563489578934

194
Baseband Pulse and Digital Signaling Chap. 3
Gaussian noise into the receiver, the effects of both ISI and channel noise are minimized if the
transmitter and receiver filters are designed so that [Sunde, 1969; Shanmugan, 1979; Ziemer
and Peterson, 1985]
and
ƒ H T (f) ƒ = 2|H e(f)| [ n (f)] 1>4
a|H(f)| 2|H c (f)|
(3–78a)
a3|H e (f)|
|H R (f)| =
(3–78b)
3H c (f) [ n (f)] 1>4
where P n (f) is the PSD for the noise at the receiver input and a is an arbitrary positive constant
(e.g., choose a = 1 for convenience). H e (f) is selected from any appropriate frequency
response characteristic that satisfies Nyquist’s first criterion as discussed previously, and H(f)
is given by Eq. (3–63). Any appropriate phase response can be used for H T (f) and H R (f), as
long as the overall system phase response is linear. This results in a constant time delay versus
frequency. The transmit and receive filters given by Eq. (3–78) become square-root raised
cosine-rolloff filters for the case of a flat channel transfer function, flat noise, and a raised
cosine-rolloff equivalent filter.
Nyquist’s Second and Third Methods for Control of ISI
Nyquist’s second method of ISI control allows some ISI to be introduced in a controlled
way so that it can be canceled out at the receiver and the data can be recovered without error
if no noise is present [Couch, 1993]. This technique also allows for the possibility of
doubling the bit rate or, alternatively, halving the channel bandwidth. This phenomenon
was observed by telegraphers in the 1900s and is known as “doubling the dotting speed”
[Bennett and Davey, 1965].
In Nyquist’s third method of ISI control, the effect of ISI is eliminated by choosing h e (t)
so that the area under the h e (t) pulse within the desired symbol interval, T s , is not zero, but the
areas under h e (t) in adjacent symbol intervals are zero. For data detection, the receiver evaluates
the area under the receiver waveform over each T s interval. Pulses have been found that
satisfy Nyquist’s third criterion, but their performance in the presence of noise is inferior to
the examples that were discussed previously [Sunde, 1969].
3–7 DIFFERENTIAL PULSE CODE MODULATION
When audio or video signals are sampled, it is usually found that adjacent samples are close
to the same value. This means that there is a lot of redundancy in the signal samples and,
consequently, that the bandwidth and the dynamic range of a PCM system are wasted when
redundant sample values are retransmitted. One way to minimize redundant transmission and
reduce the bandwidth is to transmit PCM signals corresponding to the difference in adjacent
sample values. This, crudely speaking, is differential pulse code modulation (DPCM). At the