Periodic Signals
Many signals are periodic in nature, such as short segments of
most tonal musical instruments and speech. The sinusoidal components
in a periodic signal are constrained to be harmonic, that is,
occurring at frequencies that are an integer multiple of the
fundamental frequency
.6.6 Physically, any ``driven
oscillator,'' such as bowed-string instruments, brasses, woodwinds,
flutes, etc., is usually quite periodic in normal steady-state
operation, and therefore generates harmonic overtones in steady
state. Freely vibrating resonators, on the other hand, such as
plucked strings, gongs, and ``tonal percussion'' instruments,
are not generally periodic.6.7
Consider a periodic signal with fundamental frequency
Hz.
Then the harmonic components occur at integer multiples of
, and
so they are spaced in frequency by
. To resolve
these harmonics in a spectrum analysis, we require, adapting
(5.27),
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(6.28) |
Note that





Specifically, resolving the harmonics of a periodic signal with period
samples is assured if we have at least
periods under the rectangular window,
periods under the Hamming window,
periods under the Blackman window,
periods under the Blackman-Harris
-term window,
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Tighter Bounds for Minimum Window Length
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Simple Sufficient Condition for Peak Resolution