Digital Signal Processing Reference
In-Depth Information
of injecting rise times as fast as 9-25 ps into a test structure, which can approxi-
mate a step function. The unit step function is the integral of the impulse function
(Dirac delta function),
t
u
s
(τ )
=
δ(t) dt
(8-11a)
−∞
du
s
(t)
dt
=
δ(t)
(8-11b)
where
δ(t)
is the impulse function and
u
s
(t)
is the unit step function.
8.1.5 Single-Bit (Pulse) Response
Perhaps the most useful means to characterize a channel in the time domain
is to use the
single-bit response
, also known as the
pulse response
. The utility
of the pulse response, as opposed to the impulse response, is that it is directly
measurable in the laboratory. The pulse response is obtained by driving a system
with a waveform that corresponds to a single digital bit of information for the
system being designed.
The
data rate
(DR) is defined as the maximum number of bits per seconds
the system will support. This means that the maximum data rate is determined
by the width of a single bit:
1
t
bit
DR
=
(8-12a)
where
t
bit
is the width of a single data bit, as shown in Figure 8-10a. Some-
times,
t
bit
is referred to as a
unit interval
(UI). This means that the maximum
fundamental frequency of the digital pulse train, where alternating bits of 1 and
0 are transmitted sequentially, is half the data rate, as shown in Figure 8-10b:
1
2
t
bit
f
fundamental
=
(8-12b)
The pulse response is more practical than the impulse response for two reasons.
First, the pulse response will give the engineer an intuitive feeling of how the
bus will operate because it represents how the system will respond to an actual
waveform that will be propagating on the bus. Second, it can be used to calcu-
late the worst-case eye and the worst-case bit pattern using the peak distortion
analysis, which is described in Chapter 13.
Analytically, the pulse response is calculated by convolving the input wave-
form with the system impulse response in the time domain. It is usually more
convenient to perform the convolution in the frequency domain,
Y(ω)
= F{
x
pulse
(t)
}·
H(ω)
(8-13a)
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