Blackman window
w = blackman(N)
w = blackman(N,SFLAG)
returns
the w
= blackman(N
)N
-point symmetric Blackman window in the
column vector w
, where N
is
a positive integer.
returns an w
= blackman(N,SFLAG
)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.
Note
If you specify a one-point window (set |
The following equation defines the Blackman window of length N:
$$w(n)=0.42-0.5\mathrm{cos}\frac{2\pi n}{N-1}+0.08\mathrm{cos}\frac{4\pi n}{N-1},\text{\hspace{1em}}0\le n\le M-1$$
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.
[1] Oppenheim, Alan V., Ronald W. Schafer, and John R. Buck. Discrete-Time Signal Processing. Upper Saddle River, NJ: Prentice Hall, 1999, pp. 468–471.