主题：急求“7-term blackman-harris窗”的表达式

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A FAMILY OF COSINE-SUM WINDOWS
FOR HIGH-RESOLUTION MEASUREMENTS
Hans-Helge Albrecht
Physikalisch-Technische Bundesanstalt
Abbestra?e 2-12, D-10587 Berlin, Germany
Phone: +49 30 3481 311 Fax: +49 30 3481 490
E-mail: hans-helge.albrecht(a)ptb.de

rgds
bharat pathak

Arithos Designs
www.Arithos.com

DSP design consultancy and Training Company

 

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A better terminology might be "minimum sidelobe cosine-sum" window.

harris doesn't seem to have published past 4 terms and his 4 term
optimized window had 92 dB sidelobe rejection. Nuttall provided a
correction to the 4 term coefficients to yield 98 dB sidelobe
rejection. So, harris' 4 term wasn't minimum sidelobe. Nuttall doesn't
seem to have published past 4 terms either.

So, if you want a five-term minimum sidelobe cosine-sum window you
could use:

acoef = [0.3232153788877343 0.4714921439576260
0.1755341299601972 ...
2.849699010614994e-2 1.261357088292677e-3];

from the Albrecht paper:

A family of cosine-sum windows for high-resolution measurements
Albrecht, H.H.
Acoustics, Speech, and Signal Processing, 2001. Proceedings. (ICASSP
apos;01). 2001 IEEE International Conference on
Volume 5, Issue , 2001 Page(s):3081 - 3084 vol.5

The paper gives up to 11 terms and -289 dB sidelobe rejection. At 12
terms there were numerical problems with running the optimization in
64 bit floating point. Albrecht's 4 term coefficients agree with
Nuttal's 4 term values.
The 7 term window appears in some 24-bit A-D converter application
notes published before Albrecht's paper. The values published were
consistent with Albrecht's. A number of people have successfully run
the optimization for various numbers of coefficients so I go with
"minimum sidelobe cosine-sum" window for the family.

Dale B. Dalrymple
http://dbdimages.com

Coeff. Window 1 Window 2 Window 3
A0 2.374298741532465928226 · 10??01 2.310581202331358499435 · 10??01 2.249924617087535177329 · 10??01
A1 3.994704373801009358001 · 10??01 3.922514736021656858831 · 10??01 3.851495428292902693259 · 10??01
A2 2.362644608100282475133 · 10??01 2.385553629158978655597 · 10??01 2.403597686865028390968 · 10??01
A3 9.620676838363516649024 · 10??02 1.021288669149117706979 · 10??01 1.077408077837851454781 · 10??01
A4 2.591512168016078991738 · 10??02 2.977294169292394185833 · 10??02 3.373630665800276621290 · 10??02
A5 4.307708101213669512442 · 10??03 5.586700597441296634013 · 10??03 7.046059650969717333158 · 10??03
A6 3.904113541372495568636 · 10??04 6.129851690844686016343 · 10??04 9.096091349642873804482 · 10??04
A7 1.508613505022821880403 · 10??05 3.295793164220405682537 · 10??05 6.357820763745181479203 · 10??05
A8 1.320024271202038321705 · 10??07 5.899889578740096042846 · 10??07 1.853811776589548714026 · 10??06

Albrecht, H.H.;  
Phys. Tech. Bundesanstalt, Berlin 

This paper appears in: Acoustics, Speech, and Signal Processing, 2001. Proceedings. (ICASSP '01). 2001 IEEE International Conference on
Issue Date: 2001
On page(s): 3081 - 3084 vol.5
Meeting Date: 07 五月 2001 - 11 五月 2001
Location: Salt Lake City, UT , USA
Print ISBN: 0-7803-7041-4
References Cited: 6
INSPEC Accession Number: 7153833
Digital Object Identifier: 10.1109/ICASSP.2001.940309 
Date of Current Version: <!-- 2002年8月7日 星期三-->07 八月 2002

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可惜不是IEEE会员,下载不了此论文.

coeff. 4-term window 5-term window 6-term window 7-term window
A0 3.635819267707608e-001 3.232153788877343e-001 2.935578950102797e-001 2.712203605850388e-001
A1 4.891774371450171e-001 4.714921439576260e-001 4.519357723474506e-001 4.334446123274422e-001
A2 1.365995139786921e-001 1.755341299601972e-001 2.014164714263962e-001 2.180041228929303e-001
A3 1.064112210553003e-002 2.849699010614994e-002 4.792610922105837e-002 6.578534329560609e-002
A4 1.261357088292677e-003 5.026196426859393e-003 1.076186730534183e-002
A5 1.375555679558877e-004 7.700127105808265e-004
A6 1.368088305992921e-005

此主题相关图片如下：table.jpg

coeff. 7-term window
A0 2.712203605850388e-001
A1 4.334446123274422e-001
A2 2.180041228929303e-001
A3 6.578534329560609e-002
A4 1.076186730534183e-002
A5 7.700127105808265e-004
A6 1.368088305992921e-005

 

找到了!