Blackman–Tukey transformation

Transformation

In electrical and electronic engineering, transformation from time domain to another domain, such as frequency domain, is used to focus more on the details of the waveform. Many of the details can be analyzed much easier when this transformation is done to waveform, when it goes to another domain. Different methods are present to do transformation from time domain to frequency domain; one of them is the Blackman–Tukey transformation method that also uses Fast Fourier transform. To meet the filter specification according to the requirements, several methods are used, including windowing effect.

Statistical estimation

Statistical estimation is 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 population in probability (group of subset). Because we have problem here, and in time series analysis, discrete data obtained as a function of time is usually available rather than samples of population or group of subsets taken simultaneously. The difficulty is commonly avoided by the process which is named 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 methods

This method has some procedures such as:

  1. Calculation of the autocorrelation function of the data
  2. Applying a suitable window function, and finally
  3. Computing a FFT of the data for obtaining the power density spectrum.

Autocorrelation function makes the wave smoothed rather than the 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.

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References
    • "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.
    • "Home – OnePetro". onepetro.org. Retrieved 2014-08-25.
    • Craig Stuart Sapp (17 October 1997). "Windows Package" (PDF). 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.com. Retrieved 2014-08-25.
    • Cs.dal.ca
    • Ece.unm.edu


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