Digital Signal Processing Reference
In-Depth Information
A
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(b)
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12 3
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(h)
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012
…
−4
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(i)
(j)
Fig. 12.1. Graphical derivation of the discrete Fourier transform pair. (a) Original CT signal. (b) CTFT of the
original CT signal. (c) Impulse train sampling of CT signal. (d) CTFT of the impulse train in part (c). (e) CT
sampled signal. (f) CTFT of the sampled signal in part (e). (g) DT representation of CT signal in part (a).
(h) DTFT of the DT representation in part (g). (i) Rectangular windowing sequence. (j) DTFT of the
rectangular window. (k) Time-limited sequence representing part (g). (l) DTFT of time-limited sequence in
part (k). (m) Inverse DTFT of frequency-domain impulse train in part (n). (n) Frequency-domain impulse
train. (o) Inverse DTFT of part (p). (p) DTFT representation of CT signal in part (a). (q) Inverse DFT of part
(r). (r) DFT representation of CT signal in part (a).
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