GATE EC 2024 Question Paper (11-Feb-2024) (Shift 1)

The radian frequency value(s) for which the discrete time sinusoidal signal 𝑥[𝑛] = 𝐴 cos(Ω𝑛 + 𝜋/3) has a period of 40 is/are ______.

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 lossless transmission line with characteristic impedance $Z_0=50\Omega$ is terminated with an unknown load. The magnitude of the reflection co-efficient is $|\Gamma |=0.6$. As one moves towards the generator from the load, the maximum value of the input impedance magnitude looking towards the load (in $\Omega$) is ________.

The relationship between any $N$ -length sequence $x[n]$ and its corresponding $N$ -point discrete Fourier transform $X[k]$ is defined as
$X[k]=\mathcal{F}\{x[n]\}$.
Another sequence $y[n]$ is formed as below
$y[n]=\mathcal{F}\{\mathcal{F}\{\mathcal{F}\{\mathcal{F}\{x[n]\}\}\}\}$.
For the sequence $x[n]=\{1,2,1,3\}$, the value of $Y[0]$ is ________.

For the two port network shown below, the value of the $Y_{21}$ parameter (in Siemens) is ________.