Noise and fluctuations in physical systems course

Table of contents

1. INTRODUCTION (open pdf file)
1.1. Noise and fluctuations in nature
1.2. Random noise in physical systems
1.3. What to do with noise?
1.4. Sources of noise in a system

2. MATHEMATICAL DESCRIPTION OF NOISE (open pdf file)
2.1. Probability
2.2. Probability density
2.3. Distribution function
2.4. Some practical quantities
2.5. Time dependence, stationarity, ergodicity
2.6. Correlation functions
2.6.1. Joint probability density
2.6.2. Autocorrelation function
2.6.3. Cross correlation
2.6.4. Autocorrelation of sum of multiple processes
2.7. Frequency domain description
2.7.1. Fourier transform
2.7.2. Power density spectrum
2.7.3. Power spectrum of sum of multiple processes
2.7.4. Finite time analysis
2.7.5. Time dependent spectral analysis
2.7.5.1. Wavelet analysis
2.7.5.2. Windowed Fourier transform
2.8. Classification of noises according to p(x), Rxx (t) and Sxx (f)

3. MEASUREMENT OF NOISE  (open pdf file)
3.1. Analog measurements of noise
3.1.1. Measurements of <x>, RMS(x), VAR(x)
3.1.2. Measurement of spectral density
3.1.3. Measurement of correlation
3.2. Digital measurements and digital signal processing
3.2.1. Basic elements of digital measurements
3.2.1.1. A/D converters (ADC)
3.2.1.2. D/A converters (DAC)
3.2.1.3. Digital signal processors (DSP)
3.2.2. Sampled data systems
3.2.3. Quantization and aperture jitter noise
3.2.4. Aliasing, antialiasing filters
3.2.5. Using aliasing for frequency conversion
3.2.6. Measurement of probability and p(x)
3.2.7. Measurement of power density spectrum
3.2.7.1. DFT, FFT
3.2.8. Window functions
3.2.9. Time dependent spectral analysis
3.2.9.1. Wavelets
3.2.9.2. Windowed FFT
3.2.10. Measurement of special quantities
3.3. Small signal and low noise measurements
3.3.1. Operational amplifier noise
3.3.2. Bandwidth considerations
3.3.3. External noise sources
3.3.4. Noise reduction techniques
3.3.4.1. Limiting bandwidth
3.3.4.2. Paralelling systems
3.3.4.3. Reducing source and other impedances
3.3.4.4. Using lock-in techniques
3.3.5. Reducing external noise
3.3.6. Noise shaping

4. PHYSICAL NOISES  (open pdf file)
4.1. Internal/excess noises
4.2. Thermal noise
4.3. Shot noise
4.4. Brownian motion
4.5. Diffusion noise
4.6. 1/f noise (flicker, pink noise)

5. MODELLING OF NOISE  (open pdf file)
5.1. Analog simulation
5.1.1. Operational units
5.1.1.1. Operational amplifier
5.1.1.2. Amplification
5.1.1.3. Addition
5.1.1.4. Subtraction
5.1.1.5. Integration, differentation
5.1.1.6. Log, exp functions
5.1.1.7. Multiplication, square root
5.1.1.8. Function approximation
5.1.2. Noise generation methods
5.1.2.1. White noise
5.1.2.2. Lorentzian noise
5.1.2.3. 1/f 2 noise
5.1.2.4. 1/f noise
5.1.3. Solving differential equations
5.1.4. Practical considerations
5.2. Numerical simulations
5.2.1. Monte Carlo methods
5.2.2. Generating random numbers
5.2.2.1. Linear congruential method
5.2.2.2. Additive method
5.2.2.3. Shuffling random numbers
5.2.2.4. Normal distribution
5.2.2.5. Arbitrary distribution
5.2.2.6. Generating noises with different spectra
5.2.3. Random decisions
5.2.4. Some applications of MC
5.2.4.1. Integration
5.2.4.2. Random walk
5.2.4.3. 2D Ising model
5.3. Mixed signal simulations
5.3.1. Digital signal processing
5.3.1.1. A/D and D/A conversion
5.3.1.2. Digital signal processors
5.3.1.3. Digital noise generators
5.3.2. Aliasing in numerical modellings

6. USING NOISE IN SYSTEM MEASUREMENTS (open pdf file)
6.1. Noise as a diagnostic tool
6.2. Random excitations for measurements of transfer functions
6.3. Applications of cross-correlational analysis
6.3.1. Measurement of speed
6.3.2. Reactor diagnostics
6.4. Dithering

7. NOISE IN BIOLOGICAL SYSTEMS (open pdf file)
7.1. Noise in neuro-cardiology - Basic concepts
7.2. Measurments of quantities
7.3. Methods of analysis
7.3.1. Statistical quantities (mean, RMS, p(x))
7.3.2. Spectral analysis
7.3.3. Time dependent spectral analysis
7.3.4. Correlation analysis

8. SOME RECENT RESULTS AND PROBLEMS IN NOISE RESEARCH (open pdf file)
8.1. New models and properties of 1/f noise
8.1.1. Scaling Brownian motion
8.1.2. Amplitude saturation of 1/f noise
8.2. Stochastic resonance
8.3. Biased percolation model of device degradation