If we pay attention, each term in a mathematical equation carries a meaning that resonates with common sense. Today I will explain where Lotka-Volterra equations come from. These equations describe the dynamics of a biological interaction in which a predator (e.g., foxes) and a prey species (e.g., rabbits) engage with each other in a continuous struggle for survival. We will see that the math expressions just line up to describe the phenomenon almost as in words. Moreover, they have a little connection to IQ signals, the fundamental concept in digital signal processing, that will also be presented in the article.

Continue reading## 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

Continue reading## The Reason Why the Monty Hall Problem Continues to Perplex Everyone

The Monty Hall problem is an interesting puzzle loosely based on an American TV game show Let’s Make a Deal hosted by Monty Hall. While the puzzle looked simple, it perplexed some of the brightest mathematical minds in the United States, including the great Paul Erdös who was one of the most prolific mathematicians of the 20th century. This continues to be the case today. I looked upon a number of references to find the source of confusion in the Monty Hall problem but failed. All I found was different solutions. Therefore, I built one myself with the usual from

Continue reading## 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

Continue reading## How Automatic Gain Control (AGC) Works

Alfred North Whitehead said, "Civilization advances by extending the number of important operations which we can perform without thinking of them." In today’s world, it is easy to take no notice of the level of process automation integrated into our lives. To have an idea of how things were in the early days, signal processing technology to sort out the radar picture on a map was not available and only a dot or a line could be generated on the screen representing a detected target. A radar operator had to stare at a screen for their whole shift to raise

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