PPT On Even And Odd Signals

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Even And Odd Signals Presentation Transcript:
1.EEE223 Signals & Systems

2.Outline
Transformations of the independent variable
Even and odd signals
Periodic signals
More signal transformations

3.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]

4.Transformations of the independent variable

How about
x(2t) ?
x(t/2) ?
x(-2t + 1) ?

5.Even and Odd Signals
Even signals:
x(t) = x(-t)

Odd signals:
x(t) = -x(-t)

6.Every signal can be decomposed into even and odd parts:
xe(t) = ½ { x(t) + x(-t) }

xo(t) = ½ { x(t) - x(-t) }

xe(t) + xo(t) = ????

7.Similarly for discrete-time signals:
Even signals:
x[n] = x[-n]

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

8.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]

9.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
Special case: x(t) = Constant

10.            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
Special case: x[n] = Constant

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