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Fourier Transform. I'd been writing DSP code in C and MATLAB during undergrad while thinking I knew every possible aspect thanks to the deep study we had as pa

Fourier Transform. I'd been writing DSP code in C and MATLAB during undergrad while thinking I knew every possible aspect thanks to the deep study we had as part of coursework across all the transforms methods in our ECA & Communications coursework in India. Also, dad was a self-taught hands-on Analog electronics whiz whose day job was in Telecommunications Training, and I had uncles and aunts in the Telecom/Electronics/ATC industry, so I had all these resources from a very young age to revisit the concepts that were being taught to me in school, against practical applications over and over. In week 2 or 3 of ECE490 at UofR, Prof. Heinzelman[1] broke a barrier that I did not know existed in my understanding of DSP. It was pinned to me realizing that the intuition between Fourier and Laplace transforms being the same. It was a moment that I haven't experienced since, in that I felt my brain got re-wired within that hour. It must help that her father[2] basically wrote the textbook on speech processing. [1] http://www.hajim.rochester.edu/ece/heinzelman/ http://www.hajim.rochester.edu/ece/heinzelman/ [2] https://www.ece.rutgers.edu/lawrence-rabiner https://www.ece.rutgers.edu/lawrence-rabiner

bonzini 4y ago
Interesting, Fourier transform has never been an issue for me but Laplace never clicked. I know it's kind of similar (convolution, exponential and all that) but I miss the connection with the frequency domain that is there for Fourier.
- dannymi 4y ago
  The frequency is the imaginary part of the Laplace parameter s (and the attenuation is the real part of the Laplace parameter s). Laplace transforms work on systems with attenuation—that’s the main advantage. Because the kind of transform was swapped out anyway, people used the chance to often only define one-sided Laplace transforms that only work for t > 0 (because as an engineer, thats the systems you want anyway). There’s a direct correspondence between the (usual) one-sided Laplace transform and the (unusual) one-sided Fourier transform for that reason. Since you usually have systems where f(t) = 0 for all t < 0 anyway, the distinction one-sided or not is not so important in practice for understanding.

bonzini 4y ago

Interesting, Fourier transform has never been an issue for me but Laplace never clicked. I know it's kind of similar (convolution, exponential and all that) but I miss the connection with the frequency domain that is there for Fourier.

dannymi 4y ago
The frequency is the imaginary part of the Laplace parameter s (and the attenuation is the real part of the Laplace parameter s). Laplace transforms work on systems with attenuation—that’s the main advantage. Because the kind of transform was swapped out anyway, people used the chance to often only define one-sided Laplace transforms that only work for t > 0 (because as an engineer, thats the systems you want anyway). There’s a direct correspondence between the (usual) one-sided Laplace transform and the (unusual) one-sided Fourier transform for that reason. Since you usually have systems where f(t) = 0 for all t < 0 anyway, the distinction one-sided or not is not so important in practice for understanding.