Transformation between distributions in time–frequency analysis: Difference between revisions
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To obtain that relationship suppose that there are two distributions, <math>C_1</math> and <math>C_2</math>, with corresponding kernels, <math>\phi_1</math> and <math>\phi_2</math>. Their characteristic functions are
: <math>M_1(\phi,\tau) = \phi_1(\theta,\tau)\int s^*\left(u-\dfrac{1}{2}\tau\right)s\left(u+\dfrac{1}{2}\tau\right)e^{j\theta u}\, du</math> (4)
: <math>M_2(\phi,\tau) = \phi_2(\theta,\tau)\int s^*\left(u-\dfrac{1}{2}\tau\right)s\left(u+\dfrac{1}{2}\tau\right)e^{j\theta u}\, du</math> (5)
Divide one equation by the other to obtain
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