Digital Signal Processing Reference
In-Depth Information
de ltaimpu ls e
Lo w p ass
High pass
complex FFT
Po la r /C ar te s
f-d omain
FF T c omplex
locus curve
j imaginary
Symmetrical amplitude- and phase spectrum
Amplitude
2, 00
2,5
Locus curve
1, 75
2,0
1, 50
1, 25
1,5
1, 00
0, 75
1,0
0, 50
0, 25
0,5
- 200 Hz
+ 200 Hz
0, 00
200
Phase
180
0
r esonance fr equency
200 Hz
0,0
real
150
100
-0,5
50
0
-1,0
-50
-100
-1,5
-150
- 180
0
-200
-2,0
-1,5
-1,0
-0,5
0,0
0, 5
1,0
1, 5
2,0
2,5
-500
-250
0
250
500
Hz
V
Illustration 310:
Locus curve/ frequency response of an oscillating circuit- like second order BESSEL-
filter
.
As the circuitry structure above shows, the oscillating circuit- like system was created by a series connec-
tion of low- pass and high- pass with a limiting frequency of 200Hz. Both filters are second order BESSEL-
filters. The information of amplitude and phase is contained in the locus curve
Thus it now emerges why it is sufficient to supply voltage and current in the following
form:
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
j
(
ωϕ
t
+
)
j
ϕ
j
ω
t
j
ω
t
j
(
ωϕ
t
+
)
j
ϕ
j
ω
t
j
ω
t
u
t
( )
=
Ue
=
Ue
e
=
U
e
and ( )
i t
=
Ie
=
Ie
e
=
I
e
u
u
i
i
The locus curve only has to be written
once
, not double.
Classification of signal processing systems
Theoretically and practically, a (signal processing) system is a mathematical model of one
or more physical processes which establishes a relation between input signal and output
signal. The system responds to a certain input signal.
In mathematics, we speak of a
transformation
or a
map
. This process is defined with the
help of an operator
T
, where the following applies :
y
=Τ
()
x
However straightforward this relation appears, different systems can vary greatly.
Illustration 309
shows a preliminary classification of different systems.
