Mathematica 9 is now available

DOCUMENTATION CENTER SEARCH

WindowFilter2D

WindowFilter2D[N, {f₁,f₂, ...}, {v₁,v₂, ...}] returns a 2D circularly symmetric, linear-phase, bandpass (possibly multiband) FIR filter that is optimal in the mean-squared error sense. {f₁, f₂, ...} is a list of cutoff frequencies, such that 0≤f₁≤f₂≤...≤0.5, and {v₁, v₂, ...} is a list of desired magnitude values for each of the bands.

WindowFilter2D returns a FIR filter h_t[n₁, n₂] that minimizes the integral squared error between the desired (ideal) frequency response given by H_d(

₂) and the DTFT of h_t [ n₁, n₂] 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 is known that the filter h_t[n] that minimizes the integral is a truncated copy of h_d[n].

Truncation may be implemented as a multiplication operation by a finite length sequence called the window

where w[n₁, n₂] is the 2D rectangular window sequence defined as

Typically, the rectangular window is replaced by windows with smoother frequency response characteristics.

See also User's Guide 9.4.

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]:=

Here we show an approximation of the magnitude response of the example bandstop filter.

In[3]:=

Out[3]=

Out[3]=

THIS IS DOCUMENTATION FOR AN OBSOLETE PRODUCT.

© 2013 About Wolfram