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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The Big Picture of Localization

Two way transmission

Digital Signal Processing (DSP) enables us to find the range of a device transmitting a wireless signal with a particular structure under some conditions. To understand how this process works, we need to look at the big picture of a…
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FSK Demodulation in GNU Radio

Flowgraph output

One of the most useful modulation techniques in applications requiring low receiver complexity is Frequency Shift Keying (FSK). In an FSK scheme, digital information is transmitted by changing the frequency of a carrier signal. Binary FSK Binary FSK (BFSK) is…
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Windowing an OFDM Signal in Time Domain

At the boundary of two OFDM symbols, pulse shaping smoothes the edges, resulting in the avoidance of spectral regrowth

Orthogonal Frequency Division Multiplexing (OFDM) has been introduced in a previous article as a technique suitable for high data-rate transmissions over a wireless channel. The two main advantages I mentioned were as follows: Simple one-tap equalization, and Ability to slice…
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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.


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