Saloma [Opt. Lett. 20, 1943 (1995)] proposed the concept of mirrors with point-spread functions that exhibit wavelet-related characteristics. We propose novel filters with wavelet point-spread functions. The mirrors are suggested to reform not only the phases of optical waves, but also the filters for amplitude. The transmittance functions of the filters, which are real and positive under some conditions, are given. Optical wavelet transforms can easily be made with these filters, and computer simulations for edge and corner extractions are given.