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Legacy Documentation

Digital Image Processing (2000)

This is documentation for an obsolete product.

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FrequencySamplingFilter

FrequencySamplingFilter[N, {a₁, a₂, ... }] returns a linear-phase FIR filter of length N given a list of real amplitude values {a₁, a₂, ... }.

The option EvenSymmetry → True (the default) results in linear-phase FIR filters with even symmetry.

where N is the filter length.

The option EvenSymmetry → False results in linear-phase FIR filters with odd symmetry, such as Hilbert transformers and differentiators

h[n] = - h[N-n]

where N is the filter length.

The option FrequencySamplingGrid → 0 (the default) results in a sampling of the frequency domain at points

for i=0,1,...,N-1.

The option FrequencySamplingGrid → 1/2 results in a sampling of the frequency domain at points

for i=0,1,...,N-1.

See also User's Guide 9.3.

Example

This loads the package.

In[1]:=

This returns a length N=15, symmetric, linear-phase FIR lowpass filter with the passband edge at

In[2]:=

Out[2]=

In[3]:=

Out[3]=

Out[3]=

This returns a length N=8, full-band differentiator. An even-length differentiator is a Type 4 linear-phase FIR filter.

In[4]:=

Out[4]=

This plots the filter's magnitude response.

In[5]:=

Out[5]=

Out[5]=