Digital Signal Processing Reference
In-Depth Information
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(a) Test Sequence, a Chirp
(b) Impulse Response
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(c) Correlation Sequence
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(d) Convolution Sequence
Figure 4.17:
(a) Test Linear Chirp, 0 to 512 Hz in 1024 samples; (b) Asymmetric Impulse Response;
(c) Correlation Sequence; (d) Convolution Sequence.
figure shows the entire convolution sequence, in which no distinctive peak may be seen. Contrast this to
the case in which the impulse response is the chirp in time-reversed format, as shown in Fig. 4.19.
4.8 ESTIMATING FREQUENCY RESPONSE
We've seen above how to determine the frequency content or response of a signal at discrete integral
frequencies using Eqs. (4.11) and (4.12). It is also possible to perform similar correlations at as many
frequencies as desired between 0 and the Nyquist limit for the signal, leading to a more detailed estimate
of the frequency response of a test signal when, for example, considered as a filter impulse response.
The following code will estimate the frequency response at a desired number of evenly spaced frequency
samples between 0 and the Nyquist limit for the test signal. The loop (four indented lines) may be
replaced with the commented-out vectorized code line immediately following. The cosine- and sine-
based correlations are done simultaneously with one operation by summing the two correlators after
multiplying the sine correlator by -
j
. The result from making the call
LVFreqResp([1.9,0,-0.9,0,1.9,0,-3.2],500)
is shown in Fig. 4.20 (the test signal is the same as that used in Fig. 4.17, in which the frequency response
was estimated using a linear chirp).
