value of y i n when u03b1 0 8853 this concentration of the impulse response to a short interval aids pulse location and strength estimation in subsequent processing as a second example consider an output s i n of the bandpass filter unit 31 which consists of a discrete time impulse at time n 1 1 exciting discrete time complex poles at u03b1 1 m 1 e j u03c9 1 and u03b1 2 m 2 j u03c9 2 where u03b1 1 u2260 u03b1 2 and the magnitudes m 1 and m 2 are less than unity s i n u03b1 1 n u2212 n 1 u n u2212 n 1 u2212 u03b1 2 n u2212 n 1 u n u2212 n 1 8 fig8 and 9 show the real and imaginary parts respectively of the output of bandpass filter unit 31 with exemplary values of m 1 m 2 0 88 u03c9 1 0 6283 u03c9 2 1 885 and n 1 5 for the signal of equation 8 and a nonlinear operation consisting of the magnitude the output of nonlinear operation unit 32 an example of which is shown in fig1 is for exemplary values of m 1 m 2 0 88 u03c9 1 0 6283 and u03c9 2 1 885 the global maximum of equation 9 occurs at n n 1 2 subsequent local maxima occur at n n 1 7 12 17 22 and are caused by beating between the two pole frequencies u03c9 1 and u03c9 2 for simple pulse estimation methods these subsequent local maxima can cause false pulse detections however when processed by the method of equation 1 with u03b1.