Ogilvie 



', w : Windows 



Several papers have been written on the design of windows so as to provide 

 spectral estimates with various properties. Hamming and the hanning windows 

 are the most popular ones commonly used. Just a few comments will be made 

 here on this subject. 



Putting X as the Fourier transform of x( t ) ( -T < t < T) , the smoothing effect 

 of the windows of the trigonometric sum type is expressed as follows (see Fig. 

 6): 



^ ' M-I^' J^ 277- \^ W 



J -J 



Wj R* (r) dr 



^J e ^-^ v,(r) R*^(r) dr , 



w(t) = 2] a„ 



277] _ T 

 2T_ 



T < r. 



K 



= 2" I! ^n 



27.J — r 



T = ±T, 



k > T„ . 



Figure 6 



Many windows have been designed [8], and have been checked [3] for the case of 

 simple oscillations like linear rolling in waves. The following windows, w^, Wj, 

 W3, which have been designed, are the optimum as the 1st, 2nd and the 4th order 

 type and are free from biases up to the 1st, 2nd and the 4th order respectively. 



104 



