Download Lecture Notes in Digital Communications: Sampling & Pulse Modulation and more Study notes Electrical Engineering in PDF only on Docsity!
Lecture Notes in “Digital Communications” Sampling & Pulse Modulation
Electrical Engineering | University of Anbar by: Dr. Mohammed AlMahamdy
1.7 PCM QUALITY VERSUS REQUIRED RATE
In addition to the channel effects, PCM performance depends primarily on the quantization
noise. To make the reconstructed signal like the original baseband signal we must reduce the
quantizing noise by increasing 𝐿. Now, we learned that increasing the number of quantization
levels requires more bits per sample to be transmitted. Large 𝑙 is not perfect for crowded
channels and due to some channel’s limitations. So, beside the non-uniform quantization,
several techniques are used to reduce the quantization noise at the same number of the L.
1.8 BANDWIDTH REDUCTION TECHNIQUES
The channel bandwidth is limited, and it is a valuable resource. A frequent objective of the
communications engineer is to transmit the maximum information rate via the minimum
possible bandwidth. This is especially true for radio communications in which radio spectrum
is a scarce, and therefore valuable, resource. The following systems are used to maintain the
same coding fidelity using fewer bits per sample.
1.8.1 Delta PCM
Because the samples of most of the baseband signals are highly correlated, it is possible to
transmit the information about the changes between samples instead of sending the sample
values themselves. A simple way for such systems is the Delta PCM. This method transmits the
difference between adjacent samples through code words. This difference is significantly less
than the actual sample values, hence it is coded using fewer binary symbols per word than the
conventional PCM. However, Delta PCM systems cannot accommodate rapidly varying transient
signals.
+
_
Sampler
Delay
T
S
PCM
Encoder
Delta
PCM
+
Delta
PCM
Delay
T
S
PCM
Decoder
Output
Signal
Delta PCM
Encoder
Delta PCM
Decoder
Input
Signal
Sampling & Pulse Modulation Lecture Notes in “Digital Communications”
by: Dr. Mohammed AlMahamdy Electrical Engineering | University of Anbar
1.8.2 Deferential PCM
Since neighbor samples within many information signals are highly correlated, Deferential PCM
(DPCM) uses an algorithm to predict future values. Such algorithms monitor the trend of the
baseband samples and use some models to predict the value of the incoming samples. Then
DPCM waits until the actual value becomes available for examination and transmits the
correction to the already predicted value. The correction signal represents the information
signal’s unpredictable part. By this means, DPCM reduces the redundancy in signal and allows
the information to be transmitted using fewer symbols, less spectrum, and shorter time.
1.9 DELTA MODULATION (DM)
If the quantizer of the DPCM system is restricted to one bit (i.e. the two levels only: ±∆) and the
predictor to one sample delay, then the resulting scheme is called DM. The information signal
is represented by a stepped waveform. The resolution of this waveform depends on ∆ & 𝑇 𝑠
values.
_
Sampler
Predictor
Encoder
DPCM
signal
DPCM
signal
Predictor
Decoder
Output
Signal
DPCM
Encoder
DPCM
Decoder
Input
Signal
Quantizer
Smoothing
Filter
_
DM
signal
Sampler
Delay
T
S
DM
signal
Input
Signal
Delay
T S
Output
Signal
Smoothing
Filter
DM
Encoder
DM
Decoder
Sampling & Pulse Modulation Lecture Notes in “Digital Communications”
by: Dr. Mohammed AlMahamdy Electrical Engineering | University of Anbar
However, we can calculate the optimum values for these parameters that overcome the slop-
overload problem. An estimate of the rate-of-rise condition for DM may be obtained quit easily
for sinusoidal modulation. Let the input be 𝑔
= 𝑏 cos
𝑚
, so that:
max [
] = 2 𝜋𝑏𝑓
𝑚
= maximum slop of this signal.
Since the maximum rate-of-rise =
∆
𝑇
𝑠
𝑠
, then
𝑠
𝑚
𝑠
𝑚
𝑠
𝑚
The above 𝑓
𝑠
condition may be applied to band-limited signals by letting 𝑓
𝑚
be the highest
frequency component, and 𝑏 = max|𝑔(𝑡)|.
Since the quantization noise: 𝑒
2 ̅̅̅
𝑒
2
2 ∆
∆
−∆
∆
2
3
Lecture Notes in “Digital Communications” Sampling & Pulse Modulation
Electrical Engineering | University of Anbar by: Dr. Mohammed AlMahamdy
And by filtering this noise to a bandwidth 𝐵, we get: 𝑁
𝑞
𝑞
∆
2
𝐵
3 𝑓
𝑠
The mean-square value of the information signal is:
2
𝑝
2
2
𝑠
𝑚
2
∴ SN
q
R =
𝑠
3
2
𝑚
2
Adaptive Delta Modulation
We have seen that: a large step size causes unacceptable quantization noise, and a small step
size results in sample-overload distortion. This means that a good choice for ∆ is a “medium”
value, but in some cases, the performance of the best “medium” values is not satisfactory. An
approach that works well in these cases is to change the step size according to changes in the
input: if the input tends to change rapidly, the step size is chosen to be large (and vice versa).
So, the output can follow the input quickly without distortion.
Errors in DM
If the SNR is not sufficiently high, then the DM receiver will occasionally interpret a received
symbol in error (i.e. +∆ instead of −∆ or the converse), and this is equivalent to the addition of
an error of 2 ∆ to the accumulated signal at the DM receiver, as shown below. This situation
continues until another error occurs which either cancels the first error or double it!
DM is primarily used for telemetry systems and speech transmission in telephone. It has been
found that: PCM is preferable for high quality speech transmission, whereas DM is easier to
implement and yields transmission of acceptable quality.
Adaptive DM
