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FrequencySamplingFilterKernel
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FrequencySamplingFilterKernel

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creates a finite impulse response (FIR) filter kernel using a frequency sampling method from amplitude values ai.

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creates an FIR filter kernel of type m.

Details and Options

  • Possible types m for FIR filters created for a list {a1,a2,…,ak} of amplitudes are:
  • The default type is .
  • The frequency sampling method uniformly samples the frequency domain from 0 to .
  • FrequencySamplingFilterKernel by default uses a sampling of the frequency domain at integer multiples of , where is the length of the filter. With "Shifted"->True, the frequencies are shifted from 0 by . »
  • Amplitude values should be non-negative. Typically, values ai=0 specify a stopband, and values ai=1 specify a passband.
  • The kernel ker returned by FrequencySamplingFilterKernel can be used in ListConvolve[ker,data] to apply the filter to data.
  • FrequencySamplingFilterKernel takes a WorkingPrecision option that specifies the precision to use in internal computations. The default setting is WorkingPrecision->MachinePrecision.

Examples

open allclose all

Basic Examples  (1)Summary of the most common use cases

A symmetric odd-length FIR lowpass kernel:

In[1]:=1
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https://wolfram.com/xid/0pfvje9if1wxtvxnfjwm72-2m313q
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0pfvje9if1wxtvxnfjwm72-t5yvtd
Out[2]=2

Scope  (7)Survey of the scope of standard use cases

A type 1 FIR kernel with even symmetry and odd length:

In[1]:=1
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https://wolfram.com/xid/0pfvje9if1wxtvxnfjwm72-1rxbzj
Out[2]=2

A type 2 FIR kernel with even symmetry and even length:

In[1]:=1
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https://wolfram.com/xid/0pfvje9if1wxtvxnfjwm72-dzkiv7
Out[1]=1

A type 3 FIR kernel with odd symmetry and odd length:

In[1]:=1
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https://wolfram.com/xid/0pfvje9if1wxtvxnfjwm72-32pmg6
Out[1]=1

A type 4 FIR kernel with odd symmetry and even length:

In[1]:=1
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https://wolfram.com/xid/0pfvje9if1wxtvxnfjwm72-pqpno0
Out[1]=1

A symmetric odd-length FIR highpass kernel:

In[1]:=1
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https://wolfram.com/xid/0pfvje9if1wxtvxnfjwm72-p88r9y
Out[1]=1

A symmetric even-length FIR bandpass kernel:

In[1]:=1
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https://wolfram.com/xid/0pfvje9if1wxtvxnfjwm72-076gdm
Out[1]=1

A full-band differentiator FIR kernel:

In[1]:=1
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https://wolfram.com/xid/0pfvje9if1wxtvxnfjwm72-33fogb
Out[1]=1

Options  (1)Common values & functionality for each option

"Shifted"  (1)

By default, first frequency is sampled at 0:

In[1]:=1
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https://wolfram.com/xid/0pfvje9if1wxtvxnfjwm72-08qk5h
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0pfvje9if1wxtvxnfjwm72-ivvpje
Out[2]=2

With "Shifted"->True, first frequency is offset from 0 by :

In[3]:=3
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https://wolfram.com/xid/0pfvje9if1wxtvxnfjwm72-e1ef7
Out[3]=3
In[4]:=4
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https://wolfram.com/xid/0pfvje9if1wxtvxnfjwm72-duq1t2
Out[4]=4

Applications  (2)Sample problems that can be solved with this function

Smooth data by convolving it with a lowpass filter kernel:

In[1]:=1
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https://wolfram.com/xid/0pfvje9if1wxtvxnfjwm72-oyb7mq
Out[3]=3

Apply a derivative filter to rows of an image:

In[1]:=1
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https://wolfram.com/xid/0pfvje9if1wxtvxnfjwm72-eqpqa8
Out[1]=1

Properties & Relations  (1)Properties of the function, and connections to other functions

Apply a window to an FIR filter to reduce ripple in its magnitude response:

In[1]:=1
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https://wolfram.com/xid/0pfvje9if1wxtvxnfjwm72-ch7c5v
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0pfvje9if1wxtvxnfjwm72-g6ctyz
In[3]:=3
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https://wolfram.com/xid/0pfvje9if1wxtvxnfjwm72-pa4cga
Out[3]=3
Wolfram Research (2012), FrequencySamplingFilterKernel, Wolfram Language function, https://reference.wolfram.com/language/ref/FrequencySamplingFilterKernel.html.
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Wolfram Research (2012), FrequencySamplingFilterKernel, Wolfram Language function, https://reference.wolfram.com/language/ref/FrequencySamplingFilterKernel.html.

Text

Wolfram Research (2012), FrequencySamplingFilterKernel, Wolfram Language function, https://reference.wolfram.com/language/ref/FrequencySamplingFilterKernel.html.

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Wolfram Research (2012), FrequencySamplingFilterKernel, Wolfram Language function, https://reference.wolfram.com/language/ref/FrequencySamplingFilterKernel.html.

CMS

Wolfram Language. 2012. "FrequencySamplingFilterKernel." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/FrequencySamplingFilterKernel.html.

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Wolfram Language. 2012. "FrequencySamplingFilterKernel." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/FrequencySamplingFilterKernel.html.

APA

Wolfram Language. (2012). FrequencySamplingFilterKernel. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/FrequencySamplingFilterKernel.html

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Wolfram Language. (2012). FrequencySamplingFilterKernel. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/FrequencySamplingFilterKernel.html

BibTeX

@misc{reference.wolfram_2025_frequencysamplingfilterkernel, author="Wolfram Research", title="{FrequencySamplingFilterKernel}", year="2012", howpublished="\url{https://reference.wolfram.com/language/ref/FrequencySamplingFilterKernel.html}", note=[Accessed: 30-March-2025 ]}

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@misc{reference.wolfram_2025_frequencysamplingfilterkernel, author="Wolfram Research", title="{FrequencySamplingFilterKernel}", year="2012", howpublished="\url{https://reference.wolfram.com/language/ref/FrequencySamplingFilterKernel.html}", note=[Accessed: 30-March-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_frequencysamplingfilterkernel, organization={Wolfram Research}, title={FrequencySamplingFilterKernel}, year={2012}, url={https://reference.wolfram.com/language/ref/FrequencySamplingFilterKernel.html}, note=[Accessed: 30-March-2025 ]}

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@online{reference.wolfram_2025_frequencysamplingfilterkernel, organization={Wolfram Research}, title={FrequencySamplingFilterKernel}, year={2012}, url={https://reference.wolfram.com/language/ref/FrequencySamplingFilterKernel.html}, note=[Accessed: 30-March-2025 ]}