Waveform smoothing: analysis and comparisons

Several smoothing nonrecursive filters, such as the rectangular, triangular, and Hanning filters and the exponential recursive filter with different coefficients, are analyzed and compared. These filters are applied to noisy sinusoidal waveforms with different frequencies and signal-to-noise ratios. Filter performance is based on the square of the error between the original signal considered for measurement and the clean one. The most appropriate filter to smooth such signals is determined for every frequency and for different signal-to-noise ratios. Theoretical and simulation results show that for large noise components (very low signal-to-noise ratios) the rectangular smoother gives the least amount of root-mean-square error. For signal-to-noise ratios in the range 0-10 dB, the performance of the exponential filter is better than the performance of the nonrecursive filters examined