Digital Signal Processing Reference
In-Depth Information
nite number of sinusoidal signals of a certain amplitude, phase and fre-
quency.
The time domain signal is obtained by adding together all the sinusoidal
signals at every point in time, i.e. the original signal is obtained from the
superposition. A spectrum analyzer, however, only shows us the informa-
tion about the amplitude or power of these sinusoidal part-signals, the
harmonics.
A periodic time domain signal can be resolved into its harmonics
mathematically by means of Fourier Analysis (Fig. 6.1.). This signal,
which can have any shape, can be thought of as being composed of the
fundamental wave which has the same period length as the signal itself,
and of the harmonics which are simply multiples of the fundamental. In
addition, each time domain signal also has a certain DC component. This
direct voltage corresponds to a zero frequency. Non-periodic signals can
also be represented in the frequency domain. but non-periodic signals do
not have a line spectrum but a continuous spectrum. Thus, the spectral
band contains spectral lines not only at certain points but at any number of
points.
+∞
∫
−
j
Π
2
ft
H
(
f
)
=
h
(
t
)
e
dt
;
Fourier Transform (FT)
−
∞
∞
∫
j
Π
2
ft
h
(
t
)
=
H
(
f
)
e
df
;
Inverse Fourier Transform (IFT)
−
∞
Time domain
Frequency domain
Re(f)
h(t)
F
T
IF
T
f
H(f)
Im(f)
time
f
Fig. 6.2.
Fourier Transform
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