Digital Signal Processing Reference
In-Depth Information
Fig. D.6 Implementation of
the sinusoidal digital
oscillator
sin (
b
)
y
(
n
)
δ
(
n
)
z
−1
2 cos(
b
)
z
−1
− 1
H
(
z
)
Im ( z )
b =
Ω
o
Re ( z )
− b
Ω
=
−
0
Ω
o
Ω
o
−
π
π
ω
T
s
Fig. D.7
PZ-diagram and frequency response of the sinusoidal digital oscillator
diagram of this system. The pole-zero diagram and frequency response are shown
in Fig.
D.7
.
MATLAB Simulation
In this experiment we will design a second-order IIR filter to perform as a
sinusoidal oscillator.
Task 1
The generated sinusoid has an amplitude A = 1 and frequency f
o
= 1 Hz. Choose
the sampling frequency of the system as f
s
= 100 Hz (f
s
f
o
). Write the transfer
function of the system as in Eq.
1
above, from which find the frequency response
of the system and plot it.
Task 2Now analyze the system using
zplane
function on MATLAB. Find the
poles of the system using
roots
. Find the angles of these poles, from which find
the frequency of the oscillator.
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