Projections of a sphere in Flatland

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

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Bat echolocation principle

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

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Multiple objects at different speeds for an FMCW radar

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

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Maximum velocity in an FMCW radar

FMCW Radar Part 3 – Design Guidelines

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

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Eye diagram of CQPSK demodulation with a P25 C4FM receiver

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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