Digital Signal Processing Reference
In-Depth Information
H(e
j
ω
)
Ideal
response
1
Windowed
response
ω,
rad./sec.
−ω
c
0
ω
c
FIGURE 5.6
Ideal and windowed frequency response of low-pass filter.
however, also gives a practical design procedure to estimate the order of the
filter. The order of the filter,
M
, is calculated based on desired specifications
of the filter frequency response, which comprise the maximum tolerable
ripple and the maximum tolerable transition bandwidth.
•
Bartlett (triangular) window
⎧
2
nM
,
0
≤≤
n M
2
⎪
(5.14a)
wn
()
=
22
−
nM M
,
2
<
n M
≤
⎨
⎪
⎪
0
,
otherwise
⎩
•
Hanning window
(
)
⎧
⎪
⎪
05
.
−
05
.
c s
2
π
nM
,
0
≤≤
n M
(5.14b)
wn
()
=
0
,
otherwise
•
Hamming window
(
)
⎧
⎪
⎪
054
.
−
046
.
cos
2
π
nM
,
0
≤≤
n M
(5.14c)
wn
()
=
0
,
otherwise
