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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Time-Invariant Systems

A time-invariant system with shifted input and output

A system is time-invariant if shifting the input sequence on time axis leads to an equivalent shift of the output sequence along the time axis, with no other changes.

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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