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