[[wiki-architecture]] · [[Urban Planning and City Architecture]] · [[ARCHITECTURE]] · [[000]] # Blackman–Tukey transformation The Blackman–Tukey transformation (or Blackman–Tukey method) is a digital signal processing method to transform data from the time domain to the frequency domain. It was originally programmed around 1953 by James Cooley for John Tukey at John von Neumann's Institute for Advanced Study as a way to get "good smoothed statistical estimates of power spectra without requiring large Fourier transforms." It was published by Ralph Beebe Blackman and John Tukey in 1958. == 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. == Blackman–Tukey transformation method == The method is fully described in Blackman and Tukey's 1958 journal publications republished as their 1959 book "The measurement of power spectra, from the point of view of communications engineering" and is outlined by the following procedures: Calculate the autocorrelation function with the data Apply a suitable window function, and finally Compute a discrete Fourier transform (now done with FFT) of the data to obtain the power density spectrum Autocorrelation makes the wave smoothed rather than averaging several waveforms. This function is set to window, the corresponding waveform toward its extremes. Computation gets faster if more data is correlated and if memory capacity of the system increases then overlap save sectioning technique would be applied. If the autocorrelation function in Blackman–Tukey is computed using FFT, then it will name fast correlation method for spectral estimation. == References == - [[Building Construction/Structural Systems/Timber Structures]] - [[Building Construction/Structural Systems/Foundation Systems]] - [[Environmental Design/Life Cycle Assessment]] - [[Wiki-Architecture/Buildings and Structures]] - [[Professional Practice/Codes & Standards/National Building Code of India/Part 08 - Building Services/Section 5A - Lifts]] - [[Design/Building Typologies/Hospitality Architecture]] - [[Interior Architecture]] - [[Urban and Planning/Urban Design Principles]] - [[History and Theory/Vernacular]] - [[Professional Practice/Construction Management/Contract Administration]] == External links == "Blackman–Tukey Correlogram and Cross-Spectrum". spectraworks.com. Retrieved 2014-08-25. David Meko (10 February 2013). "Spectral Analysis -- Smoothed Periodogram Method" (PDF). Archived from the original (PDF) on 17 September 2003. Retrieved 2014-08-25. "random – What is the distinction between ergodic and stationary? – Signal Processing Stack Exchange". dsp.stackexchange.com. Retrieved 2014-08-25. Nick Kingsbury (31 October 2005). "Connexions module: m11103 | Ergodicity" (PDF). Retrieved 2014-08-25. Donna Williams (15 January 2004). "Understanding FFT Windows" (PDF). Archived from the original (PDF) on 13 February 2015. Retrieved 2014-08-25. Peter Cheung (20 February 2011). "Signal Transmission through LTI Systems" (PDF). Retrieved 2014-08-25. "Windowing effect on spectral leakage and phase – Newsreader – MATLAB Central". Mathworks MATLAB Newsgroup. 2009-11-18. Archived from the original on 2016-03-04. Retrieved 2014-08-25. Santhanam, Balu. "Ergodic Processes" (PDF). Archived from the original (PDF) on 2012-01-06.