Chapter 3
Baseband Pulse And Digital Signalling
Under this topic we will look at the following:
1) analog
source
encode
>>>>>>>>>>>
baseband
pulse
signal
2) Approximation of analog signals with digital ones. How
close can we get
In our approximations
3) Processing of digital base-band signals to minimize their
bandwidth
Digital signaling is popular due to low cost of digital circuitry and the fact
that various digital data can be easily merged.
We will try to concentrate on the following four points:
1.
Study how analog waveform can be converted into digital
waveforms . Most
popular technique is pulse code modulation (PCM)
2.
Computing the Spectrum of digital signals
3.
Filtering of pulse signals and how it affects our ability to
recover the digital information at the receiver. What is
Inter Symbol Interference (ISI)
4.
Multiplexing of several digital bit streams into one high-speed
digital stream. Time Division Multiplexing (TDM)
Pulse Amplitude Modulation (PAM)
Pulse amplitude modulation (PAM) is an engineering term that is used to
describe the conversion of the analog signal to a pulse type signal where the
amplitude of the pulse denotes the analog information.
A PAM signal can be converted into a PCM (digital signal), which in turn
can be modulated onto a carrier in bandpass digital communications
systems.
Purpose of PAM signaling is to provide an other waveform that looks like
pulses yet contains the information that was present in the analog waveform.
There are two classes of PAM signaling
1. PAM that uses Natural Sampling (gating)
2. PAM that uses Instantaneous Sampling to produce flat-top pulse.
For Conversion to PCM type-2 is more useful. However, naturally sampled
type is easier to generate.
Natural Sampling (gating)
If w(t) is an analog signal band-limited to B Hz the PAM signal that uses
Natural sampling can be represented as:
ws(t) = w(t) s(t)
where,
s (t ) =
∞
 t − kTs 


∑ Π τ

k = −∞
is a rectangular wave that is acting
as the switching waveform
The spectrum of the gated PAM signal:
Ws ( f ) = W ( f ) ⊗ S ( f )
sin πnd
W ( f − nf s )
πnd
n = −∞
∞
Ws ( f ) = F {ws (t )} = d ∑
d=
τ
Ts
= duty cycle
Show
Proof of above statement
(page 130)
PAM waveform with natural-sampling requires the use of an analog switch
that is readily available in CMOS hardware {4016–quad bilateral switch}.
Note that PAM spectrum is zero for ±3fs, ±6fs etc ( d = 1/3) . The spectrum in
the harmonic band is nulled out by the sin(x)/x function.
Note that null bandwidth of the PAM signal is 3fs = 12B that is 12 times that
of the analog signal.
At the receiver the original waveform can be recovered from the PAM
signal, ws(t), by passing the PAM signal through a lowpass filter where the
cutoff frequency is:
B < f cuttoff < f s − B
B
fs-B
fs
The spectrum out of the lowpass filter will have the same shape as the
spectrum of the original signal only when fs >= 2B.
We can obtain our original PAM signal back by using a PRODUCT detector
as shown below:
the oscillator shifts the frequency band of the PAM signal that was centered
at nfs to baseband (i.e. f = 0 ) at the multiplier output.
Instantaneous Sampling (Flat-Top PAM)
Analog waveforms may also be converted into pulses by the use of Flat-Top
signaling as shown below:
Definition: If w(t) is an analog signal band limited to B hertz the
instantaneous sampled PAM signal is given by ;
ws (t ) =
∞
∑ w(kT )h(t − kT )
k = −∞
s
s
here , h(t) denotes the sampling pulse-shape, and for flat-top sampling the
pulse shape is:
 t  1
h(t ) = Π  = 
 τ  0
t <τ / 2
t >τ / 2
Spectrum for a flat-topped PAM signal is:
Ws ( f ) =
∞
1
H ( f ) ∑W ( f − kf s )
Ts
k = −∞
 sin πτf
here H ( f ) = F {h(t )} = τ 
 πτf
Show
Proof of above statement



(pages 134-135)
Spectrum of the flat-topped PAM signal is as shown below:
Transmission of either naturally or instantaneously sampled PAM over a
channel requires a very wide frequency response because of the narrow
pulse width.
Bandwidth required is much larger than that of the original signal. Noise
performance of PAM can not be better than the one achieved by transmitting
the analog signal directly. Hence PAM is not very suitable for long-distance
transmission.
However it provides a means for converting signals to a PCM signal.
Pulse Code Modulation (PCM)
Pulse code modulation is a special type of analog-to-digital conversion
where the information contained in the instantaneous samples of an analog
signal is represented by digital words in a serial bit stream.
If each word has n-binary digits there will be M = 2n unique code words.
Each codeword corresponds to an amplitude level.
We recall that each sample value from the analog signal can be any one of
an infinite number of levels, so the digital word that represents the amplitude
closest to the actual sampled value is used. This is called QUANTIZATION.
PCM is popular due to advantages listed below:
1. Inexpensive digital circuitry may be used extensively
2. PCM is suitable for merging with other digital data (TDM-Time
Division Multiplexing)
3. In long-distance digital telephone systems requiring repeaters a clear
PCM waveform can be regenerated at the output of each repeater.
4. Noise performance of digital systems are superior to that of analog
systems.
Sampling Quantizing and Encoding
A PCM signal can be generated by carrying out three basic operations
1. Sampling
2. Quantizing
3. Encoding
The quantizing operation is illustrated below for M = 8 levels. This
quantizer is called UNIFORM because all of the steps are of equal size.
Note: the peak value of the error (±1) is one half of the quantizer step size
(2).
The PCM signal is obtained by encoding each quantized sample value into a
digital word. It is up to the designer to specify the exact code word that will
represent a particular quantized level. Gray Code or Natural Code may be
used.
The above example uses binary code words. In general it is possible to use
multilevel signaling also.