I need to be able to explain the complexity of three Fast Fourier Transform algorithms: Cooley-Tukey’s, Bluestein’s and Prime-factor algorithm. Unfortunatelly, I’m a little lost in the process. Discrete Fourier Transform general formula \begin{align} x &= \{x_0, … , x_{N-1}\}\\ 0 &\leq n \leq N-1 \\ X_n &= \sum^{N-1}_{k=0}x_k \cdot e^{\frac{-i\cdot 2\pi \cdot k \cdot […]

Find the solution of the Dirichlet problem in the half-plane $y>0$. $${u_y}_y +{u_x}_x=0, -\infty<x<\infty,y>0$$ $$u(x,0)=f(x),-\infty<x<\infty$$ $u$ and $u_x$ vanish as $$ \lvert x\rvert\rightarrow\infty$$ and $u$ is bounded as $$y\rightarrow\infty$$ I’ve tried hard for this,but my answer is not matching.I’ve gone through by applying infinite fourier transformation as my text book suggests,but I’m not even getting […]

For five years I tried to understand how Fourier transform works. Read a lot of articles, but nobody could explain it in simple terms. Two weeks ago I stumbled upon the video about a 100 years old machine that calculates Fourier series mechanically: https://www.youtube.com/watch?v=NAsM30MAHLg – I watched it and suddenly it became very clear! It […]

Intereting Posts

Rubik's Cube Combination
Confused between Nested Quantifiers
Proof involving homomorphism between $\Bbb Z^n$ and an abelian group G
Show that, given spherically symmetric initial data, a solution to the heat equation is spherically symmetric
Floating point arithmetic operations when row reducing matrices
On fifth powers $x_1^5+x_2^5+\dots = y_1^5+y_2^5+\dots$
Why are clopen sets a union of connected components?
If $M$ is a nonorientable $3$-manifold, why is $H_1(M, \mathbb{Z})$ infinite?
Express $C$ in terms of the sets $A_n$
Geometric series of matrices
Using the LRT statistic to test $H_0$ vs $H_1$
How do I solve a PDE with a Dirac Delta function?
Dunford-Pettis Theorem
How to prove there exists $n_{1}a_{n_{0}}+n_{2}a_{n_{1}}+\cdots+n_{k}a_{n_{k-1}}<3(a_{1}+a_{2}+\cdots+a_{N})$
Convergence of $a_n=(1/2)^{(1/3)^{…^{(1/n)}}}$