Optimal window-transforms for FIR digital filter design

A method is given for optimizing the frequency response of finite impulse response (FIR) digital filters designed by frequency sampling. The impulse response of the filter is multiplied by a window computed by optimizing its discrete Fourier transform. A multidimensional search is used to minimize the maximum deviation of the frequency response from the design specifications. The optimal window- transform method has two advantages over conventional minimax optimal design methods [6]. One advantage is that the multidimensional search is carried out over a much smaller number of parameters. For example, it has been found that the stop-band attenuation of low-pass filters designed by this method is approximately 50 dB when optimized over one parameter and 80 dB when optimized over two parameters. The other advantage is that the functional form of the optimal window-transform with a given number of parameters is nearly constant over an entire class of filters, such as the low-pass filters, so nearly optimal prototype windows may be found.