Problem

Consider the signals in Figure P4.7. For k sufficiently large, the Fourier coefficient of...

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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Solutions For Problems in Chapter 4