# Create Moving Average filter WITHOUT filter() function

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Terry Carney on 6 May 2021
Commented: Terry Carney on 6 May 2021
Hello,
I can't seem to plot a desired output using a Hanning Moving Average equation. My goal is to create a moving average filter with a 3-point moving average with a created signal x. However, I don't notice a difference between the unfiltered signal and the filtered signal. May someone give advice on how to enter a moving average equation and it's coefficients without the use of the filter() function? Or is the 3-point moving average so small that there isn't a difference?
Hanning Moving Average filter:
y[n] = 1/4(x[n] + 2x[n-1] + x[n-2]).
fs = 200; %sampling frequency
Ts = 1/200; %sampling time
t = 0:Ts:1;
x = sin(2*pi*2*t) + sin(2*pi*10*t) + sin(2*pi*90*t) %signal
plot(t,x); %unfiltered signal
title('Signal with 2, 10, and 90 Hz');
xlabel('time (s)');
%Difference equation of Hanning Moving Average filter:
n = 3
yn = (.25*x(n)) + (.5*x*(n-1)) + (.25*(n-2)) %Attempt at creating the moving average equation.
plot(t,yn)
Thank You
Jonas on 6 May 2021
you could calculate the main part e.g. by
y=1/4*(x(3:end) + 2*x(2:end-1) + x(1:end-2))
but then you jave to think about the first two samples of y because the normal formula will have negative index. maybe you want to assume 0 before the actual x(n) starts. similar to that you have to think about two values beyond x because the formula for y contains up to n-2. this way y will be longer than your original x by two samples

Mathieu NOE on 6 May 2021
hello
try this
fs = 200; %sampling frequency
Ts = 1/200; %sampling time
t = 0:Ts:1;
x = sin(2*pi*2*t) + sin(2*pi*10*t) + sin(2*pi*90*t) %signal
plot(t,x); %unfiltered signal
title('Signal with 2, 10, and 90 Hz');
xlabel('time (s)');
%Difference equation of Hanning Moving Average filter:
yn = zeros(size(t));
%%%%%%% main loop %%%%%%%%%%%%
yn(1) = 0.25*x(1); % first iteration
yn(2) = 0.25*x(2) + 0.5*x(1); % second iteration
ind = 3:length(t); % for n>= 3
yn(ind) = (0.25*x(ind)) + (0.5*x(ind-1)) + (0.25*x(ind-2));
%Attempt at creating the moving average equation.
plot(t,x,'b',t,yn,'r')
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Terry Carney on 6 May 2021
@Jonas, I agree. But I was up for a couple nights trying to solve this. I do thank you for your guidance as well.