Is It Necessary to Select an Odd Span for Smoothing Data Using Moving Average Filter?

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Coo Boo
Coo Boo 2020-2-24
评论： Bjorn Gustavsson 2020-2-25
Hi,
When I use the moving average method in 'smooth' function, the number of data points for calculating the smoothed value must be an odd integer. If I specify span as an even number or as a fraction that results in an even number of data points, span is automatically reduced by 1. Is it necessary to select an odd span for smoothing data using the moving average filter? Does anyone know the reason?
Thanks,

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Bjorn Gustavsson
Bjorn Gustavsson 2020-2-24
编辑：Bjorn Gustavsson 2020-2-24
You can check what happens when smooting by averaging over an even number of points. simply use convolution to carry out the averaging:
Signal = zeros(107,1);
Signal(53) = 1;
filter_length = 2;
Filtered_signal = conv2(Signal,ones(filter_length,1),'same');
plot(51:60,[Signal(51:60),Filtered_signal(51:60)],'o-')
Then you'll see that there will be a shift of the filtered signal. That is rather undesired - often enough that Mathworks decided to explicitly prevent that.
HTH
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Coo Boo
Coo Boo 2020-2-25
Sorry,
But I cannot understand. When we select an odd filter length, we have the signal shift too. Can you explain more?

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