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By using phase-resolved micro-focus Brillouin light scattering spectroscopy, we demonstrate experimentally a phenomenon of wavelength conversion of spin waves propagating in tapered Permalloy waveguides. We show that this phenomenon enables efficient excitation of spin waves with sub-micrometer wavelengths being much smaller than the width of the microstrip antenna used for the excitation. The proposed excitation mechanism removes restrictions on the spin-wave wavelength imposed by the size of the antenna and enables improvement of performances of integrated magnonic devices.