interpolation and resampling problems.

I am trying to analyze the power spectral density for an unevenly sampled time-series (tachogram). Suppose the length of the data is exactly 1 hr. I want to obtain an evenly sampled series with re-sampling frequency of 4 Hz. I am planning the following steps before performing spectrum estimation.

Step 1)cubic spline interpolation, say 0:1/16:3600.

      Question 1: is this equivalent to 16 Hz sampling rate?

Step 2)anti-aliasing filter the interpolated data to eliminate the high frequency component.

      Question 2: are there any anti-aliasing functions in Matlab?

Step 3)re-sample to 4 Hz

      Question 3: which Matlab re-sample function should I use? how to calculate the re-sampling rate? 
      Question 4: If only use step 1 & 3, can the single function interp1()
do the same work?

many thanks

[Azzi Abdelmalek]

what is your question?

Answer 1

[Titus Edelhofer]

Hi Xinqi,

Q1: yes.

Q2: use a low pass filter (doc filter) to remove the high frequency components. If you have the signal processing toolbox, there are lots of examples/help for constructing appropriate filters.

Q3/Q4: again, in signal processing toolbox functions functions for resampling exist. If you have correctly filtered your data, interp1 should be sufficient.

Titus

Answer 2

[Matt J]

Question 1: is this equivalent to 16 Hz sampling rate?

Only if the original continuous signal was a cubic spline. In general, once a signal has been sampled, you cannot get better sampling of the original continuous signal unless you can reconstruct the continuous signal from its samples in some way.

Question 2: are there any anti-aliasing functions in Matlab?

Many Matlab commands can be used to perform filtering, e.g., FILTER, CONV, FFT, ... However, it doesn't make much sense to try to anti-alias if the data is already sampled.

Question 3: which Matlab re-sample function should I use? how to calculate the re-sampling rate?

If at this stage, you are downsampling from 16 Hz to 4 Hz, wouldn't you just throw samples away?

Question 4: If only use step 1 & 3, can the single function interp1() do the same work?

Yes, but I don't see why step 1 (upsampling to 16 Hz) would be necessary if ultimately you're just going to downsample again right afterward. You can use INTERP1 to obtain regularly spaced 4 Hz samples from the original data directly.