Digital Filtering Tutorial, Part II - Alvy Ray Smith Homepage
Digital Filtering Tutorial, Part II - Alvy Ray Smith Homepage
Digital Filtering Tutorial, Part II - Alvy Ray Smith Homepage
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<strong>Digital</strong> <strong>Filtering</strong> <strong>Tutorial</strong>, <strong>Part</strong> <strong>II</strong> 5<br />
Rectangular: wn ( ) = 1,<br />
0 ≤ n ≤ N −1<br />
Bartlett:<br />
ì 2n<br />
,0£ n£ N - 1<br />
ï N - 1<br />
wn ( ) = í<br />
ï 2n N - 1<br />
2 - , £ n£ N - 1<br />
ïî N - 1 2<br />
wn<br />
1é æ2pnöù = 1 cos<br />
2<br />
ê - ç<br />
è<br />
÷<br />
N - 1øú,<br />
ë û<br />
0 ≤ n ≤ N −1<br />
wn<br />
æ2pnö = 0.54 - 0.46cos ç ÷ ,<br />
èN-1ø 0 ≤ n ≤ N −1<br />
wn<br />
æ2pn ö æ4pn ö<br />
= 0.42 - 0.5cos ç ÷ + 0.08cos ç ÷ , 0 ≤ n ≤ N −1<br />
èN - 1ø èN - 1ø<br />
Hanning: ( )<br />
Hamming: ( )<br />
Blackman: ( )<br />
é 2<br />
2 ù<br />
N 1 N 1<br />
I ê æ - ö é æ - öù<br />
0 wa<br />
ç ÷ - n-<br />
ç ÷<br />
ú<br />
ê è 2 ø ê<br />
2<br />
ú<br />
ë è øû<br />
ú<br />
Kaiser: wn ( ) =<br />
ë û<br />
é æN-1öù I0<br />
êwa è<br />
ç ÷<br />
2 øú<br />
ë û<br />
where I0bg is the modified zeroth order Bessel function of the first kind.<br />
Window Peak Amplitude of<br />
Side Lobe (dB)<br />
Rectangular<br />
Bartlett<br />
Hanning<br />
Hamming<br />
Blackman<br />
-13<br />
-25<br />
-31<br />
-41<br />
-57<br />
Transition Width of<br />
Main Lobe<br />
4 p /N<br />
8 p /N<br />
8 p /N<br />
8 p /N<br />
12 p / N<br />
Figure WINDOW [adapted from [3]]<br />
Minimum Stopband<br />
Attenuation (dB)<br />
-21<br />
-25<br />
-44<br />
-53<br />
-74
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