definite integral
Z
cos(x) dx = sin(x) (6.1)
or as
Z
sin(x) dx = −cos(x) (6.2)
Differentiation
pd grapha
A
pd grapha
B
-~ 0.5
*~ 2
rzero~ 0.999
pd grapha
C
*~ 0.5
cos~
pd grapha
D
rzero~ 0.999
phasor~ -670
*~ 11
fig 6.21: Differentiation
The oppos ite of integrating a signal is differentiation. This gives us the instan-
taneous slope of a signal, or in other words the gradient of a line tangential to
the s ignal. What do you suppose will be the effect of differentiating a cosine