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I am thinking of two numbers. They add to the number 15. Tell me what the two numbers are.

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I only seek a relationship $\text{ifft}(\text{operation}(\text{fft}(x))) \equiv |x|$. So, let's $\DeclareMathOperator{\DFT}{DFT}\DeclareMathOperator{\IDFT}{IDFT}$ be a bit more clean here: The FFT (IFFT) is just a fast-to-compute implementation of the DFT, so let's use the mathematical concept instead of the method to calculate its result. You demand an $\... 2 I like where you are heading, but don't see a consistent relationship would exist and here is why: First consider a single DFT bin as a rotating phasor in time on the complex plane. The absolute value of that in time will be constant (so any single such tone would translate completely to bin 0 or the DC bin). Now consider the real tones such as a cosine or ... 2 Some key take-aways /properties to know about the Fourier Transform will help reveal the answers. There is an method to the madness in extracting some key take-aways and high level understanding of what the Fourier Transform represents that makes this exercise useful. The line under the 3 indicates the assumed position of the vertical axis, meaning$t=0$and ... 2 Spectrogram given by MATLAB is right. The frequency axis shows frequency from 0 to 110mHz which is equivalent to 0 to 0.110Hz. mHz stands for milli-Hertz. There is no problem with that plot. Now the question is why we are seeing high energy components at all frequencies in the range 0 to 110mHz. That I think is because of the Aliasing effect. The sampling ... 2 Doing direct division in Frequency Domain means you are assuming cyclic / periodic boundary conditions for your data which I don't think is the proper assumption for your data. The model I'd pursue would be as I described in my answer to Deconvolution of Synthetic 1D Signals - How To? As one can see in that question the marked answer by @Hilmar is wrong. ... 2 A standard continuous wavelet transformation (the one that produce a 2D scale/shift map) is a linear operator. It produces real or complex coefficients that are related to the amplitude on "how a given wavelet at specific shift and scale matches the signal". These coefficients are (most generally) homogeneous with the signal's amplitude. This being ... 1 0.11Hz is 110mHz Vertical lines are due to the zoom; they're the bottom row ... zoomed: This is a purely visual effect, no data is added. To make the data zoom between 0 and 2mHz, increase nfft, then zoom the spectrogram. Why Matlab Spectrogram of slow and rarely sampled signal shows high frequencies The highest frequency it's showing is 110mHz, which is ... 1 "Overlap add" or "overlap save" should work just fine here. See https://en.wikipedia.org/wiki/Overlap%E2%80%93add_method You'll have to truncate the Gaussian both in time and in frequency but since a Gaussian decays really fast, it's easy to find a length that's "good enough" for your application. You will also have to pick a ... 1 MEG data is non-stationary and FFT can provide a crude approximation on clean data at best. Instead I'd recommend time-frequency analysis, like STFT or CWT. CWT is favored as it adjusts its resolution to better discriminate higher frequencies in time, and lower frequencies in frequency, on logscale (which is appropriate for brain waves). Afterwards one can ... 1 Some comments which might answer your questions: "However when writing the frequency ϕ in polar coordinates, a term is added, the amplitude r, which was not originally there." I think you have a missunderstanding what$\phi$is. For a two-dimensional function (i.e., function on the plane) the frequencies are also two-dimensional so$\phi \in \...

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Here's an answer from me in a video form: Circular vs. Linear Convolution on YouTube and a blog post: Circular vs. Linear Convolution on TheWolfSound.com

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