Topic: Communication Systems
Consider waveforms $\cos(2\pi f_1t+\theta)$ and $\cos(2\pi f_2t)$, $(f_1>f_2)$, to be used for non-coherent binary FSK signalling. If the symbol duration is T seconds, and $\theta$ is constant arbitrary angle from 0 to $2\pi$, what is the minimum separation required between $f_1$ and $f_2$ for non-coherent, orthogonal FSK?
- A. $f_1-f_2=\frac{1}{T}$
- B. $f_1-f_2=\frac{2}{T}$
- C. $f_1-f_2=\frac{1}{4T}$
- D. $f_1-f_2=\frac{1}{3T}$
Answer: A. $f_1-f_2=\frac{1}{T}$
Explanation: For two FSK signals to be orthogonal in a non-coherent system (where phase $\theta$ is unknown), their cross-correlation must be zero for any arbitrary phase difference. This requires the frequency separation $(f_1 - f_2)$ to be an integer multiple of $1/T$. Thus, the minimum separation is $f_1 - f_2 = \frac{1}{T}$.