Given a signal X which is sampled at a certain frequency. The value we currently compute is given as the integral of the upsampled signal. Thus: Y = X but 100 times upsampled, by means of sinc interpolation or by using an FFT resampler. The integral is simply the sum of all values in Y.
The calculation of this integral is easy, yet I would like to speed it up by avoiding the upsampling step. Is there any possibility to obtain the integral of the upsampled signal, without actually resampling it ?
Preserving integral through downsampling and Do lowpass filters affect the integral over the signal? are similar questions, but deal with cases of downsampling or bandlimiting. In both cases, it is clear that an integral will not exactly be preserved by downscaling.
Yet, in this question, we are talking about upsampling. I suspect this is possibly because X does contain all information necessary to create Y.