On Efficient Design of High-Order Filters With Applications to Filter Banks and Transmultiplexers With Large Number of Channels

This paper proposes a method for designing high-order linear-phase finite-length impulse response (FIR) filters which are required as, e.g., the prototype filters in filter banks (FBs) and transmultiplexers (TMUXs) with a large number of channels. The proposed method uses the Farrow structure to express the polyphase components of the desired filter. Thereby, the only unknown parameters, in the filter design, are the coefficients of the Farrow subfilters. The number of these unknown parameters is considerably smaller than that of the direct filter design methods. Besides these unknown parameters, the proposed method needs some predefined multipliers. Although the number of these multipliers is larger than the number of unknown parameters, they are known a priori. The proposed method is generally applicable to any linear-phase FIR filter irrespective of its order being high, low, even, or odd as well as the impulse response being symmetric or antisymmetric. However, it is more efficient for filters with high orders as the conventional design of such filters is more challenging. For example, to design a linear-phase FIR lowpass filter of order 131071 with a stopband attenuation of about 55 dB, which is used as the prototype filter of a cosine modulated filter bank (CMFB) with 8192 channels, our proposed method requires only 16 unknown parameters. The paper gives design examples for individual lowpass filters as well as the prototype filters for fixed and flexible modulated FBs.