Digital Signal Processing Reference
In-Depth Information
+
+
+
+
+
7
g7
+
+
−
Sum3
1
z1
1
z
1
z
1
z
1
z
1
1
12
1/35
z
g1
sig_out
sig_in
g8
z2
z3
z4
z5
Sum2
+
+
+
+
+
+
10
g2
8
g3
6
g4
4
g5
2
g6
Sum1
Figure 3.33 Moving linear regression
The parameter p has a direct relationship with the frequency. We can see that the
initial conditions of this difference equation uniquely determine the amplitude and
phase of the desired noise-free sine wave. Now we aim at finding out the initial
conditions of this difference equation that generate the best-fit sine wave matching
the noisy generated sine wave (Figure 3.34). To formulate this problem, we choose
to write it as
¼
x
k
1
x
k
2
or
x
k
x
k
1
p
1
10
x
k
¼ x
k
1
:
ð
3
:
59
Þ
4
Estimated signal
2
0
−
2
−4
0
10
20
30
40
50
60
70
80
90
100
Samples
Figure 3.34 Fitting a sine curve to a noisy signal
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