Firebase Project Setup and Integration with React This guide will walk you through the steps of setting up a Firebase project, configuring Firebase services like Authentication and Cloud Messaging , and integrating them into a React app. Step 1: Create a Firebase Project Go to the Firebase Console . Click on Add Project and follow the steps to create a new Firebase project. You will be prompted to: Enter a project name. Enable or disable Google Analytics for the project. Choose a region for the Firebase services. Once the project is created, you will be taken to the Firebase project dashboard. Step 2: Add Firebase SDK to Your React App To integrate Firebase with your React app, you first need to install the Firebase SDK: npm install firebase After installation, import Firebase and initialize it in your React app. ...

Understanding the Q-function in BASK, BFSK, and BPSK 1. Definition of the Q-function The Q-function is the tail probability of the standard normal distribution: Q(x) = (1 / √(2π)) ∫ x ∞ e -t²/2 dt What is Q(1)? Q(1) ≈ 0.1587 This means there is about a 15.87% chance that a Gaussian random variable exceeds 1 standard deviation above the mean. What is Q(2)? Q(2) ≈ 0.0228 This means there is only a 2.28% chance that a Gaussian value exceeds 2 standard deviations above the mean. Difference Between Q(1) and Q(2) Even though the argument changes from 1 to 2 (a small increase), the probability drops drastically: Q(1) = 0.1587 → errors fairly likely Q(2) = 0.0228 → errors much rarer This shows how fast the tail of the Gaussian distribution decays. It’s also why BER drops drama...

Q-function in BER vs. SNR Calculation In the context of Bit Error Rate (BER) and Signal-to-Noise Ratio (SNR) calculations, the Q-function plays a significant role, especially in digital communications and signal processing . What is the Q-function? The Q-function is a mathematical function that represents the tail probability of the standard normal distribution. Specifically, it is defined as: Q(x) = (1 / sqrt(2π)) ∫ₓ∞ e^(-t² / 2) dt In simpler terms, the Q-function gives the probability that a standard normal random variable exceeds a value x . This is closely related to the complementary cumulative distribution function of the normal distribution. The Role of the Q-function in BER vs. SNR The Q-function is widely used in the calculation of the Bit Error Rate (BER) in communication systems, particularly in systems like Binary Phase Shift Ke...

A strict-sense stationary process is one whose complete statistical structure does not change with time — all joint distributions remain identical under time shifts. For SSS, the following all must be time-invariant: Mean Variance Autocorrelation All higher-order moments All joint PDFs All marginal PDFs Everything . That’s why SSS is a very strong condition. A random process X ( t ) X(t) X ( t ) is strict-sense stationary if for every : Positive integer n n n Any set of time instants t 1 , t 2 , … , t n t_1, t_2, \dots, t_n t 1 ​ , t 2 ​ , … , t n ​ Any time shift τ \tau τ the joint distribution satisfies: F X ( t 1 ) , … , X ( t n ) ( x 1 , … , x n ) = F X ( t 1 + τ ) , … , X ( t n + τ ) ( x 1 , … , x n ) A Large Strictly Stationary Example Let’s define a random process where: X(t) = 0 with probability 1/2 X(t) = 1 with probability 1/2 Each time point is independent. This is like an infinite sequence of fair coin flips. t:...

Dataset Transforms in PyTorch When working with image datasets in PyTorch, one of the essential tasks is transforming the image data into a format that the model can process. A common operation is converting a PIL (Python Imaging Library) image into a PyTorch tensor. This can be done efficiently using the torchvision.transforms module. 1. Introduction to Dataset Transformations The torchvision.transforms module provides a collection of functions designed for image transformations. These transformations can be applied to images after they are loaded, but before they are returned by the dataset's __getitem__ method. This allows us to preprocess images in various ways, including converting them into PyTorch tensors, normalizing pixel values, rotating, or cropping the images. 2. Available Transforms The torchvision.transforms module contains a variety of transformations that can be applied to datasets like CIFAR-10 . Some commonly used transforms in...

Understanding train=True vs train=False in Dataset Loading In machine learning, especially when using frameworks like PyTorch or TensorFlow , datasets are often divided into separate portions for training and evaluation . Many built-in dataset loaders—such as torchvision.datasets.MNIST , CIFAR10 , and FashionMNIST —include a parameter called train . Setting this parameter to either True or False determines which portion of the dataset is loaded. This distinction is fundamental to building reliable and generalizable machine learning models. Let’s explore what each option means, how it is used, and why it matters. 1. What train=True Means When train=True , the dataset loader retrieves the training portion of the data. This is the subset that the model uses to learn patterns and adjust its internal parameters . Purpose: The model is trained on this data by iteratively updating its weights to minimize er...

NOMA Downlink System Model For orthogonal multiple access (e.g., OFDMA), each orthogonal resource block is allocated to a single user. If a user’s channel condition is poor, the entire subcarrier bandwidth may be assigned to that user, which is inefficient. Non-Orthogonal Multiple Access (NOMA) addresses this by allocating more transmit power to users with weaker channels and less power to users with stronger channels. This ensures efficient spectrum usage and fairness. The transmit SNR is defined as: $$ \rho_s = \frac{P_s}{\sigma^2}, $$ where $P_s$ is the signal power and $\sigma^2 = 1$ is the noise power (assuming unit-variance Gaussian noise). Transmit Signal In downlink NOMA, the base station transmits: $$ x_s = \sqrt{a_1 \rho_s}\, x_1 + \sqrt{a_2 \rho_s}\, x_2 $$ $x_1, x_2$: unit-power transmitted symbols $\rho_s$: total transmit SNR $a_1 + a_2 = 1$ (power allocation) Typically $a_2 > a_1$ (weak user receives more power) Rece...

  GATE Electronics and Communication (EC) Questions Paper With Answer Key Download Pdf [2024] Download Question Paper                 See Answers   2025 | 2024 | 2023 | 2022 | 2021 | 2020 GATE - EC 2024 Answers with Explanations  Q.1  Answer: Option A    Q.2  Answer: Option A   Q.3 To solve this problem, we will use the given age ratios to set up equations. Let's define the current ages of Aman and his father: A = Aman's current age F = Father's current age Step 1: Analyze the first condition (5 years ago) Five years ago, the ratio of Aman’s age to his father’s age was 1:4. This means: (A - 5) / (F - 5) = 1 / 4 Rewriting the equation: 4(A - 5) = F - 5 Expanding both sides: 4A - 20 = F - 5 Simplifying: 4A - F = 15 This gives us Equation 1...