Design of digital FIR filters via optimized generalized Reimann window function

A generalized Reimann window function is presented. The original Reimann window is chosen because its Fourier transform approximates very well the Fourier transform of the ideal window; the impulse function. However, when the number of samples of this window is made finite in order to have a realizable FIR filter, the resulting filter response suffers considerably from the Gibb's phenomenon. Accordingly, this window is modified to allow three design parameters to be selected through optimization procedures as to satisfy certain design constraints. It is demonstrated through an example that the resulting designed filter meets the required specifications, where other popular windows fail. It is also demonstrated through another example that the resulting designed filter meets the required specifications with more margin than other popular windows do.