The definition for the noise equivalent bandwidth of a filter was given in terms of the transfer function of the filter in Definition 11.1. Derive an equivalent expression for the noise equivalent bandwidth of a filter in terms of the impulse response of the filter, h (t).
Answer to relevant QuestionsSuppose a filter has a transfer function given by H (f) = sinc2 (f). Find the noise equivalent bandwidth of the filter. A square pulse of width to = 1µs plus zero- mean white Gaussian noise is input to a filter with impulse response, h (t) = exp (–t / t1) u (t). (a) Find the value of the constant such t1 that the SNR at the output of the ...Suppose we are allowed to observe a random process Z (t) at two points in time, t0 and t2. Based on those observations we would like to estimate Z (t) at time t = t1 where t0 < t1 < t2. We can view this as an interpolation ...Consider a non- linear device such that the output is Y (t) = aX2 (t), where the input X (t) consists of a signal plus a noise component, X (t) = S (t) + N (t). Determine the mean and autocorrelation function for Y (t) when ...Prove that the importance sampling (IS) estimator of Equation (12.26) is unbiased. That is, show that
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