IntermediateTopic 41 of 101Signals, Control & Comms
Random signals and noise
Stochastic processes characterised by autocorrelation and power spectral density.
In depth
Random signals are described statistically: mean, variance, autocorrelation R_x(τ), and power spectral density S_x(ω) (Wiener-Khinchin). White noise has flat PSD; coloured noise is shaped by filtering. Stationarity and ergodicity let time averages estimate ensemble averages. Thermal noise follows Gaussian statistics.
Key points
- Gaussian processes
- SNR
- Noise figure
ExamplePassing white noise through a filter produces noise with the filter's spectral shape.
What is Random signals and noise?
Stochastic processes characterised by autocorrelation and power spectral density.
Why is it important to understand random signals and noise?
Random signals are the reality of most measurements, so characterising noise is needed to know what can be detected.
What is autocorrelation?
The correlation of a signal with a delayed copy of itself, which shows how long its values stay related.
What does the power spectral density show?
How the power of a random signal is distributed over frequency, and it is the Fourier transform of the autocorrelation.
How is Random signals and noise used in practice?
Typical applications include estimating the noise floor of a sensor in a precision instrument, predicting how much averaging is needed to see a small signal and describing the random vibration of a vehicle on a rough road.
What should I learn before Random signals and noise?
Study "Audio and speech processing" first (topic 40 of 101 in Signals, Control & Comms). It covers the groundwork this topic builds on.
What are the key points of Random signals and noise?
Gaussian processes. SNR. Noise figure.
Can you give an example of Random signals and noise?
Passing white noise through a filter produces noise with the filter's spectral shape.
What comes after Random signals and noise?
The next topic is "Wiener and Kalman filters", which builds directly on this one.
How difficult is Random signals and noise?
It is classed as Intermediate in Signals, Control & Comms (topic 41 of 101). It is an intermediate topic. Work through the beginner topics in Signals, Control & Comms first.