Page 16 - Special Topic Session (STS) - Volume 4

STS556 Mohd Bakri A. et al.

Figure 1 Sinusoidal function of Figure 2 Sinusoidal function of frequency
frequency 13/16 with linear trend 13/16 plus linear trend with 75%
contaminated normal noise added

Figure 2 depicts the sinusoidal of frequency plus trend with 75%
contaminated normal noise added. It is hardly to capture the general trend
and existence of seasonal oscillation with 75% contaminated normal noise
added. Two hundred signals plus the generated noise were simulated and
applied the existing and modified 4253HT smoother. The performances of
these smoothers are evaluated by regression coefficient. Consider the
following linear regression model with one independent variable:

Y =  +   +  , i = 1,..., N ; j = 1,..., k (17)
*
ij i j ij
The closer the regression coefficient to one indicates that the signal has been
extracted from noise very well. If the value of the regression coefficient is close
to zero, a smoother performs poorly in recovery the signal from noise.

3. Results and Discussion
Table 1 shows the performance of smoothers measured via regression
coefficient. The modified smoother using geometric mean was found to be

the best avenue to extract sinusoidal signal of frequency 13 from heavy noise.
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This was vouched by the value of regression coefficient that closest to 1.

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