Digital Signal Processing Reference
In-Depth Information
4
3
2
1
0
−1
−2
−3
−4
−8
−6
−4
−2
0
2
4
6
8
Lag
Figure 4.11:
The autocorrelation sequence of the sequence sin(2
π
[0:1:7]/8) plotted against Lag number.
Note that the largest value of positive correlation occurs at the zeroth lag when the waveform lies squarely
atop itself. This results in every overlying sample pair having a positive product, which in turn results in
a large positive sum or correlation value.
LVCorrSeqSinOrthog(32,128,1,12,0)
yields Fig. 4.14. Again, once the two sequences are in saturation, the output is zero. In this case, the longer
sequence (128 samples in all) exhibits a sinusoidal waveform having three cycles over every 32 samples,
as opposed to the shorter sequence (32 samples in all), which has only one cycle over its 32 samples. The
frequencies (over 32 samples) are thus 1 and 3; they differ by the integer 2.
Example 4.14.
Devise a sequence (i.e., correlator) that will yield steady state correlation sequence values
of 0 when correlated with the sequence
[1,0,-1,0,1,0,-1,0,1,0,-1,0]
Observe that the given sequence is in fact the half-band frequency, a sinusoid showing one full
cycle every four samples. Sinusoids showing 0 or 2 cycles over four samples will be orthogonal and will
yield steady-state correlation values of zero. Two possible sequences are therefore [1,1,1,1] and [1,-1,1,-1].
Two more possible sequences are [-ones(1,4)] and [-1,1,-1,1].
Example 4.15.
Devise several correlators each of which will eliminate from the correlation sequence
(in steady state) most of the high frequency information in the following test sequence.
