Blackman–Tukey transformation

Background

Transformation

In signal processing, transformation from the time domain to another domain, such as the frequency domain, is used to focus on the details of a waveform. Many of the waveform's details can be analyzed much more easily in a domain other than the original. Different methods exist to do transformation from time domain to frequency domain; the most prominent is the Fourier transform, which the Blackman–Tukey method uses. Prior to the advent of fast computers and the 1965 rediscovery of the fast Fourier transform, the large number of computations necessary for the discrete Fourier Transform motivated researchers to reduce the number of calculations required, resulting in the (now obsolete) Blackman–Tukey method based on the Wiener-Khinchin theorem.

Statistical estimation

Statistical estimation is used to determine the expected value(s) of statistical expected values of statistical quantities. Statistical estimation also tries to find the expected values. The expected values are those values that we expect among the random values, derived from samples of the population in probability (group of subset). In time series analysis, discrete data obtained as a function of time is usually the only type of data available, instead of samples of population or group of subsets taken simultaneously.

Difficulty is commonly avoided using an ergodic process, that changes with time and probability gets involved with it, and it's not always periodic at all portions of time.