DiscreteTime Complex Exponential Sequence 1 Real Exponential Signal

Discrete-Time Complex Exponential Sequence. 1

Real Exponential Signal 2

Real Exponential Signal 3

Real Exponential Signal 4

Real Exponential Signal 5

Real Exponential Signal 6

Real Exponential Signal Real-valued discrete exponentials are used to describe: 1) Population growth as function of generation. 2) Total return on investment as a function of day, month or quarter. 7

Sinusoidal Signals 8

Discrete-time Sinusoidal Signals 9

Discrete-time Sinusoidal Signals These discrete-time signals possessed: 1) Infinite total energy 2) Finite average power. 10

General Complex Exponential Signals 11

General Complex Exponential Signals 12

Periodicity Properties of Discretetime Complex Exponentials There are differences in each of the above properties for the discrete-time case of 13

Periodicity Properties of Discrete-time Complex Exponentials 14

Periodicity Properties of Discrete-time Complex Exponentials 15

Periodicity Properties of Discrete-time Complex Exponentials 16

Periodicity Properties of Discrete-time Complex Exponentials 17

Periodicity Properties of Discrete-time Complex Exponentials Second property concerns the periodicity of the discrete-time complex exponential. 18

Discrete-time Sinusoidal Signals 19

Fundamental Period & Frequency of discrete-time complex exponential 20

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Harmonically related periodic exponential sequence Considering periodic exponentials with common period N samples: This set of signals possess frequencies which are multiples of 22

Harmonically related periodic exponential sequence In continuous-time case are all distinct signals for 23

Harmonically related periodic exponential sequence Therefore , there are only N distinct periodic exponentials in the discrete harmonic sequences. 24