BeginnerTopic 2 of 101Signals, Control & Comms
Continuous and discrete signals
Continuous-time signals are defined for all t; discrete ones only at sample instants.
In depth
Continuous-time signals x(t) are defined for every real t; discrete-time signals x[n] only at integer sample indices. Sampling turns the first into the second; digital signals are also quantised in amplitude. Mathematics differs: integrals and derivatives vs sums and differences.
Key points
- Sampling interval T_s
- Analog vs digital
- Notation x(t) vs x[n]
ExampleAudio on a CD is a discrete-time signal sampled at 44.1 kHz.
What is Continuous and discrete signals?
Continuous-time signals are defined for all t; discrete ones only at sample instants.
Why is it important to understand continuous and discrete signals?
Continuous and discrete signals differ in the mathematics you use, and most digital systems work with discrete samples.
What is the difference between x(t) and x[n]?
x(t) is defined at every instant of time, while x[n] is defined only at integer indices, which are the sample times.
Can a discrete signal be turned back into a continuous one?
Yes, if it was sampled fast enough and filtered correctly, as described by the sampling theorem.
How is Continuous and discrete signals used in practice?
Typical applications include digitising a sensor output into numbers for a microcontroller, describing a daily sales record as a discrete sequence and choosing integrals for an analogue filter and sums for a digital one.
What should I learn before Continuous and discrete signals?
Study "Signals" first (topic 1 of 101 in Signals, Control & Comms). It covers the groundwork this topic builds on.
What are the key points of Continuous and discrete signals?
Sampling interval T_s. Analog vs digital. Notation x(t) vs x[n].
Can you give an example of Continuous and discrete signals?
Audio on a CD is a discrete-time signal sampled at 44.1 kHz.
What comes after Continuous and discrete signals?
The next topic is "Periodic and aperiodic signals", which builds directly on this one.
How difficult is Continuous and discrete signals?
It is classed as Beginner in Signals, Control & Comms (topic 2 of 101). It is an entry-level topic. It relies only on basic school mathematics and the ideas introduced earlier in this discipline.