made by shubhajit chatterjee

1. Topic : Impulse Response
Name : Shubhajit Chatterjee, Arendra Singh
Student Code : BWU/BEC/19/028,BWU/BEC/19/027
Course Name : signals and system
Course code : PCC-EC303
Program : Bachelor of Technology in Electronics & Communication Engineering
Semester : 3rd Semester

2. Electronics &Communication
Engineering Department
Impulse Signal
 An impulse signal has zero value,except t=0.It has
infinitely.
 High value at t=0.
 Small duration we get high amplitude.
 This signal denotes by (t).
(t)
t
t=0
X(t)
Impulse Response
systemInput Output
Impulse signal
x(t)= (t)
Impulse response
y(t)=h(t)
Impulse response is the behaviour of impulse signal.

3. Electronics &Communication
Engineering Department
F(s)= −𝛼
𝛼
𝑓(𝑡)𝑒−𝑠𝑡 𝑑𝑡
= −𝛼
𝛼
𝛿(𝑡)𝑒−𝑠𝑡 𝑑𝑡 [ℎ𝑒𝑟𝑒, 𝑓 𝑡 = 𝛿 𝑡 ]
= −𝛼
𝛼
𝛿(𝑡)𝑒−𝑠.0 𝑑𝑡 [Put, t=0]
= −𝛼
𝛼
𝛿(𝑡) 𝑑𝑡
=1
t
t =0
1
𝛿(𝑡)=1, t=0
=0, t≠0
-1
1 =𝛿(𝑡)𝛿(𝑡)=1 and

4. Electronics &Communication
Engineering Department
Impulse response in time domain
System
h(t)
y(t)x(t)
Where, y(t)=h(t) * x(t)
Impulse response in laplace domain
System
h(s)
y(s)x(s)
Where, y(s)=h(s) * x(s)

5. Electronics &Communication
Engineering Department
R(s) C(s)
System
T(s)
Gain in transfer T(s)=
Numerator
Denominator
=
c(s)
R(s)
 If numerator is zero then , gain is zero. It called zero of
the system.
 If denominator is zero then , gain is infinity. It called
pole of the system.

6. Electronics &Communication
Engineering Department
Let us take a example:
4(𝑠 + 2)
(𝑠 + 4)(𝑠 + 5)
T(s)=
If is zero,so
4(s+2)=0
s=-2
If Denominator is zero,so
(s+4)(s+5)=0
s=-4,-5
Numerator
-5 -4 -3 -2 -1 0
 
• If any system has only one pole
then that is called first order
system.
• Similarly , two pole=two order
system.

7. Electronics &Communication
Engineering Department
• Consider the following 1st order system
R(s) C(s)
𝐾
𝑇𝑠 + 1
Considering T(s)=
𝐾
𝑇𝑠 + 1
We know,
C(s)=T(s)*R(s)
=T(s) [ R(s)= 𝛿(𝑠)=1 ]
C(s)=
𝐾
𝑇𝑠 + 1



8. Electronics &Communication
Engineering Department
C(s)=
𝐾
𝑇𝑠 + 1
• Re-arrange following equation as:
C(s)=
𝐾
𝑇
𝑠 + 1
𝑇
 In order to compute the response of the system in time
domain we need to compute inverse Laplace transform of
the above equation.
If t ∞,
=0 & c(t) =0
So , this called decaying
exponential.
C(t)
Time
Devided Numerator & Denominator by T,

9. Electronics &Communication
Engineering Department
(t)
0
t
u(t)
t
0
𝑑𝑢(𝑡)
𝑑𝑡
= (t)
u(t)
(t)
(t) 𝑑𝑡 = u(t)
Differentiation
Integration

10. Electronics &Communication
Engineering Department
• The step response of the first order system is
C(t)=K(1-𝑒−𝑡/𝑇)=K-K𝑒−𝑡/𝑇
• Differentiating c(t) with respect to t yields
𝑑𝑐(𝑡)
𝑑𝑡
=
𝑑
𝑑𝑡
(K-K𝑒−𝑡/𝑇
)
=
𝐾
𝑇
𝑒−𝑡/𝑇
Relation Between Step and impulse response

11. Electronics &Communication
Engineering Department
Benefits of Impulse Response :
 loudspeaker
 Electronics processing
 Control system
 audio application

12. Electronics &Communication
Engineering Department
Thank you