# Questions tagged [fourier-analysis]

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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### Should I learn Fourier Analysis or Complex Analysis first?

Are the two subjects highly interrelated? Which draws more heavily from the other? Which do you recommend I learn first? Thank you.
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### How to remove high frequncies having fft?

What are the units of measure of FFT elements? Can I just set higher elements to zero to filter out higher frequencies? It looks like no. ...
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### Do you need to zeropad an image of 1920*1080 to 2048*2048 when using the Cooley-Tukey FFT?

User @Paul_R wrote that you need to zeropad an image of 1920*1080 = 2^20,984 to 2048*2048 = 2^22 when using the Cooley-Tukey FFT? Why don't we just zeropad it to 2^21=2048*1024?
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### How to prove this Fourier question?

How to prove this Fourier question? I hope for a procedure in detail.
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### How to define the Fourier transform on arbitrary Hilbert spaces?

The Fourier transform is a unitary operator from $L^2$ to $L^2$. But all infinite-dimensional Hilbert spaces are isometrically isomorphic to $L^2$. So that means we can define the Fourier transform ...
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### Use Laplace transforms to solve the integral equation.

enter image description here I know I have to use convolutions but I'm not sure how. Any help is appreciated. https://i.stack.imgur.com/rFwnk.png
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### Simple proof for Fourier transformation (DFT)

The question is in the image below: Image
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### Fourier series and floor function

It is easy to see that the the floor function on $[0,1]$ has Fourier expansion: $$[x] = x - {1 \over 2} + {1 \over \pi }\sum\limits_{n > 0} {{{\sin (2\pi x)} \over n}}$$. Let $a$ be a positive ...
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### Is the fourier transform of a function in two different variables, the same?

Is the Fourier transform of $f(x)$ the exact same as the Fourier transform of $f(t)$ when $t$ is related to $x$? For example if $t = x + 5$, would their Fourier transforms be the exact same? Isn't ...
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### Fourier Transform of $f'(x)$

If the Fourier transform of the function $f(x)$ is $F(k)$, find the Fourier transform of function $f'(x) = [f(-x)]^*$ I am unsure if $f'(x)$ in this case is the derivative function of $f(x)$ or just ...
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### I want to show fourier series by using matlab. help me. [closed]

I want to show basic fourier series by using matlab. I don't know where did I wrong please fix my code... this code keeps making error in matlab. ...
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### Finding a Fourier Serie from uniform converge

Question: Let $f(x)=x-x^2$ in $[0,1]$. Define the Fourier Serie in that interval. My Try: I define the Fourier Serie to $g(x)=x$ in $[0,1]$ as $\mathcal{F(g)}$. As $f$ is continuous, differentiable ...
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### Discussion on a beautiful function, $\sin(nx) / \sin x$ [closed]

In this post, I may need help with your broad knowledge on a function $$\frac{\sin{Nx}}{\sin{x}}$$ where $N$ is an positive integer. The questions are as follows. What is the name of this ...
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### Riemann-Lebesgue Lemma Theorem 11.7 Tom Apostol [closed]

I am reading page 314 of Tom Apostol's Mathematical Analysis theorem 11.7. It says that the limit on left hand side of equation (11) exists because the quotient is continuous and bounded. My questions ...
i thought if the fourier series coefficient of $f$ is neither even nor odd,$f$ must be the complex. we can know the function,$f$, is real or imaginary or complex from its FS coefficients. Now i don'...