Windowing is the technique whereby an infinite signal is truncated in the time domain. Truncation of the signal in this way has side effects, primarily the introduction of ripples in the frequency domain. These ripples show up as high frequency noise and adversely affect integrity of the datasets. The data with which we are provided is a finite subset of an infinite signal, and consequently, this process has been performed implicitly prior to any post processing. Application of a filtering function can attenuate these frequencies, resulting in a more faithful representation of the original signal. As previously stated, truncation of the signal in the time domain leads to unwanted ripples being produced in the frequency domain. The basic idea behind windowing the data prior to performing a Fourier transformation is that we can apply a weighting function to the sample in order to reduce the introduction of unwanted frequencies. This reduction is a trade off, and the cost is an increase in the width of the spectral peak and leakage of energy away from the true frequency to the side lobe skirts. This adversely effects the resolution with which we can observe the signal (for a more in depth discussion of this topic see the section on Frequency Domain Analysis theory below). We must, therefore, strike a balance between spectral peak width and the degree of high frequency attenuation. Ideally we would like to have no skirts, but in practise the best we can do is try to control them. The available windowing algorithms vary in their ability to control this while trying to retain a fine spectral peak. The attributes of each algorithm can be summarised as follows: Hanning: This algorithm provides good resolution of spectral peaks and acceptable rejection of side lobe skirts. It is a suitable choice for most applications. The Hanning window is a simple cosine offset by sufficient amount to set the minima to zero. The coefficients are calculated using the equation: eqimghanning.bmp Hamming Hamming provides finer resolution of spectral peaks than Hanning windows, however, side lobe skirts are not controlled as well as with this method. The Hamming window is a slightly modified Hanning window, with the difference being that the DC bias is marginally different and the wave is compressed. The coefficients are calculated as follows: eqimghamming.bmp Blackman Blackman peak resolution is not as fine as that produced with the Hanning method. The advantage with the Blackman window is, however, that the response shape flares out less at lower levels and rejection of side lobe skirts is better. A Blackman window is composed of two cosine waves, causing the skirts to fall away faster than the previous two and resulting in a narrower peak. the equation is: eqimgblackman.bmp Dolph-Chebyshev Dolph-Chebyshev windows are very similar to those produced by Hamming, with improved high frequency attenuation. Where Hamming can provide around 50dB attenuation for frequencies above the sampling frequency, Dolph-Chebyshev can provide approximately 63dB attenuation for the same frequencies. This window is vastly different to the other windowing implementations. The coefficients are generated by calculating the inverse Fourier transform of the Chebyshev function evaluated at n equally spaced points on the unit circle. The Chebyshev function is defined as: eqimgchebyshev1.bmp Windowing can be an effective tool in removing the undesirable effects of the Discrete Fourier Transform (DFT). Prudent use of a suitable algorithm removes the high frequencies introduced via aliasing when the the signal is truncated. Knowledge of the attributes and limitations of the individual windowing algorithms, and the judicious selection of the correct one, will assist the user in attaining optimal results from the application of the DFT.