©Lin Yangchen

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.

Signal processing and visualization were programmed using the R Language for Statistical Computing. Each stamp image was converted to matrices of grey pixel values and put through 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 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. The power spectra show that the essay (first row) has more clutter across different spatial scales compared with the issued stamps in which large-scale features stand out from the fine detail.


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