Eachharmoniccomponentisasinewaveatthefrequencymultiple

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Unformatted text preview: ingly,
equals
zero
for
a
perfect
saw‐tooth.

 ©
2010
Alexander
Ganago

 Page
1
of
4

 File:
Saw‐tooth
harmonics
 EECS
314
Winter
2010

 
 Homework
2

 Required
reading
for
Problem
2
 According
to
the
Fourier
theorem,
any
periodic
signal
can
be
expressed
as
a
sum
of
 sinusoids:
 
 f (t ) = a0 + ∑ an ⋅ cos(2π ⋅ n ⋅ f0 ⋅ t ) + ∑ bn ⋅ sin(2π ⋅ n ⋅ f0 ⋅ t ) 
 
 n =1 n =1 ∞ ∞ 
 [equation
4]
 
 Although
the
formula
above
includes
both
sine
and
cosine
waves,
some
of
their
 coefficients
may
vanish
due
to
symmetry:
for
example,
the
saw‐tooth
waveform
can
 be
built
as
the
sum
of
sine
wa...
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This note was uploaded on 12/06/2010 for the course EECS 314 taught by Professor Ganago during the Spring '07 term at University of Michigan.

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