List of top Communications Questions

Let \(X(t) = A \cos(2\pi f_0 t + \theta)\) be a random process, where amplitude \(A\) and phase \(\theta\) are independent of each other, and are uniformly distributed in the intervals \([-2, 2]\) and \([0, 2\pi]\), respectively. \(X(t)\) is fed to an 8-bit uniform mid-rise type quantizer. Given that the autocorrelation of \(X(t)\) is: \[ R_X(\tau) = \frac{2}{3} \cos(2\pi f_0 \tau), \] the signal-to-quantization noise ratio (in dB, rounded off to two decimal places) at the output of the quantizer is \(\_\_\_\_\).

A digital transmission system uses a (7,4) systematic linear Hamming code for transmitting data over a noisy channel. If three of the message-codeword pairs in this code \( (m_i ; c_i) \), where \( c_i \) is the codeword corresponding to the \( i^{th} \) message \( m_i \), are known to be \[ (1 1 0 0 ; 0 1 0 1 1 0 0), \quad (0 0 1 1 1 1 0 ; 0 1 1 1 0 ; 1 0 0 0 1 1 0), \] then which of the following is a valid codeword in this code?