I want to re-sample a particular signal in time domain.
For this I add zeros between every sample point and then I use a low pass filter on this. The effect I get is that the signal smooths when observed in the time domain. After this I take some samples out based on some other algorithm.
My question is how would the signal in time domain behave in the time domain if I use a high pass filter, also what if I use a band pass filter?
Second question: what would be the easiest way to do the entire process in the frequency domain?
While it is not easy to predict what applying different filters could do for you, I would suggest a slightly different procedure of resampling to start with: While I'm not an expert, I think it could be more awesome to linearly interpolate between sampling points. In general, one needs to think what statistical properties your signal could have on these smaller scales, such as smoothness, and then how to efficiently imitate these, for example with splines.
Let's you want to upsample a signal "s" of length N by a factor "L". You do this in two steps. First you insert L-1 zeros between each of the samples of the signal. And then you apply a low-pass filter.
The first step, zero stuffing, has the effect in the frequency domain of creating L-1 replicas, which are normally called images. Normally you apply now a low-pass filter you keep the replica at the lowest frequencies.
If you would use a high-pass filter instead of a low-pass filter you would keep the replica with the highest frequency. If we call the upsampled signal "s_u", In the time domain "s_u" coincides with you original signal at time instants 0,L, 2L...
s_u(k L)= s(L).
in the samples in between (1,2,... L-1, L+1 ...) when you apply a high-pass filter you will not see a smooth behavior, rather s_u will be "oscillating".
If you want to do the process in the frequency domain, instead of zero stuffing in time you can compute the fft of s with N points and replicate it L-1 times (you will end up with a vector of length NL). Then you apply your filter in the frequency domain and compute the ifft.
Alternatively you can compute the fft of N points, insert N(L-1) zeros in the frequency domain and compute the ifft. This will be equivalent to filtering with a sinc function in time.
You can easily check all these steps in MATLAB.
Good references for such problems are the following books:
N. Benvenuto and G. Cherubini: "Algorithms for Communications Systems and their Applications"
M. Jeruchim: "Simulation of Communication Systems: Modeling, Methodology and Techniques (Information Technology: Transmission, Processing and Storage"
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