Consider the waveform f(t) in Figure.(a) Write a mathematical expression for f (t)(b) Find...

F(s)

ROC

1. δ (t)

1

All s

2. u (t)

Re(s) > 0

3. t

Re(s) > 0

4. tn

Re(s) > –a

5. e-at

Re(s) > –a

6. te-at

Re(s) > –a

7. tn e-at

Re(s) > 0

8. sin bt

Re(s) > 0

9. cos bt

Re(s) > –a

10. e-at sin bt

Re(s) > –a

11. e-at cos bt

Re(s) > 0

12. t sin bt

Re(s) > 0

13. t cos bt

Name

Property

1. Linearity, (7.10)

2. Derivative, (7.15)

3. n th-order derivative, (7.29)

4. Integral, (7.31)

5. Real shifting, (7.22)

6. Complex shifting, (7.20)

7. Initial value, (7.36)

8. Final value, (7.39)

9. Multiplication by t, (7.34)

10. Time transformation,

11. Convolution

12. Time periodicity