Regex (Rule-Based Pattern Matching) — Email & Phone Extraction What is Regex? A regular expression (regex) is a sequence of characters that defines a search pattern for text matching. It lets you search for specific patterns like email formats or digit sequences instead of exact words or phrases.  Regex is not natural language understanding — it does not interpret meaning. Instead, it uses character patterns to find matches in text. It is widely used for extracting or validating structured data like emails and phone numbers.  Pattern 1 — Email Address Extraction Here is the regex used for matching a simple email: r"\b[\w.-]+@[\w.-]+\.\w{2,4}\b" Explanation of parts: \b — Word boundary (ensures we match a complete email, not part of a bigger word) [\w.-]+ — One or more word characters (letters, digits, underscore), dots, or hyphens @ — Literal @ symbol [\w.-]+ — Domain part with similar allowed characters \. — A literal dot before t...

Beer–Lambert’s Law Beer–Lambert’s law (also called the Beer–Lambert–Bouguer law ) explains how light is absorbed when it passes through a solution. Statement The absorbance of a solution is directly proportional to: the concentration of the absorbing species, and the path length of light through the solution. Mathematical Form A = ε · c · l Where A = absorbance (no units) ε = molar absorptivity (L·mol⁻¹·cm⁻¹) c = concentration of the solution (mol/L) l = path length of the cell (cm) Key Ideas (Easy to Remember) Higher concentration → more absorption Longer path length → more absorpt...

Time Reversal Mirror (TRM) and Fourier Transform 1. Time Reversal and Convolution In TRM, the received signal at a transducer is: y_n(t) = x(t) * h_n(t) Here, x(t) is the transmitted signal and h_n(t) is the channel impulse response. After time reversal, the signal becomes: y_n^*(-t) = x^*(-t) * h_n^*(-t) Key property: Convolution in the time domain corresponds to multiplication in the frequency domain: ℱ{x(t) * h(t)} = X(f) H(f) So in the frequency domain, the TRM operation becomes: Z(f) = X^*(f) ∑_n |H_n(f)|^2 2. Time Reversal in the Frequency Domain Time reversal in time domain ( t → -t ) corresponds to complex conjugation in the frequency domain : ℱ{x^*(-t)} = X^*(f) This is exactly why, after retransmission, the combined signal effectively becomes: z(t) ≈ x^*(-t) ...

Frequency and Timing Synchronization Synchronization in frequency, phase, and time is critical for accurate underwater communication. Relative motion introduces Doppler shifts and frequency offsets due to oscillator mismatches. These impairments reduce the received signal's SNR and reliability. Frequency Synchronization: Correlation-based methods are used to detect and compensate frequency offsets. Timing Synchronization: Determines the exact start of data packets, often by correlating known training sequences with received signals. Carrier Phase and Frequency Offset Carrier phase errors can arise from oscillator imperfections or timing mismatches. Frequency offsets caused by Doppler shifts or hardware misalignments degrade system performance. High-order modulation schemes are particularly sensitive, requiring higher SNR to achieve the same BER. Compensation techniques are essential for maintaining reliable communication.

Time Reversal Mirror (TRM) Technique The Time Reversal Mirror (TRM) method is an effective strategy to overcome multipath issues in underwater channels. It exploits the property that sound waves are reciprocal. The technique involves transmitting a signal, recording it with an array of transducers, reversing it in time, and retransmitting it. This process focuses the signal energy back to its source and mitigates inter-symbol interference (ISI). Active TRM utilizes spatial diversity at the transmitter, while passive TRM can include probe signals to estimate the channel response, allowing better signal reconstruction at the receiver. TRM Mathematical Formulation For a transmitted signal x(t) , the signal received by the n -th transducer is: y n (t) = x(t) * h n (t) , where h n (t) represents the channel impulse response. After time reversal and retransmission, the signal becomes: z(t) = Σ n y n * (-t) * h n (t) ≈ x * (-t) In the frequency domain, this can be expressed as:...

OFDM FFT-Based Channel Estimation Simulator This simulator demonstrates FFT-based channel estimation in an OFDM system. The receiver estimates the channel using: H(k) = Y(k) / X(k) Subcarriers CP Length Channel Taps Noise Std Run Simulation Read More Understand the simulator workflow: How does it work?

FFT-Based Channel Estimation Using OFDM in MATLAB Modern wireless systems such as WiFi, LTE, and 5G rely heavily on Orthogonal Frequency Division Multiplexing (OFDM) . One major advantage of OFDM is that it simplifies channel equalization using the Fast Fourier Transform (FFT) . When a cyclic prefix (CP) is inserted before each OFDM symbol, the wireless channel behaves like a circular convolution . This allows the channel response to be estimated easily in the frequency domain. After applying FFT, the received signal can be written as: Y(k) = X(k)H(k) Therefore the channel response can be estimated using: H(k) = Y(k) / X(k) System Overview The following simulation demonstrates the basic OFDM transmission chain: Random data generation BPSK modulation OFDM modulation using IFFT Cyclic prefix insertion Multipath wireless channel FFT-based channel estimation Frequency-domain equalization MATLAB Simulation Code % --------------------------...

Turbo Codes Performance Explanation 1. The "Waterfall" Effect Turbo codes are famous for their Waterfall Region . Unlike standard OOK (On-Off Keying), which improves slowly as signal power increases, Turbo codes have a specific threshold: Below Threshold (0 dB): The noise is too high for the iterative logic to converge. The decoders essentially "guess," leading to the high BER you observed. Above Threshold (1.5 dB): A mere 1.5 dB increase in power causes the Bit Error Rate (BER) to "fall off a cliff," plummeting from 0.19 to 0.00001 almost instantly. 2. Eb/N0 vs. SNR (The Energy Penalty) Using a Rate 1/3 Turbo code means you are sending 3 bits for every 1 bit of actual data. At 0 dB, your total signal energy is spread very thin. Because the energy per coded bit is so low, the decoder is struggling to piece together a puzzle where every p...