Discrete-Time Complex

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Presentation transcript:

Discrete-Time Complex Exponential Sequence.

Real Exponential Signal

Real Exponential Signal

Real Exponential Signal

Real Exponential Signal

Real Exponential Signal

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.

Sinusoidal Signals

Discrete-time Sinusoidal Signals

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

General Complex Exponential Signals

General Complex Exponential Signals

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

Periodicity Properties of Discrete-time Complex Exponentials

Periodicity Properties of Discrete-time Complex Exponentials

Periodicity Properties of Discrete-time Complex Exponentials

Periodicity Properties of Discrete-time Complex Exponentials

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

Discrete-time Sinusoidal Signals

Fundamental Period & Frequency of discrete-time complex exponential

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

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

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