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Discrete FT is just an approximate of the the continuous FT, so it follows the same uncertainty principle. It doesn't have an additional uncertainty feature, jt
by lupire 4y ago
Discrete FT is just an approximate of the the continuous FT, so it follows the same uncertainty principle. It doesn't have an additional uncertainty feature, jt just has the same approximation error that any finite model of an infinite phenomenon would have. That's not "uncertainty" because you can get arbitrarily precision by adding more samples. But Uncertainty means that it it impossible to get below the Uncertainty threshold, just like how if you squeeze a (theoretical) balloon full of incompressible fluid, you can never reduce its global volume to zero, even though you can reduce any local part of it to zero volume.
- sfpotter 4y agoI'm happy to be wrong and learn about an uncertainty principle for the DFT. I'm just not aware of one. Your comment isn't very helpful for illuminating, absence any mathematical detail.
- deleted 4y ago[deleted]
- hgsgm 4y ago
- zaccusl 4y agoI've never heard of one either. The first time I was introduced to an uncertainty principle for the DFT was in time-frequency analysis which exists due to not being able to know both time domain and frequency domain information simultaneously. There is some shared concepts from QM, but they are not the same thing.