Periodogram     Fast but high variance.     Take the raw time-domain signal x[n]x[n] of length NN.     Optionally apply a window (e.g., Hann, Hamming) to reduce spectral leakage.     Compute the DFT or FFT of the (optionally windowed) signal.     Estimate the power spectral density (PSD) from the squared magnitude of the FFT. Welch’s Method     Averaged periodogram with reduced variance.     Divide the signal into overlapping segments.     Apply a window function to each segment.     Compute the FFT and PSD of each windowed segment.     Average the PSDs across all segments. Correlogram     Estimate the autocorrelation function (ACF) of the full signal.     Apply a window if desired.     Compute the Fourier Transform of the autocorrelation to obtain the PSD. Blackman–Tukey Method     Estimate the autocorrelation function (ACF) of the signal fo...

  Fundamental Theory of Channel Impulse Response The fundamental theory behind the channel impulse response in wireless communication often involves complex exponential components such as: \( h(t) = \sum_{i=1}^{L} a_i \cdot \delta(t - \tau_i) \cdot e^{j\theta_i} \) Where: \( a_i \) is the amplitude of the \( i^{th} \) path \( \tau_i \) is the delay of the \( i^{th} \) path \( \theta_i \) is the phase shift (often due to Doppler effect, reflection, etc.) \( e^{j\theta_i} \) introduces a phase rotation (complex exponential) The convolution \( x(t) * h(t) \) gives the received signal So, instead of representing the channel with only real-valued amplitudes, each path can be more accurately modeled using a complex gain : \( h[n] = a_i \cdot e^{j\theta_i} \) Channel Impulse Response Simulator Input Signal (Unit Impulse x[n]) Multipath Delays (samples): Path A...

  In this article, we will explore how to classify categories from tabular data stored in a .csv file using a neural network built with PyTorch . Suppose you're given a dataset where each row corresponds to an instance, and it includes both numerical features and a target class label such as Class1 , Class2 , or Class3 . Your task is to train a model that can predict the correct class based on the input features. In our example, the target classes are Introvert , Extrovert , and Ambivert , and the dataset contains 29 other columns representing various input features. We aim to build a classification model using a feedforward neural network in PyTorch. This includes defining multiple layers, selecting an appropriate loss function (e.g., CrossEntropyLoss ), and optimizing the model using techniques like the Adam optimizer to improve accuracy. In the field of machine learning (ML) and deep learning (DL) , machines are particularly good at detecting patterns in data. While convo...

In machine learning and deep learning (ML/DL) , machines are quite effective at recognizing patterns. They apply various convolutional operations to extract meaningful features for tasks such as object recognition . These systems can identify not only objects but also more abstract patterns—such as word sentiment or classifying inputs into multiple categories . Today, artificial intelligence (AI) has become so advanced that it can converse like a human , provided it has some contextual input or product details. AI can also summarize and translate languages in real time using different pretrained models . These models are trained on millions of data samples, making them highly accurate. For example, ResNet-18 is a pretrained model trained on millions of images, and it is considered highly effective for image classification tasks. In this tutorial, we will use the PyTorch library to classify images. PyTorch i...

🧮 Binary Search 🧮 Two, Three, or Four Pointer Sum 🧮 Sliding Window: Check if any contiguous subarray of length 2, 3, and 4 sums to target 🧮 Activity Selection Problem using the Greedy algorithm 🧮 More ... 📚 Further Reading   Binary Search  arr = [10, 3, 5, 7] target = 3 # Store original indices with values indexed_arr = list(enumerate(arr))  # [(0, 10), (1, 3), (2, 5), (3, 7)] # Sort by value indexed_arr.sort(key=lambda x: x[1])  # [(1, 3), (2, 5), (3, 7), (0, 10)] def binary_search_with_original_index(arr, target):     left = 0     right = len(arr) - 1     while left <= right:         mid = (left + right) // 2         if arr[mid][1] == target:             return arr[mid][0]  # Return original index         elif arr[mid][1] < target:             left = mid + 1 ...

  TestClient  in FastAPI is a tool used for testing your API by simulating HTTP requests without running a live server. It lets you write and run tests for your endpoints quickly and easily.   Example Code (test.py) from fastapi.testclient import TestClient from app.main import app  # Just imports the app, doesn't start the server client = TestClient(app) def test_read_root():     response = client.get("/")     assert response.status_code == 200     assert response.json() == {"message": "Hello, FastAPI"}   Command to run this code: pytest test.py       My actual FastAPI code (main.py) that runs on the server from fastapi import FastAPI   app = FastAPI() # Root route @app.get("/") def root():     return {"message": "Welcome to the fastAPI"}     Command to run this code: uvicorn main:app --reload   Another Example   (test.py) (testing the login endpoint)   from fastapi.t...

Constellation Diagram of M-ary QAM Bitstream (e.g. 1,0,1,1): Generate Message Modulation Order (M): M must be a power of 2 and square (e.g., 4, 16, 64) Plot Constellation Diagram Explore Signal Processing Simulations   Further Reading   Online Simulator for M-ary PSK Constellation Online Simulator for M-ary QAM Signal Generator  Online Simulator for ASK, FSK, and PSK   Explore DSP Simulations

Constellation Diagram of M-ary PSK Bitstream (e.g. 1,0,1,1): Generate Message Modulation Order (M): M must be a power of 2 (e.g., 2, 4, 8, 16) Plot Constellation Diagram Explore Signal Processing Simulations Further Reading   Online Simulator for M-ary PSK Online Simulator for ASK, FSK, and PSK   Explore DSP Simulations