Discrete-Time Fourier Transform of a Moving-Average Filter

Consider a 2D moving-average filter:

In[1]:=

a=

1

25

1	1	1	1	1
1	1	1	1	1
1	1	1	1	1
1	1	1	1	1
1	1	1	1	1

;

Obtain the frequency response of the moving-average filter by applying the two-dimensional discrete-time Fourier transform (DTFT):

In[2]:=

(H[u_,v_]=ListFourierSequenceTransform[a,{u,v}])//Short

Out[2]//Short=

1

25

+

-u



25

+

1

25

-2u



+

1

25

-3u



+

1

25

-4u



+16+

-v



25

+

1

25

-2v



+

1

25

-3v



+

1

25

-4v



Visualize the frequency response:

In[3]:=

Plot3DAbs[H[u,v]],{u,-π,π},{v,-π,π},



Out[3]=

Wolfram Language Example Repository

Discrete-Time Fourier Transform of a Moving-Average Filter

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Discrete-Time Fourier Transform of a Moving-Average Filter

Related Symbols

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