I/Q signals as the gateway to DSP

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

When a new member arrives at the DSP 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 DSP). Others persist enough to push the gate open (even a little understanding is sufficient for this task). So what exactly makes this topic so mysterious? To investigate the answer, we start with an example audio signal drawn in the figure below that displays amplitude

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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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A quarter sample rate complex sinusoid

Spectral Shift without any Multiplications

One of the great advantages of Digital Signal Processing (DSP) is an unexpected simplification of operations in seemingly complicated scenarios. See the Cascade Integrator Comb (CIC) filters for how to accomplish the task of sample rate conversion along with filtering with minimal resources. As another example, in wireless communications and many other applications, a frequency translation is often required in which the spectrum of a signal centered at a particular frequency needs to be moved to another frequency. From the properties of Fourier Transform, a shift by frequency $\omega_0=2\pi F_0$ requires sample-by-sample multiplication with a complex sinusoid $e^{j\omega_0 t}$. \[

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