Sampling a Continuous-Time Signal

Spectrum of a sampled signal with aliases shown

Most signals of our interest — wireless communication waveforms — are continuous-time as they have to travel through a real wireless channel. To process such a signal using digital signal processing techniques, the signal must be converted into a sequence…
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Dealing with Complex Numbers

A complex number with its I and Q components

Although complex notation is not complex to understand, one of the themes of this text is to avoid complex notation altogether. A complex number is defined as an ordered pair of real numbers in $(x,y)$-plane. In that respect, complex numbers…
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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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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.