  We find the Stratonovich-Weyl quantizer for the nonunimodular affine group of
the line. A noncommutative product of functions on the half-plane, underlying a
noncompact spectral triple in the sense of Connes, is obtained from it. The
corresponding Wigner functions reproduce the time-frequency distributions of
signal processing. The same construction leads to scalar Fourier
transformations on the affine group, simplifying and extending the Fourier
transformation proposed by Kirillov.
