Digital Signal Processing Reference
In-Depth Information
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(a) Sequences Poised for Correlation
(b) Correlation Sequence
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(c) Sequences Poised for Convolution
(d) Convolution Sequence
Figure 4.16:
(a) Signal sequence, samples 4-7, poised to be correlated with Impulse Response, samples
0-3; (b) Correlation sequence of sequences in (a); (c) Signal, (samples -4 to -1), properly flipped to be
convolved with Impulse Response, samples 0-3; (d) Convolution sequence of sequences in (c). Note the
symmetrical Impulse Response and hence the identical correlation and convolution sequences.
4.7
MATCHED FILTERING
Let's consider the problem of detecting an asymmetrically shaped time domain signal, such as a chirp.
A good way to detect such a waveform in an incoming signal is to make sure that during convolution, it
will correlate well with the impulse response being used. For this to happen, the impulse response will
need to be a time-reversed version of the signal being sought. The script
LV xMatchedF ilter(NoiseAmp, T stSeqLen, F lipI mpResp)
(see exercises below) illustrates this point. A typical call which reverses the chirp for use as an impulse
response in convolution is
LVxMatchedFilter(0.5,128,1)
where the parameter
FlipImpResp
is passed as 1 to reverse the chirp in time, or 0 to use it in non-
time-reversed orientation as the filter impulse response. Figure 4.18, plot (a), shows the test sequence, a
chirp being received with low frequencies occurring first, containing a large amount of noise, about to be
convolved with an impulse response which is the chirp in non-time-reversed format. Plot (b) of the same
