Power spectral density and noise correlations

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.