Tuesday, August 6, 2013

PPT On Signals

Signals Presentation Transcript:
1.EEE223 Signals & Systems

2.Housekeeping
Text:
Signals & Systems
Oppenheim, Willsky & Nawab, 2nd Ed.
Reference:
Linear Systems & Signals
B.P. Lathi, 2nd Ed.

Assignments    (10)            25%
Session Exams    (2)            25%
Final Exam                    50%
Assignments are critical to understanding the course

4.Outline
Introduction to signals – continuous & discrete
Representation of signals
Transformations of the independent variable
Even and odd signals
Periodic signals
More signal transformations

5.Signals
Signals carry information – without this they are noise!
Sound waves, air temperature, blood pressure, ECG waves etc.
Daily stock market rates, daily class attendance, number of cars passing a check-post every hour etc.

6.Representation
We shall use the following conventions:
Functions of a continuous independent variable (typically time) will be written as x(t)
Functions of a discrete independent variable (also referred to as time) will be written as x[n]
Note: n ONLY takes integer values

7.Transformations of the independent variable
Important to consider signals related by transformations of the independent variable, e.g.
x(-t), x(2t), x(t/2)
x[-n]
x(t-to), x[n-no]

8.Even and Odd Signals
Every signal can be decomposed into even and odd parts:

9.Even and Odd Signals
Similarly for discrete-time signals:
Even signals:
x[n] = x[-n]

Odd signals:
x[n] = -x[-n]

10.Every discrete-time signal can be decomposed into even and odd parts:
xe[n] = ½ { x[n] + x[-n] }
xo[n] = ½ { x[n] - x[-n] }
and
x[n] = xe[n] + xo[n]

11.Periodic signals
x(t) = x(t + T) for all t and T>0
is called a periodic signal with period T
x(t) = x(t + mT) for any integer m
x(t) is also periodic with period 2T, 3T …
Smallest +ve value of T is called the Fundamental Period

12.Periodic signals
x[n] = x[n + N] for all n and N>0
is called a periodic signal with period T
x[n] = x[n + mN] for any integer m
x[n] is also periodic with period 2N, 3N …
Smallest +ve value of N is called the Fundamental Period

13.More Transformations
ax(t)
ax[n]
x(t)h(t)
x[n]h[n]
ax(t-1)h(-t+2)