Optimum FIR Transmitter and Receiver Filters for Data Transmission Over Band-Limited Channels

The paper deals with the design of digital transmitter and receiver filters with finite impulse response (FIR) for data transmission over band-limited channels. The filters are matched and satisfy a zero intersymbol interference constraint when cascaded. For baseband transmission, the filters achieve optimum spectral concentration in the frequency range
[-(1+\beta)/2T, (1+\beta)/2T]
. Mathematically, the filter design leads to a generalized eigenvalue problem which is solved numerically by a projected gradient Procedure. For transmission over bandpass channels by combined amplitude and phase modulation, the design technique is modified so that filters with complex-valued impulse response and optimum spectral concentration in the range of positive bandpass frequencies
[f_{c} - (1+\beta)/2T, f_{c} + (1+\beta)/2T]
are obtained. In addition, the complex formulation allows the design of impulse responses with enhanced spectral attenuation in the corresponding range of negative frequencies in order to minimize imageband interference. Results are shown in terms of filter coefficients, signal spectra, and spectral concentrations obtained. For example, filters designed for a voiceband data modem operating at a symbol rate of 2400 baud achieve a spectral concentration of 98.5 percent with 24 coefficients and
\beta = 0.1
, and with only 0.001 percent of the total energy in the imageband region.