### Lecture 2

```Analog-To-Digital convertor
 Sampler
 Quantization
 Coding.
Analog signal
Sampler
Discrete time
signal
Quantized signal
Quantizes
Codes
Digital signal
Sampling of analog signal
This is the conversion of a continuous-time signal into
discrete-time signal obtained by taking samples of the
continuous-time signal at discrete-time instant
Quantization of Continues –Amplitude Signals
…
Quantizer convert the continouse amplitude into
finite sets of discrete value called quantization level
There is an error due to this conversation called
quantization error
eq (n)  x q (n)  x(n)


2
 eq (n) 

2
The distance between the two levels is Δ and its
computed as
 
x max  x min
L 1
Example (1-3):- Consider the analog signal x(t) is an input to analog
to digital convertor ,what is the output of sampler and quantizer if
the sampling rate is 1Hz. Let the number of quantization level =11
Where , take only 9 samples.
Coding of Quantized Samples
With a word length of b bit we can create different binary numbers
Digital-To-Analog converters
Discrete time signals
representation of the discrete time signal
1. Functional representation, such as
1

x(n)   4
0

for n  1,3 

for n  2 
otherwise 
2. Tabular representation , such as
n
x (n )
… -2 -1 0 1 2 3 …..
… 0 0 0 1 4 1 ….
…..
3. Sequence representation
An infinite-duration signal or sequence with the time origin
(n=0) indicated by the symbol ↑ is represented as
x ( n )   , 0 , 0 ,1, 4 ,1,8 , 3 , 0 , 0 ,  
Some elementary discrete time signals
1. The unit sample sequence is denoted as δ(n) and is defined as
n  0

n  0
1
 (n)  
0
2. Unit step signal- it is denoted as u(n) and is defined as
u (n) 
1
0
n 0
n 0
3.Unit ramp signal :-it is denoted as r(n)and is defined as
n
r (n)  
0
n  0

n  0
… (2.9)
4.Exponential function: - an exponential sequence is defined by
x(n)  a
n
… (2.10)
b. Amplitude modification of discrete time signal
Amplitude scaling
The sum of two signals
The product of two signals
H.w : For the signal shown below ,sketch the following signals
X(n-2)
X(n+3).δ(n-2)
X(n-1)+u(-n+1)
Classification of discrete time signal
Even and Odd signals:A real-valued signal is said to be even if for all n
x(n) = x(-n)
Whereas a signal is said to be odd if for all n
x(n) = -x(-n)
X(n)=xe(n)+xo(n)
To find the even part of x(n)
Whereas to find the odd part of x(n)
Example 2.3: - Find the even and odd parts of the following signal:
Periodic and Aperiodic Sequences
A signal x(n) is said to be periodic if and only if
x(n)=x(n+N) for all n.
Example 2.4: Determine if the following signal is periodic or not then
find its period
```