A Real-Imaginative Guide to Complex Numbers

Plots for positive integer powers of x in 3D

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…
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A Beginner’s Guide to OFDM

OFDM slices the spectrum just like a bread

In the recent past, high data rate wireless communications is often considered synonymous to an Orthogonal Frequency Division Multiplexing (OFDM) system. OFDM is a special case of multi-carrier communication as opposed to a conventional single-carrier system.  The concepts on which…
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Minimum Shift Keying (MSK) – A Tutorial

MSK as a special case of both non-linear and linear modulation schemes

Minimum Shift Keying (MSK) is one of the most spectrally efficient modulation schemes available. Due to its constant envelope, it is resilient to non-linear distortion and was therefore chosen as the modulation technique for the GSM cell phone standard. MSK…
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Mueller and Muller Timing Synchronization Algorithm

Logic behind Mueller Muller TED

Proposed in 1976, Mueller and Muller algorithm is a timing synchronization technique that operates at symbol rate, as opposed to most other synchronization algorithms that require at least 2 samples/symbol. The most confusing thing communication engineers and radio hobbyists find…
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On Physics of Productivity

Isaac Newton

James Clear, an expert on habits formation, wrote an excellent essay titled The Physics of Productivity: Newton’s Laws of Getting Stuff Done. In that article, he explained Newton’s three laws of motion from his book The Principia: Mathematical Principles of…
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Why Building an SDR Requires DSP Expertise

Bandwidth, power and DSP correspond to the traditional trio of raw materials, energy and knowledge

In an introduction to signals, we discussed the idea that the any activities around us, starting from subatomic particles to massive societal networks, are generating signals all the time. Since mathematics is the language of the universe and digital signals…
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Costas Loop for Carrier Phase Synchronization

Output from the Costas Loop block after phase convergence

Costas loop is a carrier phase synchronization solution devised by John Costas at General Electric Company in 1956 [1]. It had an enormous impact on modem signal processing in general and carrier synchronization in particular. At that time, it was…
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There are 26 letters in English language and countless rules. The language of signal processing is simpler.

- It has only 1 letter: a sample at time 0. From there, we can build any discrete-time signal on which our 1s and 0s can be mapped.

- It has one major rule which is repeatedly employed for demapping the received signal to bits.