Digital Sound & Music: Concepts, Applications, & Science, Chapter 2, last updated 6/25/2013

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example, is formed by adding all the odd-numbered harmonics of a given

fundamental frequency, with the amplitudes of these harmonics diminishing as

their frequencies increase. The odd-numbered harmonics are those with

frequency

nf

where f is the fundamental frequency and n is a positive odd

integer. A sawtooth wave is formed by adding all harmonic frequencies related

to a fundamental, with the amplitude of each frequency component diminishing

as the frequency increases. If you would like to look at the mathematics of non-

sinusoidal waves more closely, see Section 2.3.2.

2.2.5 Frequency, Impulse, and Phase Response Graphs

Section 2.2.3 introduces frequency response graphs, showing one taken from Adobe Audition.

In fact, there are three interrelated graphs that are often used in sound analysis. Since these are

used in this and later chapters, this is a good time to

introduce you to these types of graphs. The three types of

graphs are impulse response, frequency response, and

phase response.

Impulse, frequency, and phase response graphs are

simply different ways of storing and graphing the same set

of data related to an instance of sound. Each type of graph

represents the information in a different mathematical

domain. The domains and ranges of the three types of

sound graphs are given in Table 2.2.

graph type domain (x-axis) range (y-axis)

impulse response time amplitude of

sound at each

moment in time

frequency

response

frequency magnitude of

frequency across

the audible

spectrum of sound

phase response phase phase of

frequency across

the audible

spectrum of sound

Table 2.2 Domains and ranges of impulse, frequency, and phase response graphs

Let‟s look at an example of these three graphs, each associated with the same instance of

sound. The graphs in the figures below were generated by sound analysis software called

Fuzzmeasure Pro, which we‟ll use in Section 2 as we talk about how frequencies are analyzed in

practice.

Aside: Although the term

“impulse response” could

technically be used for any

instance of sound in the time

domain, it is more often used to

refer to instances of sound that

are generated from a short

burst of sound like a gun shot

or balloon pop. In Chapter 7,

you’ll see how an impulse

response can be used to

simulate the effect of an

acoustical space on a sound.

Practical

Exercise:

Creating a

Sound Effect