the N-point DFT can be imagined by taking N arbitrarily large. In the limit, the rigorous mathematical machinery treats such linear operators as so-called integral transforms. In this case, if we make a very large matrix with complex exponentials in the rows (i.e., cosine real parts and sine imaginary parts), and increase the resolution without bound, we approach the kernel of the Fredholm integral equation of the 2nd kind, namely the Fourier operator that defines the continuous Fourier transform. A rectangular portion of this continuous Fourier operator can be displayed as an image, analogous to the DFT matrix, as shown at right, where greyscale pixel value denotes numerical quantity. See also Multidimensional transform Clock and shift matrices References The Transform and Data Compression Handbook by P. C. Yip, K. Ramamohan Rao – See chapter 2 for a treatment of the DFT based largely on the DFT matrix External links Fourier Operator and Decimation In Time (DIT) Fourier analysis Digital signal processing Matrices