Window function

Window functions are applied to avoid discontinuities at the beginning and the end of a set of data. The smaller these discontinuities are, the faster side slopes are dopping. The maximum order of deriviation which is zero at the ends determines the asymptodic behave:

• steps in the function itself: asymptodic -6 dB/oct
• continuous function, step in first derivation: -12 dB/oct
• ...

There is an intrinsic trade-off problem between:

• width of main slope
• side slope rejection

The following window functions are nonzero at [-1,+1].

Non-power-preserving analysis windows

Rechtangular window

f(x) = 1 for |x|<1, 0 otherwise

Triangular window

f(x) = 1 - |x| for |x|<1, 0 otherwise

Hamming window

Free parameter alpha. Classic Hamming window uses alpha=0.92, van Hann window has an alpha=1.00.

f(x) = 1 - alpha * sin²(x*pi/2)

Blackman/Blackman Harris window

f(x) = a + b * sin() + c*sin(2*) + d * sin(3*)

Power-preserving analysis windows

Other power-preserving windows

Create

Multiple overlap windows

When using FFT or DCT for spectral analysis a sample belongs to [b]one[/b] analysis window. When using windowing samples at the boundaries are attenuated. To reduce the effect that these samples are less important for the result, normally windows were overlapped. So samples between two blocks are attenuated, but they belong to two blocks, so their influence is still (nearly) the same as samples which are not attenuated. But it is possible to overlap more than two windows. This typically makes the transition band between main slope and side slopes smaller.

Triple overlapped cosine window

The normal cosine window do not preserve the power of the signal. Samples which are exactly between two blocks are attenuated by 6 dB, i.e. their power is reduced by a factor of 0.25. The overlapping reduces this to a factor of 0.5, which still result