1. Discrete-Time Complex
Exponential Sequence.

2. Real Exponential Signal

3. Real Exponential Signal

4. Real Exponential Signal

5. Real Exponential Signal

6. Real Exponential Signal

7. 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.

8. Sinusoidal Signals

9. Discrete-time Sinusoidal
Signals

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

11. General Complex Exponential
Signals

12. General Complex Exponential
Signals

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

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

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

19. Discrete-time Sinusoidal
Signals

20. Fundamental Period & Frequency of
discrete-time complex exponential

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

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

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