©

*Lin Yangchen*

Laboratory of Computational Philately

Coconut Academy of Sciences

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Fast Fourier transformation is widely used in time series analysis. It converts temporal oscillations or repetitive spatial patterns into a power spectrum showing the amplitudes of oscillations at different frequencies.

Stamp photographs were converted to matrices of black and white pixel values and put through two-dimensional FFT. This produces complex numbers that represent the magnitude and phase shift of the signal. The magnitude component was used to plot the power spectrum.

In the plots, the lowest frequencies are in the centre, increasing outwards. The horizontal and vertical crossed lines passing through the centre are derived from the edges of the original image. Shown in the following plots are the lowest frequencies from 1 to 250 cycles across each dimension, which exceeds the Nyquist criterion as confirmed by a visual examination of the engraved lines.

If the plot has a darker and more concentrated centre, it means the stamp design is dominated by relatively coarse detail. If dark patterns extend to the edges of the plot, it means the stamp contains distinct design elements at finer spatial scales.