# Noise Generation

You can use noise signals to perform frequency response measurements or to simulate certain processes. Several types of noise are typically used, namely uniform white noise, Gaussian white noise, and periodic random noise.

The term white in the definition of noise refers to the frequency domain characteristic of noise. Ideal white noise has equal power per unit bandwidth, resulting in a flat power spectral density across the frequency range of interest. Thus, the power in the frequency range from 100 Hz to 110 Hz is the same as the power in the frequency range from 1,000 Hz to 1,010 Hz. In practical measurements, achieving the flat power spectral density requires an infinite number of samples. Thus, when making measurements of white noise, the power spectra are usually averaged, with more number of averages resulting in a flatter power spectrum.

The terms uniform and Gaussian refer to the probability density function (PDF) of the amplitudes of the time-domain samples of the noise. For uniform white noise, the PDF of the amplitudes of the time domain samples is uniform within the specified maximum and minimum levels. In other words, all amplitude values between some limits are equally likely or probable. Thermal noise produced in active components tends to be uniform white in distribution. The following figure shows the distribution of the samples of uniform white noise.

For Gaussian white noise, the PDF of the amplitudes of the time domain samples is Gaussian. If uniform white noise is passed through a linear system, the resulting output is Gaussian white noise. The following figure shows the distribution of the samples of Gaussian white noise.

Periodic random noise (PRN) is a summation of sinusoidal signals with the same amplitudes but with random phases. PRN consists of all sine waves with frequencies that can be represented with an integral number of cycles in the requested number of samples. Because PRN contains only integral-cycle sinusoids, you do not need to window PRN before performing spectral analysis. PRN is self-windowing and therefore has no spectral leakage.

PRN does not have energy at all frequencies as white noise does but has energy only at discrete frequencies that correspond to harmonics of a fundamental frequency. The fundamental frequency is equal to the sampling frequency divided by the number of samples. However, the level of noise at each of the discrete frequencies is the same.

You can use PRN to compute the frequency response of a linear system with one time record instead of averaging the frequency response over several time records, as you must for non-periodic random noise sources. The following figure shows the spectrum of PRN and the averaged spectra of white noise.