563489578934

Sec. 2–7 Bandlimited Signals and Noise 93
T 0
T s = 1 ––– fs
t
(a) Waveform and Sample Values
t
(b) Waveform Reconstructed from Sample Values
Figure 2–17
Sampling theorem.
reconstructed from the sample values by the use of Eq. (2–169). That is, each sample value is
multiplied by the appropriate (sin x)/x function, and these weighted (sin x)/x functions are
summed to give the original waveform. This procedure is illustrated in Fig. 2–17b. The minimum
number of sample values that are needed to reconstruct the waveform is
N = T 0
1/f s
= f s T 0 Ú 2BT 0
(2–170)
and there are N orthogonal functions in the reconstruction algorithm. We can say that N is
the number of dimensions needed to reconstruct the T 0 -second approximation of the
waveform.
Impulse Sampling and Digital Signal Processing
Another useful orthogonal series is the impulse-sampled series, which is obtained when the
(sin x)/x orthogonal functions of the sampling theorem are replaced by an orthogonal set of
delta (impulse) functions. The impulse-sampled series is also identical to the impulsesampled
waveform w s (t): Both can be obtained by multiplying the unsampled waveform by a
unit-weight impulse train, yielding