#Fft windowing windows#

% Create the values for the hamming function, stored in vector called hamming Twindow = t(1:2048) %first 2048 elements of t % t is an array of times at which the hamming function is evaluated In MATLAB, you can accomplish this with vector multiplication, as shown in the commands below. The segment of audio data being transformed is simply multiplied by the windowing function before the transform is applied. Four commonly-used windowing functions are given in the table below. In Figure 2.50, the Hanning function is chosen. The drop-down menu to the left of the FFT size menu in Audition is where you choose the windowing function. In order to smooth over this discontinuity and thereby reduce the amount of spectral leakage, the windowing functions effectively taper the ends of the segments to 0 so that they connect from beginning to end. Although the audio signal actually contains only one frequency at 880 Hz, the frequency analysis view indicates that there is a small amount of other frequencies across the audible spectrum. You can see the spectral leakage Figure 2.41.

#Fft windowing windows#

In the output of the FFT, the discontinuity between the ends and the beginnings of the windows manifests itself as frequency components that donвЂ™t really exist in audio вЂ“ called spurious frequencies, or spectral leakage. (In this figure, weвЂ™ve cut and pasted a portion from the beginning of the window to its end to show that the ends donвЂ™t match up.) Figure 2.51 Discontinuity between the end of a window and its beginning The beginning and end would вЂњmatch up.вЂќ The actual discontinuity between the end of a window and its beginning is interpreted by the FFT as a jump from one level to another, as shown in Figure 2.51. If it were the case вЂ“ that is, if the window ended exactly where the cycle ended вЂ“ then the end of the cycle would be at exactly the same amplitude as the beginning. This, of course, is not generally the case. A simplifying assumption for the FFT is that each windowed segment of audio data contains an integral number of cycles, this cycle repeating throughout the audio. The purpose of an FFT windowing function is to smooth out the discontinuities that result from applying the FFT to segments (i.e., windows) of audio data. In addition to choosing the FFT window size, audio processing programs often let you choose from a number of windowing functions.