Design of novel sharp transition multiband FIR filter

This paper presents the synthesis of a linear phase, sharp transition, multiband FIR filter. The frequency response model of the filter is formulated with equiripple passband, stopband regions using trigonometric functions and well defined linear transition region. Employing trigonometric functions reduces Gibb´s phenomenon which is further reduced using variable density of ripple cycles in passband and stopband regions. Large density of ripples cycles are introduced at the transition edges which reduces the abrupt discontinuities at these edges. Thus passband ripple reduces and stopband attenuation improves. Slope equalization technique is applied to further reduce Gibb´s phenomenon. Using the filter model, for the desired filter specifications, a closed form expression for impulse response coefficients is derived. The design allows for variation in center frequency, number and width of passbands, transition bandwidth, passband ripple and stopband attenuation without the need of separate design. The proposed design is simple, analytical, gives narrow transition bandwidth, less passband ripple, good stopband attenuation with less filter order.