Optimal estimation for band-limited signals including time domain considerations

The problem of estimation for band-limited signals is investigated. The desired estimate is based on a finite number of time samples taken from a measurement interval of length TM. With no additional information, the estimate must be based on these samples alone. When the signal is band-limited with normalized bandwidth β, this provides additional information which is used to improve the estimate by extrapolating the signal. An extrapolation based on the measured time samples and the known bandwidth is concentrated in time about the measurement interval. The length of this effective extrapolation interval is . Several band-limited estimation methods of this type have been described. A new estimation method for band-limited signals is described which is also based on a time-concentrated extrapolation of the measurements. This new method improves estimates by specifically incorporating the interval TLinto the problem formulation and thereby improving the extrapolation on this relevant interval. Estimation error bounds and examples are presented in comparing these two types of band-limited estimation procedures. Estimation with imperfect data is considered. Sensitivity of the band-limited methods to errors in the data is discussed. Estimation with smoothing is utilized in reducing the effects of this noise.