This document discusses analog to digital conversion techniques. It explains that analog signals are continuous while digital signals are discrete. It also describes three main techniques in A/D conversion: sampling, quantization, and encoding. Sampling converts a continuous signal to discrete samples. Quantization maps samples to a smaller set of values, introducing quantization error. Encoding converts quantized values into a binary format.

2. A signal is the quantity that carry information and varies
with time, space, or any independent variable. It can
also be define as the function of two or more variable.
Analogue signal is continuous in nature, it differ from
digital in which a continuous quantity is represented by
a discrete function which can take on only one of the
finite number of values.

3. Man is by nature an analogue, he can interact and understand
only an analogue information. However analogue signal is
subjected to noise and distortion which progressively
degrade the signal-to-noise ratio. This degradation is
impossible to recover, since there is no sure way to
distinguish the noise from the signal, amplifying the signal
to recover attenuated parts of the signal amplifies the noise
as well. To avoid or minimise this scenario, and to take
advantage of the great capabilities available for digital data
storage,

4. processing, and computation, requires the conversion of
analog to digital. Hence, analog to digital (A/D)
conversion techniques have become extremely
important. There are three main technique involved in
the conversion of analog signals to digital signals,
these are:-
• Sampling of the continuous signal
• Quantization of the sampled signal, and
• Encoding. This can be explained below

5. sampling is the reduction of a continuous signal to
a discrete signal. A common example is the conversion
of a sound wave (a continuous signal) to a sequence of
samples (a discrete-time signal). Sampling of the signal
can be achieve with sample and hold circuit which can
be described below

6. The function of the sample and hold circuit is to sample
an analog input signal and hold this value over a
certain length of time for subsequent
processing. Below is the sampled and hold circuit

7. The operation of the sample and hold circuit can be explain in the
following steps
• During sample mode, the SOP behaves just like a regular op-amp, in
which the value of the output follows the value of the input.
• During hold mode, the MOS transistors at the output node of the SOP
are turned off while they are still operating in saturation, thus
preventing any channel charge from flowing into the output of the
SOP.
• In addition, the SOP is shut off and its output is held at high
impedance, allowing the charge on Ch to be preserved throughout
the hold mode

8. On the other hand, the output buffer of this S/H circuit is always
operational during sample and hold mode and is always providing
the voltage on Ch to the output of the S/H circuit.
The frequency at which the continuous signal is sample is explained
by the Nyquist and shannon in first half of 20th century.

9. Nyquist sampling theory provide the prescription for the minimal
sampling frequency required to avoid aliasing during the
reconstruction of the signal. It state that:-
The sampling frequency should be at least twice the highest
frequency contained in the signal, Or in mathematical terms:
fs ≥ 2 fc
where fs is the sampling frequency (how often samples are taken per
unit of time or space), and fc is the highest frequency contained in
the signal. Example if the maximum frequency component of a
signal to be sample is 2khz, the from nyquist sampling theory

10. This signal should be sampled at a frequency which is equal or grater
than 4khz. However if this signal is sample at a frequency below
this(nyquist rate), then aliasing will occur.
Aliasing is an effect that causes different signals to become
indistinguishable (or aliases of one another) when sampled It also
refers to the distortion that results when the signal reconstructed
from samples is different from the original continuous signal.
However this effect of aliasing can be eliminated by using anti-aliasing
filter

11. Quantization, is the process of mapping a large set of input values
to a (countable) smaller set – such as rounding values to some unit
of precision. A device or algorithmic function that performs
quantization is called a quantizer. The error introduced by
quantization is referred to as quantization error.
There are two main method of quantization which involved
• Truncation and
• Rounding

12. Rounding a numerical value means replacing it by another value
that is approximately equal but has a shorter, simpler, or more
explicit representation Rounding is often done to obtain a value
that is easier to report and communicate than the original. The
following table illustrated sampled values and it equivalent
quantized value using rounding technique.
s.no Sampled value of the signal. Quantized value
1 0.45 0.5
2 0.44 0.4
3 0.67 0.7
4 0.64 0.6
5 0.55 0.6

13. truncation is the term for limiting the number of digits right of
the decimal point by discarding the least significant ones.
However the error in this processing is twice than the rounding
method, below is the table showing the sampled value ofa signal
and it equivalent quantized value
s.no Sampled value of signal Quantized value using
truncation
1 3.3 3
2 4.2 4
3 5.3 5

14. The truncation and the rounding technique are important in analog to
digital conversion, but they result to quantization error. However the
quantization error can be minimise by increasing the resolution of the
conversion.

15. 1. The quantized signal is then encoded into a sequence of bits(0
and 1), there are different method for which the quantized signal
encoded into a bits sequence which can be explained below

17. Below is the diagram showing the encoding format of the above