How to ﬁnd the moving average of a 1D sequence?

Given some sequence such as $1, 2, 3, 4, 5, 6, 7$ how to ﬁnd the moving average for diﬀerent window sizes?

Mathematica

For window size $k = 2$

v = {1, 2, 3, 4, 5, 6, 7, 8}; 
f = {1/2, 1/2}; 
ListConvolve[f, v] // N

{1.5,2.5,3.5,4.5,5.5,6.5,7.5}

For window size $k = 3$

v = {1, 2, 3, 4, 5, 6, 7, 8}; 
f = Table[1/3, {3}]; 
ListConvolve[f, v] // N

{2., 3., 4., 5., 6., 7.}

Matlab

For a window size $k = 2$

V=[1 2 3 4 5 6 7 8]; 
f=[1/2 1/2]; 
conv(V,f,'valid')

ans = 
 1.5000 2.5000 3.5000 4.5000 5.5000 6.5000 7.5000

For window size $k = 3$

V = [1 2 3 4 5 6 7 8]; 
k = 3; 
f = ones(k,1)/k; 
conv(V,f,'valid')

ans = 
 2.0000 3.0000 4.0000 5.0000 6.0000 7.0000