Hello, someone worked (digital processing) on convolution of two sigma-delta modulated signals? Is possible this? Thank you
I think the easiest way is to resample the two signals with the same sample rate and then proceed to the convolution.
This topic may help you: https://www.researchgate.net/post/How_can_I_get_the_convolution_of_two_signals_in_time_domain_by_just_having_the_values_of_amplitude_and_time_using_Matlab
Hi Maxime, thank you for your answer. I refer make convolution but without resample or decimate the signals, I need make convolution directly in sigma-delta domain or PDM (Pulse Density Modulation) domain.
Regards.
Carlos,
The theory behind Sigma-delta is the same as the theory behind a 1-bit autocorrelator. I worked on this a long time ago so my memory is pretty fuzzy. There is a book of IEEE papers on this that is by John Candy but its been maybe 30 years ago. I don't have a good intuitive feel about convolving two sigma-delta outputs. If you are looking for cross-correlation functions, check into the GPS literature because they cross-correlate the spreading codes. Wish I could be more help.
Steve
Dear Carlos,
The convolution operation is performed to calculate the the time domain response of a linear time system on an input waveform. This is valid for both continuous time system and discrete time system. Mathematically the convolution operation is performed in the discrete time domain n by the operation:
The input, x[n], and output, y[n], of a discrete-time LTI system are related by the convolution sum y[n] =Summation from ∞ k=−∞ x[k]h[n − k]
where h[n] is the impulse response of the system.
So, you can consider one signal as h[n] and the other as x[n].
This from the mathematical point of view then remains the interpretation of the results.
It seems me one acts as a FIR filter for the other signal.
wish you success
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