Consider the continuous-time variable t. The half Hamming window starts at t=0, and reaches its peak value (unity) at t=T1. The window is constant at unity from t=T1 to t=T2. The quarter cycle cosine window is unity at t=T2 and decreases to zero at t=T3.
= 0 , t < 0
pi t
= (1-a) - a cos (----) , 0 <= t < T1
T1
h(t) = 1 , T1 <= t < T2
pi (t-T2)
= cos (---------) , T2 <= t < T3
2 (T3-T2)
= 0 , T3 <= t
A window of this form is used for the ITU-T G.729 8 kb/s coder and its derivatives. The G.729 discrete-time window has 240 non-zero samples, and is obtained by setting a = 0.46, T1 = 199.5, T2 = 200, T3 = 239.75. The discrete-time window is sampled at t = i, with 0 <= i < 240. The G.729 window can be obtained with the following call
FIwinHCos (win, 199.5, 200.0, 239.75, 0.46)