The discussion centers on the conversion of a continuous, aperiodic spectrum to a discrete spectrum in signal processing. It confirms that this conversion can be achieved without energy loss, provided the frequency samples are spaced less than 1/(2T) apart, aligning with Shannon's theorem. The process involves sampling the spectrum using a Dirac Comb function, resulting in a convolution of the original signal and the Fourier Transform (FT) of the comb function. The conversation also touches on the practical application of the Nyquist criterion in this context.
PREREQUISITESSignal processing engineers, audio engineers, and researchers in telecommunications who are involved in spectrum analysis and signal reconstruction techniques.
Yes. Thanks..It s exactly what I was asking for. No losses than? Of any kind?BvU said:Not sure I fully understand your question. Sampling the spectrum is equivalent to multiplying it with a Dirac Comb function and then the signal you get from transforming back to the time domain would be a convolution of the original signal and the FT of the comb function. If the original signal is only present for a limited time 0 - T , this would allow lossless reconstruction when the frequency samples are less than 1/(2T) apart
This is the equivalent of the Nyquist criterion for temporal sampling. I'm trying to get my head around how to specify the equivalent to a practical Nyquist LP filter in this process.BvU said:Not sure I fully understand your question. Sampling the spectrum is equivalent to multiplying it with a Dirac Comb function and then the signal you get from transforming back to the time domain would be a convolution of the original signal and the FT of the comb function. If the original signal is only present for a limited time 0 - T , this would allow lossless reconstruction when the frequency samples are less than 1/(2T) apart