# Question

Consider the system described where a communication system transmits a square pulse of width t1. In that example, it was found that the matched filter can be implemented as a finite time integrator which integrates over a time duration to t1 seconds. For the sake of this problem, suppose t1 = 100µ s. Suppose that due to imperfections in the construction of this filter, we actually implement a filter which integrates over a time interval of t2 seconds. Determine what range of values of t2 would produce an output SNR which is within 0.25 dB of the optimal value (when t2 = t1). The answer to this question will give you an idea of how precise the design of the match filter needs to be (or how impercise it can be).

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