w = blackman(N)
w = blackman(N,SFLAG)
w = blackman(N,SFLAG) returns an N-point Blackman window using the window sampling specified by 'sflag', which can be either 'periodic' or 'symmetric' (the default). The 'periodic' flag is useful for DFT/FFT purposes, such as in spectral analysis. The DFT/FFT contains an implicit periodic extension and the periodic flag enables a signal windowed with a periodic window to have perfect periodic extension. When 'periodic' is specified, blackman computes a length N+1 window and returns the first N points. When using windows for filter design, the 'symmetric' flag should be used.
See Definitions for a description of the difference between the symmetric and periodic windows.
The following equation defines the Blackman window of length N:
where M is N/2 for N even and (N+1)/2 for N odd.
In the symmetric case, the second half of the Blackman window M ≤ n ≤ N-1 is obtained by flipping the first half around the midpoint. The symmetric option is the preferred method when using a Blackman window in FIR filter design.
The periodic Blackman window is constructed by extending the desired window length by one sample to N+1, constructing a symmetric window, and removing the last sample. The periodic version is the preferred method when using a Blackman window in spectral analysis because the discrete Fourier transform assumes periodic extension of the input vector.
 Oppenheim, Alan V., Ronald W. Schafer, and John R. Buck. Discrete-Time Signal Processing. Upper Saddle River, NJ: Prentice Hall, 1999, pp. 468–471.