Design and application of nearly Nyquist and SR-Nyquist FIR filter based on linear programming and spectrum factorization

The Nyquist and SR-Nyquist filters are widely used to realize the zero inter-symbol interference (ISI) transmission, such as the shaping and matched filters of communication systems. However, the zero-ISI assumption results in negative effects for the other filter performance indexes, i.e., the ripple and the attenuation. In fact, the ISI constraint can be relieved to improve the ripple or attenuation performance. Accordingly, this paper puts forward to design a nearly Nyquist FIR filter by the linear programming (LP), which obtains better ripple and attenuation performance at the cost of non-zero ISI. Note that this ISI is controllable in the constraint. Moreover, this paper also employs the spectrum factorization technique to decompose the above nearly Nyquist filter into two nearly SR-Nyquist filter, where an iterative search process is exploited to make a performance trade-off. Besides, the nearly SR-Nyquist filter is applied in the digital down-converter (DDC) and the computer simulation shows a good performance.