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Published byGabriel Green Modified over 9 years ago
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X – arbitrary fixed input distribution holds for scalar and vector signals Notes Mean of Filtering (causal) MMSE = Smoothing (noncausal) MMSE Γ uniformly distributed in [0,snr] Continuous time time
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1. Some direct implications on other results: Equivalency with De Bruijn’s identity which connects the differential entropy h( ) to the Fisher’s information matrix J( ) (connected to the CRLB) Derivative of the divergence gets an interesting form can be used also in multiuser systems: Information Theory Estimation Theory 2. Duality Information Theory Estimation Theory: New lower/upper bounds on MMSE and mutual info. I( ; ) Results from one domain can be applied to the other Results from one domain can be obtained/proven by the other e.g., linking the filtering and smoothing by a direct expression in continuous time domain and sandwiching relation in discrete time
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