Use (4.23) and the integral tables in Appendix A to verify the Fourier coefficients for the following signals in Table:
(a) Square wave
(b) Sawtooth wave
(c) Triangular wave
(d) Rectangular wave
(e) Full-wave rectified wave
(f) Half-wave rectified wave
(g) Impulse train
Verify each preceding result, using the symbolic mathematics of MATLAB. Simplify each expression to agree with Table.
(h) Use the results of Parts (a) and (b) to show that all the Fourier coefficients of x(t) in Part (c) are zero except for C0 = A.
TABLE Fourier Series for Common Signals
Name | Waveform | C0 | Ck, k ≠ 0 | Comments |
1. Square wave | 0 | Ck = 0, k even | ||
2. Sawtooth |
| |||
3. Triangular wave | Ck = 0, k even | |||
4. Full-wave rectified |
| |||
5. Half-wave rectified | Ck = 0, k odd, except | |||
6. Rectangular wave | ||||
7. Impulse train |
|
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