reconstruc a signal using a filter

I have a vector Xs that represents the values of a sampled signal.

How can I reconstruct the original signal?

I know that I should multiply the vector Xs with a low pass filter, but how can I choose its order and cutoff frequency?

Answer 1

[Jan]

You cannot reconstruct the original signal. The recorded signal contains only the measured information, while the process of measurement reduces the level of information.

But if you have additional information, e.g. that the original signal is a clean sine wave, you can find a physically motivated set of parameters for the filter. So please explain, what you have measured and which arguments you have for filtering.

[biomed]

The initial signal is aperiodic. Using Fourier I extimated its band value and its sampling frequency.

Then I sampled the signal using its sampling frequency and now I need to reconstruct it to verify that the sampling frequency was correct.

Can I use a filter or should I try in another way, maybe using "interp1"?

Thank you for your help!!

[Walter Roberson]

Sampling frequencies do not apply to Fourier Transforms, only to Discrete Fourier Transforms.

If you have a sampled signal, then you cannot reconstruct the original signal unless you have information about limitations on the original signal. If the signal did a "happy dance" between every sample (as it does if you measure the signal precisely enough), then you would never know because of all finite sampling is sub-sampling.