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How to recover the original signal from a noisy signal?

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Afaq Ahmad
Afaq Ahmad on 14 Jan 2021
Commented: Jon on 15 Jan 2021
I am trying to recover the original signal as shown in (3,1,1). I have represented the signal using 10 discrete numerical values in (3,1,2). After adding some noise using randn(), I have received the "noisy" signal in (3,1,3). Now, I want to retrieve the original data (3,1,1) from the noisy signal. I am confused here on how to implement the logic.
The same concept goes for the (3,1,2) as well. The only difference is the noise (randn()) function. I don't know to get the (3,1,1) from either (3,1,2) or (3,1,3).
The code I've written:

Accepted Answer

Jon on 14 Jan 2021
Edited: Jon on 14 Jan 2021
You need to low pass filter the data and then downsample it.
If you have the Signal Processing Toolbox you can do these together using the decimate function.
Otherwise you need to first low pass filter your data (at least in the case where the data is noisy) and then downsample it.
The downsampling part, can be done without the Signal Processing Toolbox simply by indexing. So for example for a vector x to select every 10th value
idx = 1:10:numel(x)
xds = x(idx)
or more compactly
xds = x(1:10:numel(x))

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