What is spatial frequency? Every one is familiar with the idea of Fourier analysis of a time domain signal; that is to say, taking a continuous time signal such as a speech pattern in which pressure is a function of time, and decomposing it into the sum of numerous sinusoidal harmonics each of which has its own frequency, amplitude and phase. This is a very useful technique not only because it allows us to consider signals in frequency space which is normally more intuitive but also because, for linear systems at least, we can work out the effect of complete systems by considering their influence on each of the input frequency components separately and adding them all up at the end. The same concept can be applied to two dimensional images where the luminance is a function not only of time but also of position in space. Starting with the case of a static image such as a photograph we can decompose our picture into the sum of spatial harmonics each of which has a spatial frequency, amplitude and phase. Unlike temporal frequency which can be understood as individual notes played on a piano, spatial frequency is less intuitive but can be useful to think about it as a measure of feature size. Things with big dimensions contain low spatial frequencies while small things or those with sharp edges have a large high spatial frequency content. Obviously the apparent size of something depends on the position of the observer relative to it so spatial frequencies are measured as the angle subtended by one cycle of the waveform at the observer in units of cycles per degree (cpd). For example, the fence posts (spacing 2m) at the bottom of the garden (distance 30m) have a fundamental spatial frequency of 0.3cpd. There are of course many higher frequencies present as well which are needed to define the exact shape of the posts, the surface texture etc. It is convenient to remember that with a 57cm viewing distance one cycle of a 1cpd waveform measures 1cm.

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