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[m−1] + x[m] + x[m+1])

Where te frequency variable ωˆ is a continuous variable. While calculating H(ejωˆ) I will have to choose suitable samples of ωˆ, so that the graph of |H(e^jω)| versus ωˆ looks smooth.

[Paul]

What do you have so far?