New approach to the synthesis of sharp transition FIR digital filter

A model is proposed for a linear phase, sharp transition, lowpass FIR filter. The filter model is formulated using sinusoidal functions of frequency to evaluate the impulse response coefficients in closed form. Filter transfer function is evolved in frequency and time domain. This design approach is found to be closely comparable to FRM techniques in terms of arithmetic complexity with added advantage of simpler design and having closed form expressions for impulse response coefficients. Approach can be extended to design sharp transition arbitrary passband highpass, bandpass and bandstop filters.