1Definition of a one-dimensional linear system.2Definition of a two dimensional linear system.3Behavior of a linear system4“Proof” of the convolution theorem5i(t) is the input waveform; h(t) is the impulse response function; o(t) is the output waveform. Ditto for the two dimensional case.6Definition of the weighting function of a linear system.7Cross correlation version of the convolution theorem89Sine wave gratings of different contrasts, but the same spatial frequency and phase.10Summing sine waves to create a square wave.11Summing spatial sine waves to create a spatial square wave.12Cosine and sine transforms define the Fourier transform. The relationship of the cosine and sine transforms to the amplitude and phase transforms.131415A spatial sine wave with equal vertical and horizontal spatial frequencies.16Fourier amplitude spectrum of a square wave grating.17Fourier amplitude spectrum of a natural
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