FFT Window

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FFT Window

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The Fast Fourier Transform is an approximation of the standard Fourier Transform, using a time limited set of data. The begin and end parts of this limited data set may lead to spectral leakage effects (i.e. yielding not existing frequency peaks). Especially when using small data sets leakage may lead to unwanted results.


To reduce spectral leakage, the data set can be preprocessed using special windowing functions. These windowing functions reduce the values at the begin and end of the data set and thus reduce the leakage effects. Given an input array A[i] and an output array B[i], with = 1,2,...,N.


20-sim supports the following windows:

None: no preprocessing; B == A
Hamming Window: B(i) = (0.54 + 0.46*cos(pi*(i-1)/(N-1)))*A(i), i = 1,2,...,N.
Hann Window: B(i) = 0.5*(1 + cos(pi*(i-1)/(N-1)))*A(i), i = 1,2,...,N.
Quadratic Window: B(i) = (1 - 2*((i-1)/(N-1))**2)*(1 - (i-1)/(N-1))*A(i), i = 1,2,...,(N-1)/2+1; B(i) = 2*(1 - ((i-1)/(N-1))**3)*A(i), i = (N-1)/2+2,...,N.