Notes

Phase Dithering and Modern Error Correction

Wireless Communication
How Networks Survive Chaos Understanding Phase Dithering and Modern Error Correction Transmitter 1 (Static) Transmitter 2 (Dithering) Receiver (Composite Sum) Phase Dithering When multiple antennas transmit the exact same signal simultaneously, there is a risk that the waves will collide out-of-phase and permanently cancel each other out (destructive interference). Phase Dithering is a deliberate, pseudo-random ... Read More

Frequency, Amplitude and Phase: RF Characteristics

Wireless Communication
The 3 Core RF Characteristics Understanding how wireless signals travel and interact Frequency Tuning Measured in Hertz (Hz), frequency represents the number of complete wave cycles that occur in exactly one second. Analogy: Just like childhood walkie-talkies, the transmitter and receiver must be tuned to the exact same frequency (channel) to communicate. Amplitude Power Amplitude ... Read More

Hashing, Hash Tables and Scatter Tables

Data Structure and Algorithm
1. Hashing The process of transforming input data (a Key) of any size into a fixed-size value (a Hash). This value is usually a single number. 2. Hash Table A data structure that stores Key-Value pairs. It uses Hashing to calculate an index into an array, allowing you to find any entry instantly (O(1)). 3. ... Read More

Fundamental Data Structures – DSA

Data Structure and Algorithm
1. Dynamic Arrays A dynamic array grows automatically when it runs out of space. Watch what happens when the capacity (initially 4) is reached! Push Element Reset Current Capacity: 4 | Elements: 0 Real-World Examples: Shopping Carts: E-commerce sites use dynamic arrays to store items in your cart because they don’t know how many items ... Read More

Data Encoding – Quantum Machine Learning

Quantum Machine Learning
For classical data to be used by quantum circuit, it needs to be encoded which is called data encoding. In qiskit, we can use tools like z_feature_map or zz_feature_map etc. which includes rotation layers and entangling layers. Normalization is required in quantum machine learning similar to in classical machine learning. Normalization Before classical data can ... Read More

Matrix Transformations – Linear Algebra

Linear Algebra, Mathematics
1. Functions and Transformations In standard algebra, a function takes a single number as an input and outputs a new number: f(x) = y. In Linear Algebra, we scale this concept up. A Transformation (often denoted as T) is a mathematical rule that takes an entire Vector as an input and assigns it to a ... Read More

Algebraic Properties of Matrices

Linear Algebra, Mathematics
1. Properties of Matrix Arithmetic Matrix arithmetic shares many rules with standard algebra, but there are crucial differences. Here are the core laws: Commutative Law for Addition: A + B = B + A Associative Law: A + (B + C) = (A + B) + C A(BC) = (AB)C Distributive Law: A(B + C) ... Read More

Bayesian Decision Theory

Machine Learning
Beginner’s Guide to Bayesian Decision Theory Making Sense of the Unknown The term “Bayesian Decision Theory” sounds like something you’d only hear in a graduate-level statistics lecture. It can definitely feel intimidating at first glance! But at its core, it’s actually a highly intuitive concept. In fact, it’s a mathematical formalization of how we naturally ... Read More

Calculus – $a^x$ and $log_a x$

Calculus, Mathematics
In calculus, exponential functions with a base other than e (like ax) and logarithms with base a (like loga x) are handled by converting them into their “natural” forms. Since the natural exponential ex and natural log ln(x) have very simple derivatives, we use them as the bridge to understand ax and loga x. Interactive ... Read More
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