In a digital communication system employing Frequency Shift Keying (FSK) ...

Q

In a digital communication system employing Frequency Shift Keying (FSK), the 0 and 1 bits are represented by sine waves of 10 kHz and 25 kHz respectively. These waveforms will be orthogonal for a bit interval of: (a) 45 µsec    (b) 200 µsec    (c) 50 µsec    (d) 250 µsec

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Solution

Given:
Binary FSK system with frequencies

• \( f_1 = 10 \text{ kHz} \)
• \( f_2 = 25 \text{ kHz} \)

For orthogonality in BFSK:

\[ |f_2 - f_1| = \frac{1}{2T} \]

Frequency separation:

\[ \Delta f = 25 - 10 = 15 \text{ kHz} \]

So,

\[ 15 \times 10^3 = \frac{1}{2T} \]

\[ T = \frac{1}{2 \times 15 \times 10^3} \]

\[ T = \frac{1}{30 \times 10^3} \]

\[ T = 33.3 \,\mu s \]

Among the given options, the closest value is:

\[ \boxed{45 \,\mu s} \]

Correct Answer:

(a) 45 µsec