GATE 2024 Electronics & Communication Q14

Question

A digital communication system transmits through a noiseless bandlimited channel [-W W]. The received signal z(t) at the output of the receiving filter is given by $z(t) = \sum_n b[n]x(t-nT)$ where b[n] are the symbols and x(t) is the overall system response to a single symbol. The received signal is sampled at t = mT. The Fourier transform of x(t) is X (f). The Nyquist condition that X (f) must satisfy for zero intersymbol interference at the receiver is _________.

Answer

$\sum_{m=-\infty}^{\infty} X\left(f+\frac{m}{T}\right)=T$

Answer

$\sum_{m=-\infty}^{\infty} X\left(f+\frac{m}{T}\right)=\frac{1}{T}$

Answer

$\sum_{m=-\infty}^{\infty} X(f+mT)=T$

Answer

$\sum_{m=-\infty}^{\infty} X(f+mT)=\frac{1}{T}$