(a) For the full-wave rectified signal in Table, prove that for y(t) = x(– t), the Fourier coefficients are unaffected.
(b) For the full-wave rectified signal in Table, find the Fourier coefficients for y(t) = x(t – T0/2).
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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