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Stephen
Stephen
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Fundamentally, it appears you have no choice but to make an assumption about what the signal is doing outside your window of data, or use windowing.

If you claim that the signal is periodic, then use the fft to identify frequency components and interpolate based on those.

If you claim that the signal is zero outside the window (or a constant), then use sinc interpolation.

If you know nothing about what the signal is doing outside the window, then use (Barycentric) Lagrange interpolation, which, for a finite dataset, is the equivalent of sinc interpolation with a binomial window (it is also the equivalent of using a Taylor series expansion of all datapoints with as many terms as datapoints then solving the system of equations). Since the degree of your polynomial will be low (that is, less than 10), it is highly unlikely that you will have any issues. I recommend, especially if you use the Barycentric form. In papers I've come across on various topics, Lagrange interpolation has been the most common approach used by researchers to prove various results.

Fundamentally, it appears you have no choice but to make an assumption about what the signal is doing outside your window of data, or use windowing.

If you claim that the signal is periodic, then use the fft to identify frequency components and interpolate based on those.

If you claim that the signal is zero outside the window (or a constant), then use sinc interpolation.

If you know nothing about what the signal is doing outside the window, then use (Barycentric) Lagrange interpolation, which, for a finite dataset, is the equivalent of sinc interpolation with a binomial window (it is also the equivalent of using a Taylor series expansion of all datapoints with as many terms as datapoints then solving the system of equations). Since the degree of your polynomial will be low (that is, less than 10), it is highly unlikely that you will have any issues. I recommend the Barycentric form. In papers I've come across on various topics, Lagrange interpolation has been the most common approach used by researchers to prove various results.

Fundamentally, it appears you have no choice but to make an assumption about what the signal is doing outside your window of data, or use windowing.

If you claim that the signal is periodic, then use the fft to identify frequency components and interpolate based on those.

If you claim that the signal is zero outside the window (or a constant), then use sinc interpolation.

If you know nothing about what the signal is doing outside the window, then use (Barycentric) Lagrange interpolation, which, for a finite dataset, is the equivalent of sinc interpolation with a binomial window (it is also the equivalent of using a Taylor series expansion of all datapoints with as many terms as datapoints then solving the system of equations). Since the degree of your polynomial will be low (that is, less than 10), it is highly unlikely that you will have any issues, especially if you use the Barycentric form. In papers I've come across on various topics, Lagrange interpolation has been the most common approach used by researchers to prove various results.

Source Link
Stephen
Stephen
  • 1.2k
  • 1
  • 9

Fundamentally, it appears you have no choice but to make an assumption about what the signal is doing outside your window of data, or use windowing.

If you claim that the signal is periodic, then use the fft to identify frequency components and interpolate based on those.

If you claim that the signal is zero outside the window (or a constant), then use sinc interpolation.

If you know nothing about what the signal is doing outside the window, then use (Barycentric) Lagrange interpolation, which, for a finite dataset, is the equivalent of sinc interpolation with a binomial window (it is also the equivalent of using a Taylor series expansion of all datapoints with as many terms as datapoints then solving the system of equations). Since the degree of your polynomial will be low (that is, less than 10), it is highly unlikely that you will have any issues. I recommend the Barycentric form. In papers I've come across on various topics, Lagrange interpolation has been the most common approach used by researchers to prove various results.