This document discusses analog-to-digital conversion techniques. It describes pulse code modulation (PCM) and delta modulation (DM) in detail. PCM involves sampling, quantization, and encoding an analog signal into digital form. It includes sampling the analog signal at discrete time intervals, dividing the signal amplitude range into discrete levels, and representing each level with a binary code. DM uses a simpler approach by only encoding changes in the analog signal level into a stream of 1s and 0s. While less complex than PCM, DM still introduces quantization error during conversion.

1. COMSATS UNIVERSITY OF SCIENCES AND TECHNOLOGY
29,OCT 2016
Analog-toDigitalConversion

2. Analog-to Digital Conversion
Analog-to-digital conversion is an electronic process in which a continuously variable (analog)
signal is changed, without altering its essential content, into a multi-level (digital) signal.
The input to an analog-to-digital converter (ADC) consists of a voltage that varies among a
theoretically infinite number of values. Examples are sine waves, the waveforms representing
human speech, and the signals from a conventional television camera. The output of the ADC, in
contrast, has defined levels or states. The number of states is almost always a power of two -- that
is, 2, 4, 8, 16, etc. The simplest digital signals have only two states, and are called binary. All
whole numbers can be represented in binary form as strings of ones and zeros.
CONVERSION TECHNIQUES:
There are two techniques.
 Pulse code modulation.
 Delta modulation.
Pulse code modulation:
Pulse code modulation is a most common method
used to convert an analog signal into a digital signal. So that it can be transmitted through a digital
communication network, and then converted back into the original analog signal.
The PCM process includes three steps:
1) Sampling
2) Quantization
3) Encoding
 SAMPLING:
Sampling is the process of reading the values of the filtered analogue signal at discrete time
intervals (i.e. at a constant sampling frequency, called the sampling frequency). A scientist called
Harry Nyquist discovered that the original analogue signal could be reconstructed if enough
samples were taken. He found that if the sampling frequency is at least twice the highest frequency
of the input analogue signal, the signal could be reconstructed using a low-pass filter at the
destination.

3. There are three sampling methods.
1) Ideal sampling
2) Natural sampling
3) Flat-top
 IDEAL SAMPLING:
Impulse (Ideal) sampling can be performed by multiplying input signal with impulse train 'T'. The
amplitude of impulse changes with respect to amplitude of input signal. You cannot use this
practically because pulse width cannot be zero and the generation of impulse train is not possible
practically.
 NATURAL SAMPLING:
Natural sampling is similar to impulse sampling, except the impulse train is replaced by pulse train
of period T. i.e. you multiply input signal to pulse train
 FLAT-TOP:
During transmission, noise is introduced at top of the transmission pulse which can be easily
removed if the pulse is in the form of flat top. Here, the top of the samples are flat i.e. they have
constant amplitude. Hence, it is called as flat top sampling or practical sampling.

4.  Sampling Rate:
According to the Nyquist theorem, to reproduce the original analog signal, one necessary condition
is that the sampling rate be at least twice the highest frequency in the original signals.
 A signal with infinite bandwidth cannot be sampled.
 Second the sampling rate must be at least 2 times the highest frequency, not the bandwidth.
 IF the analog signal is low pass, the bandwidth and the highest frequency have the same
value.
 QUANTIZATION:
Quantization, in digital signal processing, is the process of mapping a large set of input values to
a (countable) smaller set. Quantization is opposite to sampling. It is done on y axis. When you are
quantizing an image, you are actually dividing a signal into quanta (partitions). On the x axis of the
signal, are the co-ordinate values, and on the y axis, we have amplitudes. So digitizing the
amplitudes is known as Quantization.
The following are the steps in quantization:
 We assume that the original analog signal has instantaneous amplitude between Vmin and Vmax.
 We divide the range into L zones, each of height (delta).
 We assign quantized values of 0 to L-1 to the midpoint of each zone.
 We approximate the value of the sample amplitude to the quantized values.
The quantization process selects the quantization value from the middle of each zone .This means
that the normalized quantized values are different from the normalized amplitudes .The difference
is called the normalized error.
 QUANTIZATION LEVELS:
If the amplitude of a signal fluctuates between two values only, we need only two levels: if the
signal like voice has many amplitude values, we need more quantization levels .In audio digitizing,
level is normally chosen to be 256, in video it is normally thousands.
 QUANTIZATION ERROR:
The input values to the quantizer are the real values, the output values are the approximated
values .The output values are chosen to be the middle value in the zone .If the input value is also
at the middle of the zone, there is no quantization error; otherwise there is an error .The
quantization error changes the signal to noise ratio of the signal, which in turn reduces the upper
limit capacity according to Shannon.

5.  UNIFORM VS NON-UNIFORM QUANTIZATION:
For many applications, the distribution of the instantaneous amplitude in the analog signal is not
uniform. Changes in amplitude often occur more frequently in the lower amplitudes than in the
higher ones. For these types of application it is better to use non-uniform zones.
Non uniform quantization can also be achieved by using a process called companding and
expanding. Companding means reducing the instantaneous voltage amplitude for large values.
While expanding is the opposite process.
 ENCODING:
The last step in PCM is encoding .After each sample is quantized and the number of Bits per
sample is decided, each sample can be changed to an nb-bit code word. Note that the number
of bits for each sample is determined from the number of quantized levels. If the number
of quantization levels is L, the number of bits is nb=log2L.
Components of PCM decoder
 PCM Bandwidth:
The minimum bandwidth of a line-encoded signal is Bmin=cx N*(1/r).We substitute the value of N
in this formula
This mean the minimum bandwidth of the digital signal is nb times greater than the bandwidth of
the analog signal.
Delta Modulation (DM):
PCM is a very complex technique.Other technique have been developed to reduce the complexity
of PCM.The simplest is delta modulation.DM finds the change from the previous sample.

6.  MODULATOR:
The modulator is used at the sender site to create a stream of bits from an analog signal .The
process records the small positive or negative changes called delta .if the delta is positive the
process records a 1; if it is negative the process records 0.The modulator at each sampling interval,
compares the values of the analog signal with the last value of the staircase signal.
If the amplitude of the analog signal is larger, the next bit in the digital data is 1; otherwise it is
0.Note that we need a delay unit to hold the staircase function for a period between two
comparisons.
 DEMODULATOR:
The demodulator takes the digital data and using the staircase maker and the delay unit, creates the
analog signal .The created analog signal however need to pass through a low-pass filter for
smoothing.
 ADAPTIVE DM:
A better performance can be achieved if the value of delta is not fixed.In adaptive delta modulation
,the value of delta changes according to the amplitude of the analog signal.
 QUANTIZATION ERROR:
It is obvious that DM is not perfect.Quantization error is always introduced in the process.The
quantization error of DM ,however is much less than that for PCM.