Iterative For Loop for calculating multiple passes of a moving average?

I am trying to smooth a given data set (y) with multiple passes of a moving average. I have the code to simply do one pass (I am aware of the smooth function)however, this is for an assignment and the instructor wants us to create our own smoothing code.

What I would like to do is supply a vector of different spans, and have the moving average act on the previous moving average. This way I will be able to find a span set that best smoothes the data.

 % Creates a moving average with a defined set of spans.
span = [9,11,21];
y_smooth = y;

    for i = 1:length(span)

    d = [(span(i)-1)/2];
    y_smooth = conv(y_smooth,ones(1,d)/d,'same');

    end
%

Does this appear to work?

Answer 1

[Image Analyst]

You want an array of all 1's divided by the number of 1's in the span so that the product and sum will sum to the same average value as the original y. And I will interpret "the span" to mean the whole window width, not half the width like you're doing. So I'd do

kernel = ones(1, spans(k)) / spans(k)
y_smooth = conv(y, kernel, 'same');

Here's a full demo:

% Create sample data:
numPoints = 100;
x = 1 : numPoints;
y = cos(2*pi*x/50) + 0.85*rand(1, numPoints); % Sample data.
% Plot original noisy data
plot(x, y, '-', 'LineWidth', 2);
hold on;
legends{1} = 'Original';
% Creates a moving average with a defined set of spans.
spans = [9, 11, 21];
for k = 1:length(spans)
  kernel = ones(1, spans(k)) / spans(k)
  y_smooth = conv(y, kernel, 'same');  
  plot(x, y_smooth, '-', 'LineWidth', 2);
  legends{k+1} = sprintf('Span = %d', spans(k));
end
grid on;
legend(legends);

[Jacob B]

This makes sense now. Thank you very much!

[Shelby Jacobs]

How could this code be edited to combine spans so that the data would pass through all indicated spans before plotting?

[Image Analyst]

I have no idea what that means. What does "pass through" mean exactly? And what are the "Indicated" spans?

Answer 2

[Jyotish Robin]

Hi Jacob,

Span parameter usually refers to the number of terms in the moving average, which is the window size If N is the number of neighboring data points on either side of a sample value , then 2N+1 is the span.

If we want to do moving average by convolution having a window size of w, we shall use the following k kernel:

k=[1/w 1/w...1/w 1/w]

Hope it helps!