Let xa(t) be the half-wave rectified signal in Table 4.3. Let xb(t) be the same signal delayed by 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 |
|
(a) Find the coefficients in the exponential form for xb(t). Hint: Consider time delay.
(b) Show that the Fourier coefficients of the sum [xa(t) + xb(t)] are those of the fullwave rectified signal in Table.
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