Fundamentals of Statistics contains material of various lectures and courses of H. Lohninger on statistics, data analysis and here for more.

Physical Origin of Noise

Noise is called fundamental when it arises from the particle nature of light and matter and can never be totally eliminated, while non-fundamental (or excess) noise is due to imperfect components and instrumentation and can at least theoretically be eliminated. Non-random noise is never fundamental.

Fundamental noise:

  • Thermal noise is generated by the thermal (Brownian) motion of electrons or charged particles in electrical components (e.g. resistor, or capacitor) and disappears only at an absolute temperature of zero Kelvin.
  • Quantum noise (also called shot noise) is caused when, e.g. electrons or charged particles move across a junction. These events are quantized and therefore Poisson-distributed.

Non-fundamental noise:

  • Flicker noise is formed at transformation points or readout systems and can cause drifts. When the magnitude of the noise is inversely proportional to its frequency, then one speaks of 1/f noise. If the variance is proportional to the signal, this type of noise is also called proportional, multiplicative or heteroscedastic.
  • Environmental or interference noise is frequency-dependent. Often it is present only at certain discrete frequencies, e.g. by picking up electromagnetic radiation (50/60 Hz + harmonics from AC power).
  • Impulse noise originates, e.g. from turning instruments on/off and can cause so-called spikes. A source of this type of noise often encountered in labs is refrigerators. They create a large surge of electrical current when they are switched on, and create high voltages on the power line when the motor is switched off.
  • Quantization noise is due to the finite resolution of analog-to-digital converters.

Since an instrument consists of a lot of different components, which individually introduce noise into the signal, the resulting measurement is contaminated by noise which may show complex properties. Fortunately, either one component is dominant so that the other contributions can be neglected, or the central limit theorem applies. In the second case, the noise in the system shows normal distribution.