temporal rectangular window
Hi Friend, see my clarification:
When the DFT of a sequence is taken, off-bin frequencies leak to some extent into all bins. The result can be, in the general case, a greatly diminished ability to distinguish discrete frequencies from each other when they are close.Leakage can, however, be reduced bymultiplying the signal sequence by a smoothing function called a Window prior to taking the DFT.
Hence, the leakage will be generated due to the discontiuity in time domain. The bigger the discontinuity, the more the leakage. To reduce the effect of spectral leakage, a window function can be used whose amplitude tapers smothly and gradually toward zero at both ends. Applying the window function w
to a data sequence x
to obtain a windowed sequence x
w is better illusterated in the following equation,
x
w=x
w
for n=0,1,2......,N-1
The common window functions are listed as follows (these are not all the types),
1. The rectangular window (no window function):-
W
R=1 0≤n≤N-1
2. The triangular window:-
W
tri=1-{|2n-N+1|/(N-1)} 0≤n≤N-1
3. The Hamming window:-
W
ham=0.54-0.46 cos(2Πn/(N-1)) 0≤n≤N-1
4. The Hanning window:-
W
hn=0.5-0.5 cos(2Πn/(N-1)) 0≤n≤N-1
Now, tell me my friend, is that enough?