GATE EC 2024 Set 1 Q4 — Digital Communications

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 $z(t)=\sum_{n} b[n] x(t-n T)$ where $b[n]$ are the symbols and $x(t)$ is the overall system response to a single symbol. The received signal is sampled at $t=m T$. 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 $\_\_\_\_\_\_$.