Lecture

Power spectral density and noise correlations

Graph Chat

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

Description

This lecture covers the concepts of power spectral density and noise correlations in the context of Cavity Quantum Optomechanics. It explains correlation functions, variance, Wiener-Khinchine theorem, common voltage noise spectra, and provides a harmonic oscillator example. The lecture delves into autocorrelation, Fourier representation of fluctuations, and the inverse Fourier transform of correlation functions. It discusses voltage noise examples such as white noise spectrum, Lorentzian power spectrum, and pink noise power spectrum. The summary emphasizes the importance of correlation functions, the Wiener-Khintchine theorem, and different types of classical noise categories like white noise and 1/f noise, with a focus on thermal noise in a harmonic oscillator.

Official source

Ontological neighbourhood

Information engineering

Signal processing: Digital image processing

Related concepts (31)

Shot noise

Shot noise or Poisson noise is a type of noise which can be modeled by a Poisson process. In electronics shot noise originates from the discrete nature of electric charge. Shot noise also occurs in photon counting in optical devices, where shot noise is associated with the particle nature of light. In a statistical experiment such as tossing a fair coin and counting the occurrences of heads and tails, the numbers of heads and tails after many throws will differ by only a tiny percentage, while after only a few throws outcomes with a significant excess of heads over tails or vice versa are common; if an experiment with a few throws is repeated over and over, the outcomes will fluctuate a lot.

Colors of noise

In audio engineering, electronics, physics, and many other fields, the color of noise or noise spectrum refers to the power spectrum of a noise signal (a signal produced by a stochastic process). Different colors of noise have significantly different properties. For example, as audio signals they will sound differently to human ears, and as they will have a visibly different texture. Therefore, each application typically requires noise of a specific color.

Noise (electronics)

In electronics, noise is an unwanted disturbance in an electrical signal. Noise generated by electronic devices varies greatly as it is produced by several different effects. In particular, noise is inherent in physics and central to thermodynamics. Any conductor with electrical resistance will generate thermal noise inherently. The final elimination of thermal noise in electronics can only be achieved cryogenically, and even then quantum noise would remain inherent. Electronic noise is a common component of noise in signal processing.

Johnson–Nyquist noise

Johnson–Nyquist noise (thermal noise, Johnson noise, or Nyquist noise) is the electronic noise generated by the thermal agitation of the charge carriers (usually the electrons) inside an electrical conductor at equilibrium, which happens regardless of any applied voltage. Thermal noise is present in all electrical circuits, and in sensitive electronic equipment (such as radio receivers) can drown out weak signals, and can be the limiting factor on sensitivity of electrical measuring instruments.

Pink noise

Pink noise, noise or fractal noise is a signal or process with a frequency spectrum such that the power spectral density (power per frequency interval) is inversely proportional to the frequency of the signal. In pink noise, each octave interval (halving or doubling in frequency) carries an equal amount of noise energy. Pink noise sounds like a waterfall. It is often used to tune loudspeaker systems in professional audio. Pink noise is one of the most commonly observed signals in biological systems.

Related lectures (64)

Signal Processing Fundamentals

Explores signal processing fundamentals, including discrete time signals, spectral factorization, and stochastic processes.

Noise and Measurements

Explores electronic, thermomechanical, and amplifier noise, calibration of amplitude, frequency tracking, and system limits.

Noise in Devices and Circuits

Explores different types of noise in devices and circuits, including interference noise, inherent noise, and random signals.

Laser Fundamentals: Coherence and Noise

Explores laser fundamentals, including coherence and noise characteristics, such as relaxation oscillations and shot noise.

Laser Noise: Understanding Laser Line Width and Coherence