Problem

Let xa(t) be the half-wave rectified signal in Table 4.3. Let xb(t) be the same signal del...

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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Solutions For Problems in Chapter 4