TR No. 22 
The equally spaced values of velocity can be considered to result 
from sampling the average velocity 
Met (12) 
at intervals of ZXx. Equation 12 can be written as a centered moving 
average; 
Bliotie doh U-x') du! 
SEO (13) 
where 
ih OW Wace 
Et? Du Vam Te 
O* otherwise 
(14) 
If the Fourier transform of u(x) is dz( K ) and that of @(x) is @(K des 
é then, applying the convolution theorem, 
a) Kox) 
sin (2 ae lk) 
( Be ) (15) 
Siy ca ise %) 
ISESION 
eel) 
A (k) = 
The quantity 
is the Fourier transform of h(x) and operates on the energy spectrum as a 
low pass filter. Variations in velocity occuring at wave numbers greater 
than around TWHAK = 0.157 cm~! are strongly attenuated. Since this value 
