Projections of a sphere in Flatland
DSP / Wireless and SDR

Two Birds with One Tone: I/Q Signals and Fourier Transform – Part 2

In Part 1 on I/Q fundamentals series, we saw the implications of orthogonality in amplitude and phase shift. This led to our treatment of signals as two dimensional complex numbers in time I/Q plane. Now we talk about orthogonality in frequency, how it gives rise to a different I/Q plane and see its implications in signal processing applications. Let us start with a new perspective that will lift more veils from the I/Q puzzle. A Basic Building Block Humans use the power of logic to uncover the rules according to which the world works. But our minds struggle to retain

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Plots for positive integer powers of x in 3D
DSP / Miscellaneous

A Real-Imaginative Guide to Complex Numbers

June 18, 2020 On a cold morning in August 2015, I narrowly missed a train to my office in Melbourne city. With nothing else to do in the next 20 minutes, my mind wandered towards an intuitive view of complex numbers, something that has puzzled me since long. In particular, I wanted to seek answers to the following questions. (a) What is the role of the number $\sqrt{-1}$ in mathematics? What sets it apart from other impossible numbers, e.g., a number $k$ such that $|k|=-1$? (The origins of this question might lie in how I cut apple slices for my

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Eye diagram of CQPSK demodulation with a P25 C4FM receiver
Wireless and SDR

Demodulating P25 CQPSK Signals Using a C4FM Receiver

Usually a modulation of one species can only be demodulated with the radio signal processing chain of the same species. But P25 has a very interesting and unusual concept of demodulating a signal from one modulation species using the receiver of another species. APCO Project 25, commonly known as P25, is a suite of digital radio standards designed for public safety and first responder communications across North America which is similar to European Terrestrial Trunked Radio (TETRA). The main purpose of its development was to ensure seamless interoperability among federal, state and local agencies. Hence, it enables radios from different

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Pied Piper of Hamelin
Machine Learning

AI – An Advanced Civilization or a One-Trick Pony

Oct 19, 2024 Author’s Note This article, unlike the others on this website, is not about how some AI algorithms work. Instead, it is a personal opinion on AI and the future of our world. My hope is to generate more discussions on AI from this perspective. In such an undertaking, it is likely that I have made mistakes and failed to consider some critical aspect of the whole picture. Please feel free to comment and help me learn more. After some false starts, we are witnessing the true dawn of Artificial Intelligence (AI) today. Many people, including high profile

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An illustration of bandwidth-delay product
Radar and Localization / Wireless and SDR

An Intuitive View of Time-Bandwidth Product (TBP)

Time-Bandwidth Product (TBP) of a waveform is a foundational term frequently used in communications and radar community. However, I have never seen any book or online resource explain the core idea in an intuitive manner. Even though I understood the concepts of degrees of freedom and packing of resources in an $N$-dimensional space, I found it hard to come up with a visualization of time-bandwidth product in my head. This is what I set out to accomplish in this article. Let us start with the term Bandwidth-Delay Product (BDP), a term frequently used in communication networks. We will shortly relate

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