  {.2in} {\small {\bf Abstract.} Due to the extra degrees of freedom, special
affine Fourier transform (SAFT) has achieved a respectable status within a
short span and got versatile applicability in the areas of signal processing,
image processing,sampling theory, quantum mechanics. However, due to its global
kernel, SAFT fails to obtain local information of non-transient signals. To
overcome this, we in this paper introduce the concept of novel special affine
wavelet transform (NSAWT) and extend key harmonic analysis results to NSAWT
analogous to those for the wavelet transform. We first establish some
fundamental properties including Moyal's principle, Inversion formula and the
range theorem. Some Heisenberg type inequalities and Pitt's inequality are
established for SAFT and consequently Heisenberg uncertainity principle is
derived for NSAWT.
