The Bloom’s Taxonomy describes the levels of mastery one attains in a field. Its last two stages are Synthesis and Evaluation. This is where the masters can be differentiated from the experts. In a job interview, for example, a good technique to judge a candidate’s ability is to ask them where the system in question breaks. A little learning is a dangerous thing Drink deep, or taste not the Pierian spring There shallow draughts intoxicate the brain And drinking largely sobers us again While the first two parts of the FMCW radar series addressed the lower levels, Part 3 is where we get into a system evaluation framework. In Part 1, we described how a radar estimates the range of

Continue reading# Tag: Frequency Modulation (FM)

## FMCW Radar Part 2 – Velocity, Angle and Radar Data Cube

In Part 1 of FMCW radar series, we described how a radar estimates the range of one or more 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 a wonderful 1991 paper "Wireless Digital Communication: A View Based on Three Lessons Learned", Andrew Viterbi summarizes the Shannon theory for digital communications in the form of 3 lessons, the first of which was the following. "Never discard information prematurely that may be useful in making a decision until after all decisions related to that information have been completed." The applications of this

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 is one of the most beautiful applications of this approach. The apparently logical method to measure the range of an

Continue reading## Design 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 not only to investigate how things are, but also to understand how they change with time (or another variable). While

Continue reading## Frequency Modulation (FM) and Demodulation Using DSP Techniques

Frequency Modulation (FM) is as old as the history of wireless communications itself. The past few decades saw the rise of digital signal processing in all spheres of life that pervaded even the implementation of analog modulation schemes. Today many of the FM systems are built using discrete-time techniques instead of the conventional circuitry as described below. Frequency Modulation In digital communications, data is sent through altering a characteristic of an electromagnetic wave such as amplitude, frequency or phase in discrete steps (e.g., $M$ number of levels). Such systems are known as Amplitude Shift Keying (ASK), Frequency Shift Keying (FSK) and Phase Shift Keying (PSK), respectively. Analog modulation schemes, on the other hand, vary the desired parameter in a continuous

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