The document discusses various operations that can be performed on continuous time signals, including shifting, scaling, reflection, and decomposing a signal into its even and odd parts. It provides examples of applying each operation to a sample signal and includes the corresponding Matlab code. Key operations covered are shifting a signal by adding a time delay, compressing or expanding a signal through scaling, flipping the signal vertically through reflection, and extracting the even and odd parts of a signal based on their symmetry properties.

1. Operations on continuous time
signals

2. Presented By
Mahruf Zaman Utso
044
Md. Iftekhar Ahmed Nasim
117
Shanawaz Ahmed
103

3. Overview:
Introduction
Operations
Conclusion

4. What is signal ?
-In electrical engineering, the fundamental quantity of
representing some information is called a signal. It does
not matter what the information is i-e: Analog or digital
information. In mathematics, a signal is a function that
conveys some information.
Types of signal:
1. Continuous time signal.
2. Discrete time signal.
Introduction:

5. Continuous time signal :

6. Operation on signal:
1. Shifting.
2. Reflection.
3. Scaling.
4. Symmetric or not.
5. Even part of the signal.
6. Odd part of the signal.

7. Consider a signal :
Graphical Expression of the signal:
𝒙 𝒕 =
𝒕 + 𝟑 , −𝟑 ≤ 𝒕 ≤ −𝟐
𝟏 , −𝟐 < 𝒕 ≤ −𝟏
𝒕 + 𝟐 , −𝟏 < 𝒕 ≤ 𝟎
−𝟑𝒕 + 𝟐 , 𝟎 < 𝒕 ≤ 𝟏
−𝟏 , 𝟏 < 𝒕 ≤ 𝟐
𝒕 − 𝟑 , 𝟐 < 𝒕 ≤ 𝟑
𝟎, 𝒐𝒕𝒉𝒆𝒓𝒘𝒊𝒔𝒆
-4 -3 -2 -1 0 1 2 3 4
-4
-3
-2
-1
0
1
2
3
4
x(t)
y(t)

8. t=-6:0.001:6;
x=zeros(size(t));
t1= t>=-3 & t<=-2;
x(t1)=t(t1)+3;
t2= t>-2 & t<=-1;
x(t2) = 1;
t3 = t>-1 & t<=0;
x(t3) = t(t3)+2;
t4 = t>0 & t<=1;
x(t4) = -3*t(t4)+2;
t5 = t>1 & t<=2;
x(t5) = -1;
t6 = t>2 & t<=3;
x(t6) = t(t6)- 3;
plot(t,x);
xlim([-4 4]);
ylim([-4 4]);
grid on;
Matlab Source code:

9. Shifting operation:
x (t-t0) represent a time-shifted version of x(t).
If t0>0 then the signal is delayed by t0 second.
If t0 <0 then the signal represent the advanced
replica of x (t).

10. Shifting operation:
𝒙 𝒕 + 𝟐 =
𝒕 + 𝟓 , −𝟓 ≤ 𝒕 ≤ −𝟒
𝟏 , −𝟒 < 𝒕 ≤ −𝟑
𝒕 + 𝟒 , −𝟑 < 𝒕 ≤ −𝟐
−𝟑𝒕 − 𝟒 − 𝟐 < 𝒕 ≤ −𝟏
−𝟏 , −𝟏 < 𝒕 ≤ 𝟎
𝒕 − 𝟏 , 𝟎 < 𝒕 ≤ 𝟏
𝟎, 𝒐𝒕𝒉𝒆𝒓𝒘𝒊𝒔𝒆
𝒙 𝒕 =
𝒕 + 𝟑 , −𝟑 ≤ 𝒕 ≤ −𝟐
𝟏 , −𝟐 < 𝒕 ≤ −𝟏
𝒕 + 𝟐 , −𝟏 < 𝒕 ≤ 𝟎
−𝟑𝒕 + 𝟐 , 𝟎 < 𝒕 ≤ 𝟏
−𝟏 , 𝟏 < 𝒕 ≤ 𝟐
𝒕 − 𝟑 , 𝟐 < 𝒕 ≤ 𝟑
𝟎, 𝒐𝒕𝒉𝒆𝒓𝒘𝒊𝒔𝒆

11. Shifting operation:
-4 -3 -2 -1 0 1 2 3 4
-4
-3
-2
-1
0
1
2
3
4
x(t)
y(t)
-6 -5 -4 -3 -2 -1 0 1 2
-4
-3
-2
-1
0
1
2
3
4
x(t)
y(t)

12. Matlab Source Code:
t=-6:0.001:6;
x=zeros(size(t));
t1= t>=-5 & t<=-4;
x(t1)=t(t1)+5;
t2= t>-4 & t<=-3;
x(t2) = 1;
t3 = t>-3 & t<=-2;
x(t3) = t(t3)+4;
t4 = t>-2 & t<=-1;
x(t4) = -3*t(t4)-4;
t5 = t>-1 & t<=0;
x(t5) = -1;
t6 = t>0 & t<=1;
x(t6) = t(t6)- 1;
plot(t,x);
xlim([-6 2]);
ylim([-4 4]);
grid on;

13. Scaling operation:
x (Ƞt) is the scaled version of x(t). If |Ƞ|>1 then x (Ƞt) is the
compressed version. If |Ƞ|<1 then x (Ƞt) is the expended signal.
𝒙 𝒕 =
𝒕 + 𝟑 , −𝟑 ≤ 𝒕 ≤ −𝟐
𝟏 , −𝟐 < 𝒕 ≤ −𝟏
𝒕 + 𝟐 , −𝟏 < 𝒕 ≤ 𝟎
−𝟑𝒕 + 𝟐 , 𝟎 < 𝒕 ≤ 𝟏
−𝟏 , 𝟏 < 𝒕 ≤ 𝟐
𝒕 − 𝟑 , 𝟐 < 𝒕 ≤ 𝟑
𝟎, 𝒐𝒕𝒉𝒆𝒓𝒘𝒊𝒔𝒆
𝒙 𝟐𝒕 =
𝟐𝒕 + 𝟑 , −𝟏. 𝟓 ≤ 𝒕 ≤ −𝟏
𝟏 , −𝟏 < 𝒕 ≤ −𝟎. 𝟓
𝟐𝒕 + 𝟐 , −𝟎. 𝟓 < 𝒕 ≤ 𝟎
−𝟔𝒕 + 𝟐 , 𝟎 < 𝒕 ≤ 𝟎. 𝟓
−𝟏 , 𝟎. 𝟓 < 𝒕 ≤ 𝟏
𝟐𝒕 − 𝟑 , 𝟏 < 𝒕 ≤ 𝟏. 𝟓
𝟎, 𝒐𝒕𝒉𝒆𝒓𝒘𝒊𝒔𝒆

14. Scaling operation:
-4 -3 -2 -1 0 1 2 3 4
-4
-3
-2
-1
0
1
2
3
4
x(t)
y(t)

15. Matlab Source Code:
t=-6:0.001:6;
x=zeros(size(t));
t1= t>=-1.5 & t<=-1;
x(t1)=2*t(t1)+3;
t2= t>-1 & t<=-0.5;
x(t2) = 1;
t3 = t>-0.5 & t<=0;
x(t3) = 2*t(t3)+2;
t4 = t>0 & t<=0.5;
x(t4) = -6*t(t4)+2;
t5 = t>0.5 & t<=1;
x(t5) = -1;
t6 = t>1 & t<=1.5;
x(t6) = 2*t(t6)-3;
plot(t,x);
xlim([-4 4]);
ylim([-4 4]);
grid on;

16. Reflection operation:
x(-t) is the reflected version of x(t). It flips
the signal vertically
𝒙 𝒕 =
𝒕 + 𝟑 , −𝟑 ≤ 𝒕 ≤ −𝟐
𝟏 , −𝟐 < 𝒕 ≤ −𝟏
𝒕 + 𝟐 , −𝟏 < 𝒕 ≤ 𝟎
−𝟑𝒕 + 𝟐 , 𝟎 < 𝒕 ≤ 𝟏
−𝟏 , 𝟏 < 𝒕 ≤ 𝟐
𝒕 − 𝟑 , 𝟐 < 𝒕 ≤ 𝟑
𝟎, 𝒐𝒕𝒉𝒆𝒓𝒘𝒊𝒔𝒆
𝒙 −𝒕 =
−𝒕 − 𝟑 , −𝟑 ≤ 𝒕 ≤ −𝟐
−𝟏 , −𝟐 < 𝒕 ≤ −𝟏
𝟑𝒕 + 𝟐 , −𝟏 < 𝒕 ≤ 𝟎
−𝒕 + 𝟐 , 𝟎 < 𝒕 ≤ 𝟏
𝟏 , 𝟏 < 𝒕 ≤ 𝟐
−𝒕 + 𝟑 , 𝟐 < 𝒕 ≤ 𝟑
𝟎, 𝒐𝒕𝒉𝒆𝒓𝒘𝒊𝒔𝒆

17. Reflection operation:
-4 -3 -2 -1 0 1 2 3 4
-4
-3
-2
-1
0
1
2
3
4
x(t)
y(t)
-4 -3 -2 -1 0 1 2 3 4
-4
-3
-2
-1
0
1
2
3
4
x(t)
y(t)

18. Matlab Source Code:
t=-6:0.001:6;
x=zeros(size(t));
t1= t>=-3 & t<=-2;
x(t1)=-t(t1)-3;
t2= t>-2 & t<=-1;
x(t2) = -1;
t3 = t>-1 & t<=0;
x(t3) = 3*t(t3)+2;
t4 = t>0 & t<=1;
x(t4) = -t(t4)+2;
t5 = t>1 & t<=2;
x(t5) = 1;
t6 = t>2 & t<=3;
x(t6) = -t(t6)+ 3;
plot(t,x);
xlim([-4 4]);
ylim([-4 4]);
grid on;

19. A signal x(t) is even symmetric if x(t) = x(-t).
A signal x(t) is odd symmetric if x(t) = -x(-t)
𝒙 𝒕 =
𝒕 + 𝟑 , −𝟑 ≤ 𝒕 ≤ −𝟐
𝟏 , −𝟐 < 𝒕 ≤ −𝟏
𝒕 + 𝟐 , −𝟏 < 𝒕 ≤ 𝟎
−𝟑𝒕 + 𝟐 , 𝟎 < 𝒕 ≤ 𝟏
−𝟏 , 𝟏 < 𝒕 ≤ 𝟐
𝒕 − 𝟑 , 𝟐 < 𝒕 ≤ 𝟑
𝟎, 𝒐𝒕𝒉𝒆𝒓𝒘𝒊𝒔𝒆
𝑥 −𝑡 =
−𝑡 − 3 , −3 ≤ 𝑡 ≤ −2
−1 , −2 < 𝑡 ≤ −1
3𝑡 + 2 , −1 < 𝑡 ≤ 0
−𝑡 + 2 , 0 < 𝑡 ≤ 1
1 , 1 < 𝑡 ≤ 2
−𝑡 + 3 , 2 < 𝑡 ≤ 3
0, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
Symmetric Signal:

20. Symmetric Signal:
Here, x(-t) ≠ x(t) . So, the signal is not even symmetric
-4 -3 -2 -1 0 1 2 3 4
-4
-3
-2
-1
0
1
2
3
4
x(t)
y(t)
-4 -3 -2 -1 0 1 2 3 4
-4
-3
-2
-1
0
1
2
3
4
x(t)
y(t)

21. Symmetric Signal:
Here, x(-t)≠ -x(t).So, the signal is not odd symmetric.
-4 -3 -2 -1 0 1 2 3 4
-4
-3
-2
-1
0
1
2
3
4
x(t)
y(t)

22. Mathematical Expression:
𝑿 𝒆(𝒕) =
2𝑡 + 2 , −1 ≤ 𝑡 ≤ 0
−2𝑡 + 2 , 0 < 𝑡 ≤ 1
0, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
Even Part:
For even part xe(t) =[x(t)+x(-t)]/2

23. Even part:
For even part xe(t) =[x(t)+x(-t)]/2
-4 -3 -2 -1 0 1 2 3 4
-4
-3
-2
-1
0
1
2
3
4
x(t)
y(t)

24. Matlab Source Code:
t=-6:0.001:6;
x=zeros(size(t));
t1= t>=-1 & t<=0;
x(t1)=2*t(t1)+2;
t2= t>0 & t<=1;
x(t2) = -2*t(t2)+2;
plot(t,x);
xlim([-4 4]);
ylim([-4 4]);
grid on;

25. Odd Part:
For odd part xo(t) =[x(t)-x(-t)]/2
Mathematical Expression:
𝑿 𝒐(𝒕) =
𝑡 + 3 , −3 ≤ 𝑡 ≤ −2
1 , −2 < 𝑡 ≤ −1
−𝑡 , −1 < 𝑡 ≤ 1
−1 , 1 < 𝑡 ≤ 2
𝑡 − 3 , 2 < 𝑡 ≤ 3
0, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒

26. Odd Part:
For odd part xo(t) =[x(t)-x(-t)]/2
-4 -3 -2 -1 0 1 2 3 4
-4
-3
-2
-1
0
1
2
3
4
x(t)
y(t)

27. Matlab Source Code:
t=-6:0.001:6;
x=zeros(size(t));
t1= t>=-3 & t<=-2;
x(t1)=t(t1)+3;
t2= t>-2 & t<=-1;
x(t2) = 1;
t3 = t>-1 & t<=1;
x(t3) = -t(t3);
t4 = t>1 & t<=2;
x(t4) = -1;
t5 = t>2 & t<=3;
x(t5) = t(t5)- 3;
plot(t,x);
xlim([-4 4]);
ylim([-4 4]);
grid on;

28. Any Question or
Suggestions
?

29. Thank You