Week 14. Review 1.Signals and systems 2.State machines 3.Linear systems 4.Hybrid systems 5.LTI systems & frequency response 6.Convolution 7.Fourier Transforms.

Week 14. Review1. Signals and systems2. State machines3. Linear systems4. Hybrid systems5. LTI systems & frequency response6. Convolution7. Fourier Transforms8. Sampling & reconstruction

1. Signals & systems

2. State machines

System is represented by a state machine M

M1 M2

M3

M

3. Linear state machine [A,b,cT,d], SISO

4. Hybrid system

5. LTI and frequency response

6. Convolution

7. The four Fourier Transforms

Aperiodic time, cont frequency

Periodic time,disc frequency

Aperiodic freq, continuous time

CTFTInvCTFT

FSInvFS

Periodic freq, discrete time

DTFTInv DTFT

DFTp

InvDFTp

8. Sampling and reconstruction

Find the appropriate FT or DTFT

T-T

1

Example

T-T