Uncertainty principle for the two sided quaternion windowed Fourier transform (Q2174854)

Uncertainty principles are mathematical results that give limitations on the simultaneous concentration of a function and its Fourier transform. They have implications in two main areas: quantum physics and signal analysis. In quantum physics, they tell us that a particle's speed and position cannot both be measured with infinite precision. In signal analysis, they tell us that if we observe a signal only for a finite period of time, we will lose information about the frequencies the signal consists of. All the elements of such a construction may be very specific, and there are many settings where such problems are studied. In this paper, the quaternion windowed Fourier transform is adjusted to several types of uncertainty principle. These are the Beckner's uncertainty principle in term of entropy, Lieb uncertainty principle and the Heisenberg uncertainty principle for the quaternion windowed Fourier transform, the radar quaternion ambiguity function and the quaternion-Wigner transform.