A method simulating the filtering of a current pulse in a series of pulses. The method includes receiving a series of n+1 consecutive pulse addresses, including a pulse address for the current pulse as the last in the series of n+1, each pulse address being in a range of m values; storing the n pulses addresses prior to the current pulse address; building a composite address from the current pulse address and the prior n pulse addresses and applying the composite address to read a pulse shape from a memory of at least m.sup.n+1 pulse shapes. Also, apparatus issuing high speed pulses of programmable length. The apparatus includes a field of programmable memory to store a pulse length; a pulse clock line carrying a pulse clock signal having a pulse frequency; a frequency multiplier connected to receive the pulse clock signal and the pulse length stored in the programmable memory field and producing a sample clock signal having a frequency equal to the pulse length times the pulse clock frequency; a pulse memory holding the samples for a pulse; a DAC coupled to the pulse memory and generating analog pulses from samples received from the pulse memory; and a signal path carrying the sample clock signal to set the sampling frequency of a DAC and to clock samples from the pulse memory to the DAC.