Frequency Modulation Message Frequency (Hz): Generate Message Carrier Frequency (Hz): Generate Carrier Message Signal Amplitude: Carrier Signal Amplitude: Generate Modulated Signal Demodulate Further Reading   

Digital Filters + Add Signal Combine Signals Plot Noisy Signal Plot Filtered Signal Reset All Filter Type: Moving Average Filter FIR Lowpass Filter Butterworth Filter

Amplitude Modulation Message Frequency (Hz): Generate Message Carrier Frequency (Hz): Generate Carrier Gain A: Gain B: Generate Modulated Signal Demodulate

  Step 1: Initial Access and Synchronization The Base Station (BS) periodically transmits synchronization signals that help new Mobile Stations (MS) detect and align with the cell. The MS uses correlation techniques to identify these signals, enabling it to synchronize in both time and frequency. After synchronization, the MS initiates a random access procedure to request a connection. This is essential for establishing timing alignment and resource allocation. Step 2: Pilot Transmission and Channel Estimation Once connected, pilot symbols (also called reference signals ) are exchanged between the BS and MS. These pilot signals are known and designed to be orthogonal across users to prevent interference. By comparing the received pilot with the known sequence, the receiver estimates the channel impulse response , which is critical for demodulating the actual data correctly. Step 3: Data Transmission and Communication With the channel now estimated, the system proceeds to data ...

  FastAPI is amazing! You can create APIs using FastAPI very quickly. With these APIs, you can connect the backend to the frontend. You can access user data through the API and process it on a Uvicorn server.  Here is an example of a FastAPI app you can start with from fastapi import FastAPI from fastapi.middleware.cors import CORSMiddleware app = FastAPI() # CORS setup app.add_middleware(     CORSMiddleware,     allow_origins=["*"],  # Consider restricting this in production     allow_credentials=True,     allow_methods=["*"],     allow_headers=["*"], ) # Root route @app.get("/") def root():     return {"message": "Welcome to the fastAPI"} How to Run It Go to the project or file directory and run the command: uvicorn main:app --reload Output  You will see output like this at the URL: http://localhost:8000/ In the code, we are using CORS middleware to allow connections between different platforms, such as t...

  To analyze the frequency content of a data stream, we use the Fast Fourier Transform (FFT) , which efficiently computes the Discrete Fourier Transform (DFT) . One of the most widely used FFT algorithms is the Cooley–Tukey algorithm , which is a radix-2 divide-and-conquer method . It breaks down a DFT of size N (where N N is a power of 2) into smaller DFTs of size  N /2 , recursively, which reduces computational complexity from  O ( N 2 ) O(N^2)  to O ( N log ⁡ 2 N ) O(N \log_2 N) .   Python Code for FFT  To use this code, you need a sampled signal and the corresponding sampling frequency .     def compute_fft(self, signal):         fft_result = np.fft.fft(signal)         freq = np.fft.fftfreq(len(signal), d=1/self.samplingFrequency)         return np.abs(fft_result), freq     In our case, we will perform the Fast Fourier Transform (FFT) on sine, cosine, rectangula...

  MATLAB Code This is a simple MATLAB code snippet that computes the Fourier Transform of any signal. I will show you different examples below the main code. Remember, to find the Fourier Transform of any signal using this code snippet, you need a sampled signal and its corresponding sampling frequency . n = length(signal); f = (-n/2:n/2-1)*(fs/n); % Frequency axis centered at 0 S_f = abs(fftshift(fft(signal)/n));  % Normalize FFT S_f_dB = 20*log10(S_f / max(S_f));  % dB scale with normalization Example for finding FFT of a sine wave clc; clear all; close all; fm = 10;      % Message signal frequency (Hz) fs = 1000; % Sampling frequency (100 kHz) t = 0:1/fs:1-1/fs; % Time vector over 1 second signal = sin(2*pi*fm*t); % Compute frequency spectrum in dB n = length(signal); f = (-n/2:n/2-1)*(fs/n); % Frequency axis centered at 0 S_f = abs(fftshift(fft(signal)/n));  % Normalize FFT S_f_dB = 20*log10(S_f / max(S_f));  % dB scale with normalizatio...

Low and High Level Modulation Simulator Message Frequency (Hz): Carrier Frequency (Hz): Amplification Factor: Run Simulation