Linear vs Circular Convolution Linear convolution vs circular convolution Linear convolution (what nature does) If: x[n] = transmitted signal h[n] = channel impulse response (multipath) Then the received signal is: y[n] = x[n] * h[n] This means: Past symbols spill into future symbols Causes inter-symbol interference (ISI) DFT of y[n] is not a simple product Circular convolution (what DFT assumes) The DFT assumes periodic signals : y[n] = x[n] ⊛ h[n], where indices wrap around modulo N Only under circular convolution does the DFT satisfy: Y[k] = X[k] · H[k] This is what enables one-tap frequency-domain equalization . What happens in the real channel (linear convolution) The channel performs linear convolution: y[n] = Σ l=0 Lh−1 h[l] x[n-l] But because: CP absorbs the “spillover” Receiver discards CP before DFT The useful part of the received symbol becomes: y[n] = Σ l=0 Lh−1 h[l] x[(n-l) mod N] Modulo inde...

Role of Cyclic Prefix in OFDM The simple frequency-domain equalizer is possible only if the channel performs circular convolution . However, in practice, all wireless channels perform linear convolution . This linear convolution is converted into circular convolution by adding a cyclic prefix (CP) in the OFDM architecture. The cyclic prefix makes the linear convolution imparted by the channel appear as circular convolution to the DFT process at the receiver. Demonstration Concept To demonstrate this, consider an OFDM signal s[n] of length 8 and a channel impulse response h[n] of length 3. When s[n] is convolved with h[n] : Linear convolution and circular convolution give different results. This mismatch causes interference in OFDM systems. Adding Cyclic Prefix A cyclic prefix is added by copying the last N CP samples of the OFDM symbol and appending them to the beginning. If the cyclic prefix length is at least equal to the channel delay spread, the foll...

In the MATLAB code below, a comparison between  frequency-selective fading  and  flat fading  is shown. In frequency-selective fading, multipath propagation causes multiple delayed copies of the signal to arrive at the receiver. When the channel delay spread exceeds the symbol duration, these delayed components overlap, resulting in inter-symbol interference (ISI). In flat fading, ISI does not occur because the signal bandwidth is much smaller than the channel’s coherence bandwidth . Therefore, the channel response remains approximately constant across the signal bandwidth, and all symbols experience the same fading. MATLAB Code for frequency selective fading channel % OFDM over frequency selective Rayleigh fading channel clc; clearvars; close all ; % Simulation parameters nSym = 10^4; % Number of OFDM symbols EbN0dB = 0:2:20; % Eb/N0 range MOD_TYPE = 'MPSK' ; % 'MPSK' or 'MQAM' M = 4; % QPSK N = 64; % Total number ...

Floyd–Warshall Algorithm Floyd–Warshall is an algorithm used to find the minimum cost between every pair of nodes in a graph. In our problem: Each letter ( a – z ) is a node Each allowed transformation is a directed edge The edge has a cost 1. Think of Letters as Cities Imagine each letter is a city and transformations are one-way roads with tolls. c → e (1) e → b (2) c → b (5) Even though there is a direct road from c → b , it may be cheaper to go via another city. 2. Distance Table We create a table where: dist[i][j] = minimum cost to go from i to j Initial rules: dist[i][i] = 0 Direct transformation → given cost No transformation → infinity ...

  WIPT / WPT: Wireless Information and Power Transfer & Harvesting 1. RF Signals as Energy In WIPT/WPT systems, the transmitter sends radio-frequency (RF) electromagnetic waves instead of light. RF signals carry energy through oscillating electric and magnetic fields. The power received by an antenna depends on: Transmit power Distance Frequency Antenna gains More transmitted RF power means more harvestable energy at the receiver. 2. RF Energy Harvesting (Rectenna) The receiver uses a rectifying antenna (rectenna) to convert RF signals into electrical energy. RF waves are captured by an antenna. The AC RF signal is fed to a rectifier. The rectifier converts AC to DC. The DC power charges a battery or capacitor. This is the core principle of wireless power harvestin...

SLIPT Power Splitting and Energy Harvesting 1. Light as Energy The receiver in SLIPT/VLC receives visible light from an LED or laser source. Light carries photons which have energy: E photon = h f Where h is Planck's constant and f is the light frequency. More light power means more energy is available. 2. Photovoltaic Effect (Energy Harvesting) The receiver has a solar-cell-like or photodiode circuit that converts light into electricity: Light hits the photodiode. Photons excite electrons in the semiconductor material. Electrons flow as DC current → can charge a battery or capacitor. 3. AC/DC Split The received light signal contains two components: AC component: contains information (modulated data). DC component: contains average power, which can be converted to energy. The power-splitting circuit divides the ligh...

Main Differences: OAuth2, JWT, OAuth2 + JWT What each term actually is OAuth2 OAuth2 is an authorization framework , not a token format. It defines how clients get permission, how tokens are issued, and how protected resources are accessed. Example use cases: Login with Google Third-party apps accessing user data JWT (JSON Web Token) JWT is a token format . It is a compact, signed JSON object used to securely transmit claims. Can be used with OAuth2 Can be used without OAuth2 Commonly used for API authentication OAuth2 + JWT This means OAuth2 is used as the authorization framework and JWT is used as the access token format . This is very common in modern APIs and microservices. Comparison Table ...

Sync vs Async JavaScript Explorer Run Sync Functions Run Async Functions What is Synchronous JavaScript? Synchronous JavaScript runs code in order, one line at a time , waiting for each operation to complete before starting the next. So the program executes lines in sequence — X waits for Y to finish before starting Z.  // Example: console.log("First"); console.log("Second"); console.log("Third"); // Output: First, Second, Third What is Asynchronous JavaScript? Asynchronous JavaScript lets long tasks (like timers or server requests) run in the background while the rest of the code continues. JavaScript uses an event loop to manage this. When an async task finishes, its callback runs later, after the curr...