DSP Archives | Wireless Pi

Theory of relativity and age of planet Earth

May 19, 2024 DSP / Localization

The Easiest Tutorial on Kalman Filter

Kalman filter is one of the most important but not so well explained filter in the field of statistical signal processing. As far as its importance is concerned, it has seen a phenomenal rise since its discovery in 1960. One of the major factors behind this is its role of fusing estimates in time and space in an information-rich world. For example, position awareness is not limited to radars and self driving vehicles anymore but instead has become an integral component in proper operation of industrial control, robotics, precision agriculture, drones and augmented reality. Kalman filter plays a major role

March 23, 2025 DSP / Wireless/SDR

Two Birds with One Tone: I/Q Signals and Fourier Transform – Part 1

When a new member arrives at the Signal Processing Club, this is what they find at the club gate: I/Q signals. Perhaps a secret plot to keep most people out of the party? Some return from here to try another area (e.g., machine learning, which pays more and is easier to understand but less interesting than signal processing). Others persist enough to push the gate open for implementation purposes (even a little understanding is sufficient for this task) but never fully grasp the main idea. So what exactly makes this topic so mysterious? To investigate the answer, we start with

May 28, 2025 DSP / Wireless/SDR

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

In Part 1 of I/Q signals 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

Plots for positive integer powers of x in 3D

June 26, 2020 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

September 30, 2023 DSP / Localization

FMCW Radar Part 1 – Ranging

This is Part 1 of a 3-Part series in which we describe how an FMCW radar finds the range of multiple stationary targets. In Part 2, we talk about estimating the velocities of several moving targets and their directions through forming a structure known as the radar cube. Part 3 presents system design guidelines for an FMCW radar. In his book Multirate Signal Processing, Fred Harris mentions a great problem solving technique: "When faced with an unsolvable problem, change it into one you can solve, and solve that one instead." We will see in this article how an FMCW radar