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DOCUMENTATION CENTER SEARCH
Function Index
WindowFilter
WindowFilter[
N
,
{
f
_{1}
,
f
_{2}
,
...
},
{
v
_{1}
,
v
_{2}
,
...
}]
returns a 1D linear-phase, bandpass (possibly multiband) FIR filter that is optimal in the mean-squared error sense. {f
_{1}
, f
_{2}
, ...} is a list of cutoff frequencies, such that 0≤f
_{1}
≤f
_{2}
≤...≤0.5, and {v
_{1}
, v
_{2}
, ...} is a list of desired magnitude values for each of the bands.
WindowFilter[
N
,
{
f
_{1}
,
f
_{2}
,
...
},
{
v
_{1}
,
v
_{2}
,
...
},
"
type
"]
returns a 1D linear-phase FIR filter of given
type
, where
type
may be either "differentiator" or "Hilbert".
WindowFilter
returns a FIR filter h
_{t}
[n] that minimizes the integral squared error between the desired (ideal) frequency response given by H
_{d}
(
) and the DTFT of h
_{t}
[n] given by H
_{t}
(
).
The desired frequency response H
_{d}
(
) is typically specified as piecewise constant with sharp transitions between passbands and stopbands. The corresponding impulse response h
_{d}
[n] is then infinite in extent. It has been shown that the filter h
_{t}
[n] that minimizes the integral is a truncated copy of h
_{d}
[n].
h
_{t}
[n] = h
_{d}
[n] for -M≤n≤M
Truncation may be implemented as a multiplication operation by a finite length sequence called the window
h
_{t}
[n] = h
_{d}
[n]* w[n]
where w[n] is the so-called rectangular window sequence defined as
w[n] = {1
Typically, the rectangular window is replaced by windows with smoother frequency response characteristics.
See also User's Guide
9.3
.
Example
This loads the package.
In[1]:=
Here we design a bandstop filter. Two passbands are defined at 0≤f
_{p1}
≤0.2 and 0.35≤f
_{p2}
≤0.5, while the stopband is defined for the frequency range 0.2≤f
_{s}
≤0.35. The band edge frequencies are therefore at 0.2 and 0.35.
In[2]:=
Out[2]=
Here we show the magnitude response (in dB) of the example filter.
In[3]:=
Out[3]=
THIS IS DOCUMENTATION FOR AN OBSOLETE PRODUCT.