Abstract
Basically, the term “Filtering” is referred to a technique to extract information (signal in this context) from noise contaminated observations (measurements). If the signal and noise spectra are essentially non-overlapping, the design of a frequency domain filter that allows the desired signal to pass while attenuating the unwanted noise would be a possibility. A classical filter could be either low pass, band pass/stop or high pass. However, when the noise and information signals are overlapped in spectrum, then the design of a filter to completely separate the two signals would not be possible. In such a situation the information has to be retrieved through estimation, smoothing or prediction. Figure 2.1 shows a general diagram of an open-loop system (plant) subject to noise contamination at the output end.
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Notes
- 1.
The cumulative distribution function gives the probability that the random variable X satisfies
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Chandra, K.P.B., Gu, DW. (2019). State Observation and Estimation. In: Nonlinear Filtering. Springer, Cham. https://doi.org/10.1007/978-3-030-01797-2_2
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