Probability, Signals, Noise |
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Appendix applying Eqn arbitrary associated autocorrelation function belonging Borel field bounded causal centred Chapter complex spectrum conditional Consider constant contains continuous convergence convolution defined definition denoted differentiable discrete distribution enables equal equivalent event Example Exercise exists fact filter finite mean power follows follows from Eqn Fourier transform frequency function g gaussian immediately implies important impulse response independent infinity instant integrable interval limit linear mapping matrix mean value measurable function measurable space noted numerical obtained parameter periodic Poisson positive positive measurable practice probability density probability law probability space Prove r.v.s defined random signal random variable real r.v. realized relation represented respect result sampling satisfies sequence Show spectral sub-Borel field subsets Suppose symbol taking tends theorem transfer function trial variance vector Verify weakly stationary write written zero