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 readingFMCW 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 readingHow 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
Continue readingDesign of a Discrete-Time Differentiator
Many signal processing algorithms require computation of the derivative of a signal in real-time. Some of the examples are timing recovery, carrier frequency synchronization, FM demodulation and demodulation of LoRa signals. An analog or digital filter that computes such a derivative is known as a differentiator. Before we design such a discrete-time differentiating filter, let us review some of the fundamentals. A Derivative The following quote is attributed to Heraclitus, a Greek philosopher, from 535 BC. Change is the only constant in life. This was brought into the realm of science by Newton and Leibniz. The purpose of science is
Continue readingNoise is Not Always the Enemy
Noise is usually considered the main enemy in all DSP applications. As David Tse once said: “Noise is the reason for our existence (communication engineers)!” This short article briefly describes why noise sometimes plays a positive role, e.g., in the context of analog-to-digital conversion when the signal is very weak. Introduction Noise is the enemy to be conquered, particularly in communications and radar systems. In a noise-limited regime, we hit a performance brick wall due to the presence of noise. Think of parameter estimation in which the primary criteria is to establish a certain performance against a target signal-to-noise ratio.
Continue reading