# Tagged Questions

Fourier analysis, also known as spectral analysis, encompasses all sorts of Fourier expansions, including Fourier series, Fourier transform and the discrete Fourier transform (and relatives). The non-commutative analog is (representation-theory).

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### Sawtooth Waves that grow in magnitude

Are there functions that generate sawtooth waves that grow in magnitude?
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### Fast evaluation of an integral convolution with an “expanding kernel”

Suppose I have a 1-D integral convolution transform like this: $$g(x) = \int_{-\infty}^{+\infty} dy\, f(y)\, K(x-y). \qquad (1)$$ Say the kernel $K(x)$ is a known analytic function, and say we have ...
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### Inverse Fourier Transform of $\left| \cos\left(\frac{2 \pi f}{100}\right) \right|$

I made 2 approaches: Am I any close...how do i procced?
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### Kernel of Helmholtz Equation on a plane

On the $z=0$ plane I have the boundary conditions $V=\delta(x)\delta(y)$ I want to solve for $z>0$. Helmholtz equation is $\nabla ^2 V +k^2 V=0$ I though that spherical harmonics would be useful. ...
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### Why does inputting complex exponentials into a system give its frequency response?

Let's say I have an FIR filter with the equation: $$y[n] = \sum_{i=0}^{N-1} h[i] x[n-i]$$ I know that to find the frequency response of this filter, I need to input a complex exponential in place ...
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### Can someone explain negative frequencies when doing the Fourier transform?

I apologize if this question has been asked before. I have looked and have not found a clear explanation. When doing the discrete Fourier transform (e.g. fft in MATLAB) for a vector of discrete time ...
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### Numerical integration with FFT

Suppose I am faced with the following integral: $$F(\bf{x}) = \int \frac{d^{2}\bf{k}}{(2\pi)^{2}} exp(-i\bf{k}\cdot \bf{x})f(\bf{k})$$ where $f$ is some (known) function ...
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