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Upper and lower bounds to probability of error in binary communication systems with intersymbol interference are presented. Closed-form formulas are given for systems with filters having a finite number of lumped elements. Explicit results are given when the filters are Butterworth filters of order . Four systems are considered: with a sample detector (SD), with an integrate-integrated-and-dump detector (IDD), with a filter in receiver only, and with filters in receiver and transmitter. The transmitted signal is assumed to be of the nonreturn-nonreturn-to-zero (NRZ) form.