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.

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,

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

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

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

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

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.

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

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

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

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

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

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.

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

Below is the diagram showing the encoding format of the above