Intersymbol interference due to an ideal filter with linear amplitude attenuation

The square pulse response of an ideal low-pass filter with linear amplitude attenuation is evaluated in terms of the exponential integral function. This result is used to determine the intersymbol interference terms for binary phase-shift keyed (BPSK) and quadrature phase-shift keyed (QPSK) transmissions through the corresponding bandpass channel filter. Properties of the intersymbol interference are obtained, and necessary conditions for convergence of the maximum intersymbol interference are given in the case a nonzero attenuation slope. For BPSK transmission, it is found that the channel bandwidth-bit duration product must be an integer. For QPSK, the condition for convergence is that the channel bandwidth-symbol duration product must be an even integer.<>