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.

Pulse Shaping Filter

Illustration of peak ISI and asymmetry about -3dB point

From the previous articles, we have seen how a Tx generates a signal from the numbers and the Rx recovers those numbers from that signal. In time domain, everything looks nice and perfect. Let us investigate the system characteristics in…
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Demodulation – From Signals Back to Numbers

The blue line is the signal template and while red is the matched filter. Notice the same magnitude on each spectral line but exactly opposite phase

Remember that in the article on correlation, we discussed that correlation of a signal with proper normalization is maximum with itself and lesser for all other signals. Since the number of possible signals is limited in a digital communication system,…
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Sampling a Continuous-Time Signal

Spectrum of a sampled signal with aliases shown

The 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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