Digital Signal Processing Reference
In-Depth Information
Four-stroke
Two-stroke
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1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0
0
0
500
1000
1500
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500
1000
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(a)
(b)
Figure 4.14 Time average spectrum
music concert be x
k
. Then the problem formulation is to decompose the this time
series as
x
k
¼
z
k
þ
z
k
...þ
z
k
¼
X
N
z
i
k
i
¼
1
Each time series z
i
k
corresponds to a specific instrument say violin as if they are
recorded using a seperate micro-phone. This problem is very complex and is very
important in replay proving a value to the listner.
4.8 Frequency Estimation via DFT
Signals are ordinarily monochromatic in nature, but discontinuities while acquiring
a signal or intentional phase variations cause its spectrum to spread. Under these
conditions it is difficult to estimate the frequency by conventional methods. Here we
demonstrate the use of a DFT instead of an adaptive notch filter (ANF), even though
there are other ways of tackling the problem. Problems of this type occur in
underwater signal processing, radar signal processing and array signal processing.
Making accurate frequency estimates is a significant problem. We consider an
example from radar signal processing.
4.8.1 Problem Definition
Let each signal record r
i
of length N be defined as
r
i
ð
k
Þ¼
X
j
¼
iN
1
sin
ð
2
fj
þ
i
Þð
k
j
Þ;
ð
4
:
32
Þ
j
¼ð
i
1
Þ
N
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