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hello and welcome today weamp;#39;re going to be talking about two dimensional Fourier series and it turns out this is related to something that youamp;#39;re probably familiar with before that is the JPEG file format probably one of the most widely used formats for images in the world and it turns out that it is effectively a Fourier series so letamp;#39;s talk about Fourier series in two dimensions of course weamp;#39;re going to have X is going to be on a some interval 0 to W thatamp;#39;s a width okay and then we have Y thatamp;#39;s going to be on a range from 0 up to some height ok and then what we have are these cosine and sine Fourier series modes so we have feet n comma M of X comma Y is equal to cosine of n PI over W x times cosine M PI over H Y thereamp;#39;s a another one for the signs and itamp;#39;s much similar but in this video weamp;#39;re gonna be focusing mostly on the cosine ones and it turns out thatamp;#39;s because this is the basis for the JPEG the the
