frequency response function H(e^jω)

I need to find the frequency response of a M point averaging filter of an image, using the following equation:
y[m]= 1/3( x[m1] + x[m] + x[m+1])
Where te frequency variable ωˆ is a continuous variable. While calculating H(eˆ) I will have to choose suitable samples of ωˆ, so that the graph of |H(e^jω)| versus ωˆ looks smooth.

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2021-4-17

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2021-4-18

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