No! This is a huge misconception that misses the essence of quantum mechanics.
The Uncertainty is not due to finite information. It is an inherent property!
Uncertainty is due to (or better, "modeled by", because FT is math, not physics, and you could use wavelets or something instead), Fourier (and similar transforms) is a (bidirectional) function that maps (local) points to (dispersed) waves, and vice versa. This holds true even with infinite precision/information.
"Qualitatively, this means a narrow function has a wide Fourier transform, and a wide function has a narrow Fourier transform. In either domain, a wider function means there is literally a wide distribution of data, so there always exists uncertainty in one domain."
Uncertainty is due to (or better, "modeled by", because FT is math, not physics, and you could use wavelets or something instead), Fourier (and similar transforms) is a (bidirectional) function that maps (local) points to (dispersed) waves, and vice versa. This holds true even with infinite precision/information.
http://math.uchicago.edu/~may/REU2021/REUPapers/Dubey.pdf
"Qualitatively, this means a narrow function has a wide Fourier transform, and a wide function has a narrow Fourier transform. In either domain, a wider function means there is literally a wide distribution of data, so there always exists uncertainty in one domain."