Frequency estimation is the process of estimating

Estimation theory

Estimation theory is a branch of statistics and signal processing that deals with estimating the values of parameters based on measured/empirical data that has a random component. The parameters describe an underlying physical setting in such a way that their value affects the distribution of the...

 the complex frequency

Frequency

Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...

 components of a signal

Digital signal processing

Digital signal processing is concerned with the representation of discrete time signals by a sequence of numbers or symbols and the processing of these signals. Digital signal processing and analog signal processing are subfields of signal processing...

 in the presence of noise

Noise

In common use, the word noise means any unwanted sound. In both analog and digital electronics, noise is random unwanted perturbation to a wanted signal; it is called noise as a generalisation of the acoustic noise heard when listening to a weak radio transmission with significant electrical noise...

. The most common methods involve identifying the noise subspace

Linear subspace

The concept of a linear subspace is important in linear algebra and related fields of mathematics.A linear subspace is usually called simply a subspace when the context serves to distinguish it from other kinds of subspaces....

 to extract these components. The most popular methods of noise subspace based frequency estimation are Pisarenko's Method

Pisarenko harmonic decomposition

Pisarenko harmonic decomposition, also referred to as Pisarenko's method, is a method of frequency estimation . This method assumes that a signal, x, consists of p complex exponentials in the presence of white noise...

, MUSIC

Multiple signal classification

MUltiple SIgnal Classification is an algorithm used for frequency estimation and emitter location.- MUSIC algorithm :In many practical signal processing problems, the objective is to estimate from measurements a set of constant parameters upon which the received signals depend...

, the eigenvector solution, and the minimum norm solution.

For example, consider a signal, , consisting of a sum of complex exponentials in the presence of white noise

White noise

White noise is a random signal with a flat power spectral density. In other words, the signal contains equal power within a fixed bandwidth at any center frequency...

, .