Specifications

CHAPTER 6

Shaping sound

The signal generators we’ve seen so far are the phasor, cosinusoidal oscillator,

and noise source. While these alone seem limited they may be combined using

shaping oper ations to produce a great many new signals. We are going to make

transformations on waveforms, pushing them a little this way or that, moulding

them into new things. This subject is dealt with in two sections, amplitude

dependent shaping where the output depends only on current input values, and

time dependent signal shaping where the output is a function of current and

past signal values .

SECTION 6.1

Amplitude dependent signal shaping

Simple signal arithmetic

Arithmetic is at the foundation of signal processing. Examine many patches

and you will ﬁnd, on average, the mos t common object is the humble multiply,

followed closely by addition. Just as all mathematics builds on a few simple

arithmetic axioms complex DSP ope rations can be reduced to adds and mul-

tiplies. While it’s rarely of practical use, it’s worth noting that multiplication

can be seen as repeated addition, so to multiply a signal by two we can connect

it to both inlets of

and it will be added to itself, which is the same as mul-

tiplying by two. The opposite of addition is subtractio n. If you are s ubtr acting

a constant value from a signa l it’s okay to use

but ex press the subtracted

amount as a negative number, as with

+~ -0.5

, though of cour se there is a

unit too. Addition and multiplication a re commutative (symmetrical) opera-

tors, so it doesn’t matter which way round you connect two signals to a unit.

On the other hand, subtraction and division have ordered arguments, the right

value is subtracted from, or is the divisor of, the left one. It is common to divide

by a constant and so

is generally used with an argument that’s the reciprocal

of the required divisor. For example, instea d of dividing by two, multiply by

half. There are two reasons for this. Firstly, divides were traditionally more

expensive so many programmers are entrenched in the habit of avo iding divides

where a multiply will do. Secondly, an accidental divide by zero traditionally

causes problems, even crashing the program. Neither of these things are actually

true of Pd running on a modern processor, but because of such legacies you’ll

ﬁnd many a lgorithms written accordingly. Reserve divides for when you need

to divide by a va riable signal and multiply by decimal fractions everywhere else