Huron & SNAP Documentation

Hamming Window
Blackman Window
Harris Window
THE ENGINEERING TOOLS
The Von Hann function can be expressed simply with only two
terms in the cosine series. The Von Hann window function is
defined by equation 3.
HURON TECHNICAL MANUAL PAGE 248
( )
hn
N n
⎛ ⎞
= 05 . + 05 . cos⎜⎟ ⎝ ⎠
π
N N
n = −
,..., −101
, , ,..., (3)
2
2
The mainlobe is twice the width of the rectangular windows and
its highest sidelobe is attenuated relative to the mainlobe by
32dB.
The Hamming window is also a member of the cos(x) series
window family. It is an extension of the Von Hann window and
is sometimes called the generalised Von Hann window. It is a
raised cosine of the form in equation 4.
( )
hn
N kn
⎛ ⎞
= 054 . + 046 . cos⎜⎟ ⎝ ⎠
π
N N
n = (4)
−
,..., −101
, , ,...,
2
2
The mainlobe of the Hamming window matches the mainlobe
width of the Von Hann, and its main sidelobes attenuate at
43dB relative to the mainlobe. However, the sidelobes do not
decay as rapidly as the Von Hann window.
A cosine series with three terms, rather than the two for Von
Hann and Hamming windows was researched by Blackman.
One can view the generalised cosine series over K terms as that
in equation 5.
hn ( ) ak
N kn
K ⎛ π ⎞
= ∑ ( )cos⎜⎟
⎝ ⎠
k=
0
N N
n = −
,..., −101
, , ,..., (5)
2
2
For the Blackman window used by Wingen the coefficients
a(0), a(1) and a(2) are shown in 6 (Next page).
a(
0) = 0. 42659071
a(
1) = 0. 49659062
a(
2) = 0. 07684867
The Harris window introduces a fourth term in the cosine series
of 5. Coefficients for the Harris window in Wingen are:
(6)