Digital Signal Processing Reference
In-Depth Information
1
15
0.5
10
0
5
−0.5
0
−1
0
10
20
30
0
1
2
3
4
5
(a) Sample
(b) Freq of 2nd Cosine
1
15
0.5
10
0
5
−0.5
0
−1
0
10
20
30
0
1
2
3
4
5
(c) Sample
(d) Freq of 2nd Sine
Figure 4.4:
(a) First cosine,
k
1 = 3; (b) CZL between first and second cosines, the second cosine frequency
k
2 varying between 0 and 5 cycles per 32 samples; (c) First sine,
k
1 = 3; (d) CZL between first and second
sines, the second sine frequency
k
2 varying between 0 and 5 cycles per 32 samples.
The call
s = LVSumCE(2,32)
for example, yields the sum as
s
= -3.3307e-016, which differs from zero only by reason of computer
roundoff error, whereas a call in which the frequency argument is equal to
N
, such as
s = LVSumCE(32,32)
yields
s
= 32.
4.3.5 IDENTIFYING SPECIFIC SINUSOIDS IN A SIGNAL
We now consider the problem of identifying the presence or absence of sinusoids of specific frequency
and phase in a signal. We begin the discussion with a specific problem set forth in the following example.
[
]
[
+
]
[
+
]
Example 4.7.
where
n
is the sample index,
N
is the sequence length,
θ
is a variable phase which may assume the values 0,
π/
4,
π/
2,3
π/
4,or
π
radians. Devise a way to determine the signal present in
A
A sequence
A
n
can assume the values of 0, sin
2
πn/N
θ
,orsin
4
πn/N
θ
[
n
]
using correlation.
Let's consider several cases to see what the difficulties are:
