HP 50g User Manual page 520

The amplitudes A
a measure of the magnitude of the component of f(x) with frequency f
The basic or fundamental frequency in the Fourier series is f
other frequencies are multiples of this basic frequency, i.e., f
can define an angular frequency,
is the basic or fundamental angular frequency of the Fourier series.
0
Using the angular frequency notation, the Fourier series expansion is written as
A plot of the values A
spectrum for a function. The discrete spectrum will show that the function has
components at angular frequencies
fundamental angular frequency
Suppose that we are faced with the need to expand a non-periodic function into
sine and cosine components. A non-periodic function can be thought of as
having an infinitely large period. Thus, for a very large value of T, the
fundamental angular frequency,
. Also, the angular frequencies corresponding to
2, ..., ), now take values closer and closer to each other, suggesting the need
for a continuous spectrum of values.
The non-periodic function can be written, therefore, as
(
f x
where
will be referred to as the spectrum of the function and will be
n
f ( x ) a
0
∑
a a
0 n
n 1
vs. is the typical representation of a discrete
n n
∫
) [ ( ) cos(
C
0
1
( )
C
2
= 2n /T = 2 f
n
∑
A cos(
n n
n 1
cos x b
n n
which are integer multiples of the
n
.
0
2 /T, becomes a very small quantity, say
0
) (
x S
∫
( ) cos(
f x
= 1/T, thus, all
0
= n f
n
= 2 n f = n
n 0
x ).
n
sin x
n
= n = n
n 0
) sin( )]
x d
) ,
x dx
= n/T.
n
. Also, we
0
, where
0
, (n = 1,
,
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