What is the intuition of "averaging is a low pass filter"?
Consider a sequence of numbers

x = [1, 100, 1, 100, 1, 100]


If we send this sequence through an averaging transformation

y(i) = 0.6*x(i) + 0.4*x(i-1)


we get

y = [1, 60.4, 40.6, 60.4, 40.6, 60.4]


Original signal x had a lot of sudden changes 1 -&gt; 100, 100 -&gt; 1 where as signal y has smaller changes 60 -&gt; 40, 40 -&gt; 60

When we say that a signal has high frequency components we mean that the values change rapidly with time. So x had rapid changes in amplitude, while y does not have that much of rapid changes in values. This is the intuition behind why averaging is equivalent to low-pass filtering (disallowing high frequencies).

--

Another way to look at it

x = [1, 100, 1, 100, 1, 100]


could be written as sum of two sequences, x1 and x2

Low(zero?) frequency component

x1 = [50, 50, 50, 50, 50, 50]


High frequency component

x2 = [-49, 50, -49, 50, -49, 50]


After averaging transformation, we get 

y = [1, 60.4, 40.6, 60.4, 40.6, 60.4]


Which has low frequency component of

y1 = [50, 50, 50, 50, 50, 50]


and high frequency component

y2 = [-49, 10.4, -9.4, 10.4, -9.4, 10.4]


As you can see that y2 has much smaller absolute amplitudes than x2, meaning that we have diminished the high frequency components in x by doing averaging.