I want to apply moving average filter! could you tell me how can I do that?

p = textread('Rainfall of Busan (11.5.1981 11.5.2021).txt');

dt = 1;

totalL = 14611;

T = [dt:dt:dt*totalL];

freqs = linspace(0,1/dt,totalL+1);

freqs = freqs(1:end-1);

y=fft(p);

I want to apply moving average filter! then what do I have to do...?

[Adam Danz]

That's not specific enough. What kind of filter? How large is the window? Should the window move in increments of 1 or by window-width?

Answer 1

[William Rose]

@James James, everything @Adam Danz said is correct.

But here's an example, assuming you want a "flat" moving average:

t=0:100;
x=sin(2*pi*t/100)+rand(size(t))-.5; %for demonstration purposes
xf=zeros(size(x));
M=9;    %window width, assumed to be odd
for i=(M+1)/2:101-(M-1)/2
    xf(i)=sum(x(i-(M-1)/2:i+(M-1)/2))/M;
end
plot(t,x,'-r.',t,xf,'-b.',t,sin(2*pi*t/100),'-k');
legend('Raw','Filtered','No Noise');

Modify if you do not want output at every point. Modify as desired to handle the edges in a nicer way (e.g. extend the original signal to the sides before smoothing, with x(1) and x(end) respectively, or with a time-reversed and inverted extension, or whatever...). If you want a non-flat window, you have to do a bit more. For example, a triangular window of width M:

b=conv(ones(1,(M+1)/2),ones(1,(M+1)/2));
b=b/sum(b);  %normalize so gain=1 at DC

Multipy elements of b by appropriate elements of x to get filtered version.

Answer 2

[William Rose]

@James James,

Here's a method that hadles the edges better, and is more elegant, because it eliminates for loops.

t=0:100;
x=sin(2*pi*t/100)+rand(size(t))-.5; %for demonstration purposes
M=9;    %window width, assumed to be odd
bf=ones(1,M)/M;   %flat window
bt=conv(ones(1,(M+1)/2),ones(1,(M+1)/2))/((M+1)^2/4); %triangular window
xf=conv(x,bf);
xf=xf((M+1)/2:end-(M-1)/2);
xt=conv(x,bt);
xt=xt((M+1)/2:end-(M-1)/2);
plot(t,x,'-r.',t,xt,'-g.',t,xf,'-b.',t,sin(2*pi*t/100),'-k');
legend('Raw','Tri','Flat','No Noise');

Try.