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…
Read more

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,…
Read more

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…
Read more

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.