Correlation is a foundation over which the whole structure of digital communications is built. In fact, correlation is the heart of a digital communication system, not only for data detection but for parameter estimation of various kinds as well. Throughout,…
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Linear Systems

A linear system with scaled input and output

A linear system implies that if two inputs are scaled and summed together to form a new input, the new output of the system is also a scaled sum of their individual outputs. [Scaling] For scaling to hold, if \begin{align*}…
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A Digital Signal

A digital signal and its underlying continuous waveform

We have talked about obtaining a discrete-time signal through sampling the time-axis and obtaining a discrete frequency set through sampling the frequency axis. The same concept can be applied to the amplitude-axis, where the signal amplitude can be sampled to…
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Pulse Amplitude Modulation (PAM)

Block diagram of a pulse amplitude modulator and demodulator

In the article on modulation – from numbers to signals, we said that the Pulse Amplitude Modulation (PAM) is an amplitude scaling of the pulse $p(nT_S)$ according to the symbol value. What happens when this process of scaling the pulse…
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Some DFT Properties

The purpose of this article is to summarize some useful DFT properties in a table. If you feel that this particular content is not as descriptive as the other posts on this website are, you are right. As opposed to…
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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.