Simple Exponential Smoothing and Its Control Parameter: A Reassessment

Simple exponential smoothing (SES) is a popular form of smoothing which can be regarded as a recursive system with infinite impulse response (IIR). As a consequence, it suffers heavily from the threat of instability and phase nonlinearity. Here an effort has been made to get a finite impulse response (FIR) estimation of the SES to acquire the benefits of an optimal speed and computational efficiency in addition to the usual advantages like stability and phase linearity. The optimal order of the filter, its corresponding transfer function, has been worked out, and the frequency response has been estimated for this FIR form of the SES. The frequency response has been compared with the actual IIR form of the SES. In addition to this an effort has been made to get a suitable estimation of the control parameter also called smoothing constant (α) in order to have an effective smoothing taking the cut-off frequency, computational limitation of the transfer function, minimum MSE, SNR improvement and suitable window function realisation of the FIR form of SES into consideration. A magnitude of 0.5615 is found to the most suitable value of the control parameter.

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