(a) Time domain
(b) Spectral domain
Figure 10: Calculating the moving average to reduce the noise and to reject the high frequency. Panel (a) shows the original function (gray line) and the noisy sampling points (open symbols). The result of the moving average in the time domain is given in (a) for the convolution (dashed) and the shifted FFT (dash-dotted). (b) displays the spectrum of the original function (gray), the filtered result (black), and the kernel function (dashed).