What is the difference between dft and idft

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We can represent it using the following equation. Read the equation carefully. Probably the only things that you can notice in this equation are the fact that the summation is over some finite series. Additionally, the exponential function seems to have gotten a bit more complicated. Optical Fiber Communication ensures that data is delivered at blazing speeds. In this OFC course, we will learn all about data transmission using light. Satellite Communication is an essential part of information transfer.

In this free course, we will understand how this communication is established. A completely free course on the concepts of wireless communication along with a detailed study of modern cellular and mobile communiation protocols. If x is an acceleration, based on the above relationships, X also is an acceleration. However, the FT X should be a velocity. Where is the problem?

Absolutely true. But that happens in the case of the Fourier transform. However, in the case of discrete Fourier transform you are using a vector of samples and the answer will also be a vector of samples.

So to summarize, you are correct in terms of Fourier transform which will distribute your units over frequency. But this does not apply to DFT. Improve this question. BaluRaman BaluRaman 1 1 gold badge 7 7 silver badges 12 12 bronze badges. But overall, a very interesting and insightful article. Show 1 more comment. Active Oldest Votes. Improve this answer. Deve Deve 4, 15 15 silver badges 26 26 bronze badges. I'll change that. What about the DFT output: would you rather call it finite or periodic?

From the technical point of view, it transforms finite to finite. From the point of view that it computes the coefficients of a trigonometric polynomial, one might say that it transforms infinite discrete periodic to finite. But one can shift the window of frequencies used to represent the input, and the amplitudes over all possible frequencies form again a periodic sequence. This is a direct consequence of the DFT output being discrete. Show 4 more comments.

That is a point I always forget. Has anyone ever performed an infinite-length DFT? From what I remember say, from reading george silov's dover book, if you make the number of fourier coefficients large enough by using a fine enough grid of frequencies, then the fourier series can reproduce a period continuous function arbitrarily closely.

Bob K Bob K 8 8 bronze badges. Add a comment. Is that output a sequence of numbers or a continuous function an equation? Sign up or log in Sign up using Google.