Category: DSP

Digital Signal Processing

Projections of a sphere in Flatland
DSP / Wireless and SDR

Two Birds with One Tone: I/Q Signals and Fourier Transform – Part 2

In Part 1 on I/Q fundamentals 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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Plots for positive integer powers of x in 3D
DSP / Miscellaneous

A Real-Imaginative Guide to Complex Numbers

June 18, 2020 On a cold morning in August 2015, I narrowly missed a train to my office in Melbourne city. With nothing else to do in the next 20 minutes, my mind wandered towards an intuitive view of complex numbers, something that has puzzled me since long. In particular, I wanted to seek answers to the following questions. (a) What is the role of the number $\sqrt{-1}$ in mathematics? What sets it apart from other impossible numbers, e.g., a number $k$ such that $|k|=-1$? (The origins of this question might lie in how I cut apple slices for my

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Orange vs tangerine
DSP

The Fourier Doppelgangers

It is well known that Fourier Transform is unique under certain conditions that are satisfied by almost all practical signals. Then, how can we resolve the following contradiction? Consider a sinc pulse and Linear Frequency Modulated (LFM) pulse (a chirp) in time domain. The sinc pulse is defined as \[ \text{sinc}(t) = \frac{sin(\pi t)}{\pi t} \] Now the spectrum of a sinc pulse in time in an ideal case is a rectangular signal in frequency domain, which is the most fundamental relation in signal processing. Both the sinc pulse and its spectrum are plotted in the left half of the

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Feedback AGC block diagram
DSP / Wireless and SDR

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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Wideband differentiator frequency and impulse responses
DSP

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

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