Scribd
Upload
28 views13 pages

Introduction To DSP

The document discusses digital signal processing and related concepts. It defines digital signal processing as representing signals as discrete numbers and processing them using algorithms. It also defines sequences as discrete signals represented by numbers at distinct time values. Common sequences like impulse, step, and sinusoidal sequences are described. Linear time-invariant systems and their properties of linearity and time-invariance are covered. The impulse response and input-output relationship using convolution is also discussed.

Uploaded by

Ritam Majumder
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
28 views13 pages

Introduction To DSP

The document discusses digital signal processing and related concepts. It defines digital signal processing as representing signals as discrete numbers and processing them using algorithms. It also defines sequences as discrete signals represented by numbers at distinct time values. Common sequences like impulse, step, and sinusoidal sequences are described. Linear time-invariant systems and their properties of linearity and time-invariance are covered. The impulse response and input-output relationship using convolution is also discussed.

Uploaded by

Ritam Majumder
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
You are on page 1/ 13

DIGITAL SIGNAL PROCESSI NG

NAME:HRISHAV KARMAKAR
STREAM : ECE
SECTION : A
YEAR : 3RD YEAR
ACADEMIC YEAR : 2022-23
CONTENTS
Block diagram of a digital signal processing system showing
all the elements

What is digitalsignal processing?

What is a sequence? Show with proper diagram.


Examples of sequences. Digital impulse sequence, unit
step sequence, sinusoidal sequence, delayed sequences

Description of LTI system. Linearity and time invariance.

Impulse response of LTI system.

Input output relationship of an LTI system. Development of


convolution summation.
BLOCK DIAGRAM OF DSP
WHAT IS DIGITAL SIGNAL PROCE SSING?
Digital Signal Processing is the process of representing
signals in a discrete mathematical sequence of numbers
and analyzing, modifying, and extracting the information
contained in the signal by carrying out algorithmic
operations and processing on the signal.
WHAT IS A SEQUENCE?
The signals, which are defined at discrete times are known as discrete signals.
Therefore, every independent variable has distinct value. Thus, they are
represented as sequence of numbers.
The figure above depicts a discrete signal’s
discrete amplitude characteristic over a
period of time. Mathematically, these types
of signals can be formularized as;
∞ ∞
x={x[n]},− <n<
Where, n is an integer.
It is a sequence of numbers x, where nth number in the sequence is represented
as x[n].
EXAMPLE OF SEQUENCE S
1.Digital Impulse sequence
The discrete-time unit impulse function(n), also called unit sample sequence, is defined
as :
𝛿 (𝑛) = { 1 𝑓𝑜𝑟 𝑛 = 0
0 𝑓𝑜𝑟 𝑛 ≠ 0
This means that the unit sample sequence is a signal that is zero everywhere,
except at n = 0, where its value is unity.
The shifted unit impulse function(n – k) is defined as:
𝛿 (𝑛 − 𝑘) = { 1 𝑓𝑜𝑟 𝑛= 𝑘
0 𝑓𝑜𝑟 𝑛≠ k
2.UNIT STEP SEQUENCE
The step sequence is an important signal used for analysis of many discrete-
time systems. If a step function has unity magnitude, then it is called unit
step function.
The discrete-time unit step sequence u (n) is defined as :
U (n) = { 1 𝑓𝑜𝑟 𝑛 ≥ 0
0 𝑓𝑜𝑟 𝑛 < 0
The shifted version of the discrete-time unit step sequence u(n – k) is defined
as: U (n - k) = { 1 𝑓𝑜𝑟 𝑛 ≥ 𝑘
0 𝑓𝑜𝑟 𝑛 < k
3.SINUSOIDAL SEQUENCE
The discrete-time sinusoidal sequence is given by
∅
X(n) = A sin (𝜔𝑛 + )
Where A is the amplitude, 𝜔 is angular frequency,∅ is phase angle in
radians and n is an integer.
The period of the discrete-time sinusoidal sequence is:
N = 2𝜋/ 𝜔m
4.DELAYED SEQUENCE
Delayed unit step sequence
A sinusoidal sequence is the fundamental periodic signal having just one single
frequency.
LTI SYSTEM
A system that possesses two basic properties namely linearity and
time invariant is known as linear time-invariant system or LTI
system.

There are two major reasons behind the use of the LTI systems−

The mathematical analysis becomes easier.

Many physical processes through not absolutely LTI systems can


be approximated with the properties of linearity and time-
invariance.
IMPULSE RESPONSE OF LTI SYSTEM

Here, the input to the system is an impulse signal, i.e.,


𝑥(𝑛) = 𝛿(𝑛)
And the discrete-time impulse response of the system is,
𝑦(𝑛) = ℎ(𝑛) = 𝑇[𝛿(𝑛)]

According to the shifting property of signals, any signal can be expressed


as a combination of weighted and shifted impulse signal, i.e.,
THEREFORE, THE IMPULSE RESPONSEOF THE SYSTEM IS,

The expression of Eqn. (3) is known as convolution sum. The


convolution sum can be represented symbolically as,
𝑦(𝑛) = 𝑥(𝑛) * ℎ(𝑛) … (4)
Also,
THANK YOU

You might also like