A nonrecursive digital filter for data transmission

High-speed digital data transmission systems often require special filter functions for spectral shaping with prescribed phase characteristics. One such filter is the cosine roll-off filter, which has applications in both serial and parallel data transmission systems. This filter is of special interest, because in such applications it is common to utilize two identical cosine roll-off filters in a cascade connection, i.e., one in the transmitter and one in the receiver. The composite response of the cascade connection has the raised-cosine roll-off characteristic, which yields low intersymbol interference. Because a linear phase characteristic is further required, the digital filter type chosen for this application is nonrecursive. The difference equation coefficients are determined from the coefficients of a Fourier series expansion of the magnitude-frequency characteristic in the form of a cosine series. The linear phase characteristic is the direct result of setting the sine terms of the Fourier series to zero. Two criteria have been selected as a measure of the digital filter performance: minimum stop-band attenuation and an RMS measure of intersymbol interference. Performance was calculated as a function of the number of terms in the cosine series used to approximate the desired function. Performance graphs, which summarize the results of this investigation, are included. The application of digital filtering techniques in the field of data transmission systems is shown to have practical value.