The contents are, Transformation of dependant and independant variable

1. By
Prof.N.S.Patil
Department of E&TC , SVERI's COE, Pandharpur

2. INDEX
 Elementary CT and DT signals
 Unit step signal
 Unit ramp signal
 Unit impulse signal
 Rectangular signal
 Exponential signal
 Signum signal
 Transformation on dependant and independent variable
(Operations on signals)
 Time Shifting
 Time scaling
 Time reversal
 Amplitude scaling
 Amplitude reversal
 Addition/Multiplication

3. Sr.
No
.
Signal Continuous Time Discrete time
4 Rectangular
signal
Mathematical expression
π(t)=1 for -0.5≤t≤0.5
=0 otherwise
----------

4. Sr.
No
Signal Continuous Time Discrete time
5 Exponential
signal
Mathematical expression
at
etx )(
at
etx 
)(
t
etx 0
)( 
n
anx )(

5. Sr.
No
.
Signal Continuous Time Discrete time
6 Signum
signal
Mathematical expression
sgn(t)=1 for t ≤ 1
= -1 for t ≥ -1
= 0 otherwise
Mathematical expression
sgn(t)=1 for n < 1
= -1 for n > -1
= 0 otherwise

6. Sr.
No
.
Signal Continuous Time Discrete time
7 Sinc
function
Mathematical expression
The normalized sinc function is the
Fourier transform of the
rectangular function with no scaling.
It is used in the concept of
reconstructing a continuous band
limited signal from uniformly spaced
samples of that signal
------
t
t
tx

sin
)( 

7. Transformation of dependant and
independent variable

8. Time shifting X(t)= x(t-T)
 If T=+ve, signal will be shifted towards Right
 If T=-ve, signal will be shifted towards Left

10. Time scaling X(t)= x(at)
 If a>1, signal will be compressed
If a<1 , signal will be expanded

12. Time reversal X(t)= x(-t)
 Exact mirror image of the signal will be obtained

13. Amplitude reversal x(t)= -x(t)

14. Amplitude scaling x(t)= a.x(t)
 Simply multiply by the scaling factor ‘a’ to amplitude

15. Addition/Multiplication
 Add/Multiply the amplitudes of given signal

16. 1. What is the obligatory sequence that need to be performed or
executed in time shifting ,scaling and time reversal operational
processes under the category of continuous time signals? (Marks :
02)
a. Time Shifting, Time Scaling & Time Reversal
b. Time Scaling, Time Reversal & Time Shifting
c. Time Shifting, Time Reversal & Time Scaling
d. Time Reversal, Time Scaling & Time Shifting
2. Any signal that exhibits symmetry on Y-axis is called as _______ (Marks : 01)
a. odd signal
b. even signal
c. periodic signal
d. exponential signal

17. Q. Solve the following.
1. x1[n]={1,1,2,3} and x2[n]={1,2,1,1}
Perform the following operations:
a) 2.x1[n]
b) x1[n]+x2[n]
c) x1[n].x2[n]
2. X[t]
n0 1 2 3
y(t)=x(2t+1.5)