Consider the signals in Figure P4.7. For k sufficiently large, the Fourier coefficient of the k th harmonic decreases in magnitude at the rate of 1/km. Use the properties in Section 4.4 to find m for the signals shown in the following figures:
(a) Figure (a)
(b) Figure (b)
(c) Figure (c)
(d) Figure (d)
(e) Figure (e)
(f) Figure (f)
Check your results using Table.
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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