Dealing with Complex Numbers

A complex number with its I and Q components

Although complex notation is not complex to understand, I attempt to avoid complex notation altogether while reading DSP articles. If you are interested in where these complex numbers come from, you can read my real-imaginative guide to complex numbers. A…
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What is a Signal?


In traditional Digital Signal Processing (DSP) courses, we usually learn about signals in a narrow context. While this is probably the correct approach for an introduction to this field, there is a broader theme to the concept of signals. Let…
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How a Frequency Locked Loop (FLL) Works

Minimum distance rule based detector decisions in a QPSK constellation in the presence of a carrier frequency offset

A Phase Locked Loop (PLL) is a device used to synchronize a periodic waveform with a reference periodic waveform. It is an automatic control system in which the phase of the output signal is locked to the phase of the…
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Computing Error Rates

Spectral efficiency R_b/B versus E_b/N_0 determines the overall merit of a modulation scheme. This figure is drawn for BER = 10^{-5} and a Square-Root Raised Cosine pulse with 50% excess bandwidth

Having built a simple digital communication system, it is necessary to know how to measure its performance. As the names say, Symbol Error Rate (SER) and Bit Error Rate (BER) are the probabilities of receiving a symbol and bit in…
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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.