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DISCRETE SIGNAL REPRESENTATIONS
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approximation arbitrary autocorrelation function band-limited bandpass signal bandwidth basis functions binary channel characterized complex envelope components consider constraint corresponding defined degenerate operator duration-limited eigenvalues elements energy equation equivalence relation equivalence sets evaluate example Exercise expressed finite Fourier transform frequency domain given Hence Hilbert impulse response inner product input signal integral intersymbol interference interval Kuu(f Kxx(f likelihood ratio linear functional linear space linear transformation lowpass filter mapping matched filter mean-squared error metric space modulation multiplication n-tuple norm obtained optimal optimum filter orthogonal projection orthonormal set parameter physical realizability power spectral density probability density function problem properties quadratic functional random process random variables received signal result sampling scalar Section self-adjoint sequence shown in Figure signal processing signal space solution stationary process statistically independent subset subspace transfer function transmission vector waveform wide-sense stationary wide-sense stationary process zero zero-mean