Transform Definition and 1000 Threads

Hi, I noticed that in some cases we first call fit_transform(), and afterwards we call transform(). Like in the following example: from sklearn.preprocessing import PolynomialFeatures X_train = np.array([6, 8, 10, 14, 18]).reshape(-1, 1) X_test = np.array([6, 8, 11, 16]).reshape(-1, 1)...

Homework Statement Homework Equations If i solve the wave equation using separation of variable and laplace tranform. Will i get the same answer ? The Attempt at a Solution

Hi, the three main types of complex matrices are: 1. Hermitian, with only real eigenvalues 2. Skew-Hermitian , with only imaginary eigenvalues 3. Unitary, with only complex conjugates. Shouldn't there be a fourth type: 4. Non-unitary-non-hermitian, with one imaginary value (i.e. 3i) and a...

Homework Statement For example : How to inverse z-domain function (z2+3z+7)/(z2+4z+3) The Attempt at a Solution Whatever I use partial fraction to simply the z-domain function, I cannot continue the next step, such as 1/(z+3)

I am studying online course notes from University of Waterloo on 'Analytical mathematics in geology' in which the author describes a 'modified Fourier transform' which can be used to incorporate 3rd kind of boundary conditions. The formula is ## \Gamma \small[ f(x) \small] = \bar{f}(a) =...

Homework Statement Homework EquationsThe Attempt at a Solution I'm kind of lost now, how do I go about getting this into the right form for partial fraction exapnsion. And also what do I do with the V(0'). There was no information given about it.

Homework Statement I need to calculate the derivative of a function using discrete Fourier transform (DFT). Below is a simplified version of my code (just for sin function) in python Homework Equations from __future__ import division import numpy as np from pylab import * pi = np.pi def...

Homework Statement In special relativity the metric is invariant under lorentz transformations and therefore so is the determinant of the metric. How does the metric determinant transform under a more general transformation $$x^{a\prime}=J^{a\prime}_{\quad a}x^{a}$$ where $$J^{a\prime}_{\quad...

Homework Statement An LTI system has an impulse response h(t) = e-|t| and input of x(t) = ejΩt Homework Equations Find y(t) the system output using convolution Find the dominant frequency and maximum value of y(t) Ω = 2rad/s The Attempt at a Solution I have tried using the Fourier transform...

Hi, I am a neophyte in Discrete Fourier Transform and I am procticing with discrete Sine-transform. Specifically I want to calculate $$ \mathcal{F}_s \lbrace x \cdot e^{-x^2} \rbrace = \int\limits_{0}^{\infty } x \cdot e^{-x^2} \cdot \sin\left(x\right)\, \mathrm{d}x = \frac{1}{2} \pi^2 \omega...

Homework Statement 4(d2x/dt2) +3x = t*e-3tsin(5t) Homework EquationsThe Attempt at a Solution So I know how to take the Laplace transform and find the function for the Laplace domain: X(s) = 10(s+3)/(((s+3)2+25)2)(4s2+3) + (10s/(4s2+3)) + (2/(4s2+3)) But trying to convert...

When you do a Fourier transform of spacetime.. what do you get? (or how does spacetime look in frequency domain? And what applications do this and what results are they looking or solving for?

Hi, this thread is an extension of this one: https://www.physicsforums.com/posts/5829265/ As I've realized that the problem is that I don't know how to properly use FFTW, from http://www.fftw.org. I am trying to calculate a derivative using FFTW. I have ##u(x)=e^{\sin(x)}##, so...

Hi. I was checking the library for the discrete Fourier transform, fftw. So, I was using a functition ##f(x)=sin(kx)##, which when transformed must give a delta function in k. When I transform, and then transform back, I effectively recover the function, so I think I am doing something right...

Homework Statement L-1{[(2s-1)]/[(s^2)(s+1)^3]} Homework Equations L{f(t)e^(at)}=F(s-a) The Attempt at a Solution I have tried million ways but the different exponents in the denominator are throwing me off. The other problem is that I cannot use partial fractions, the homework instructions...

Hello buddies! Please, check out these equations... Tell me, please, are they mathematically correct or not? I need a simple YES/NO answer. I have not sufficient knowledge to understand them. I just need to know whether they are correct... Thank you! P.S. Am is amplitude; I guess it is a...

Homework Statement Q/ in this inverse Fourier problem, how did he come with the results of integration of (Sinc) function and how did he come up with those results of integration with the inverse part (as in the attached picture) here is the problem: https://i.imgur.com/Ir3TQIN.png Homework...

Homework Statement Hello everyone, am trying to solve this Fourier Trans. problem, here is the original solution >> https://i.imgur.com/eJJ5FLF.pngQ/ How did he come up with this result and where is my mistake? Homework Equations All equation are in the above attached picture The Attempt at a...

Could you explain a bit about the relationship between locality and uncertainty in Fourier pairs? Many pages talk about uncertainty principle stating that the precision at which we can measure time duration of signal cannot unlimitedly grow without affecting precision on bandwidth. Many other...

Homework Statement [/B] I am trying to match each of the following 28-point discrete-time signals with its DFT: Set #1: Set #2: Homework EquationsThe Attempt at a Solution Set #1 We have already established (here) that: ##Signal 1 \leftrightarrow DFT3## ##Signal 4 \leftrightarrow...

Hi! 1. Homework Statement From the website http://www1.uprh.edu/rbaretti/MomentumspaceIntegration8feb2010.htm we can see the Fourier transform of the ground state hydrogenic wave function : Φ(p) = ∫ ∫ ∫ exp(-i p r) (Z3/π )1/2 exp(-Zr) sin(θ) dθ dφ r² dr (1.1) After intregation...

Homework Statement Match each discrete-time signal with its DFT: Homework EquationsThe Attempt at a Solution I am mainly confused about Signal 7 and Signal 8. Signal 1 is the discrete equivalent to a constant function, therefore its DFT is an impulse (Dirac ##\delta##), so it corresponds...

Homework Statement 1. The common form of the heat-diffusion equation governing the temperature distribution $$\rho C_p \frac{\partial T}{\partial t}=k\nabla^2T$$ Is this equation valid in any inertial frame of reference? (i.e. does it have the property of Galilean invariance?) If not, can it...

Homework Statement I got the laplace transfer function H(s) = 1/(s + 2) and I'm suppose to find the inverse Z transform by first converting to H(z) by s = Ts/2*(z-1)/(z+1) Then do inverse Z-transform using the "displacement rule" - Never heard of. Homework Equations H(s) = 1/(s + 2) s =...

Hello! Why do we need to impose a change on the basis vector, when going from a reference frame to another. I understand that the components of the vector and the basis change using inverse matrices (the components use a matrix and the vector basis the inverse). But the transformation condition...

Homework Statement I have to take the inverse Laplace of this function (xoms+bxo)/(ms2+bs+k) this can not be broken into partial fractions because it just gives me the same thing I started with. How is this done? This is coming from the laplace of the position function for a harmonic oscillator...

Homework Statement $$u_{xx}=u_t+u_x$$ subject to ##u(x,0)=f(x)## and ##u## and ##u_x## tend to 0 as ##x\to\pm\infty##. Homework Equations Fourier Transform The Attempt at a Solution Taking the Fourier transform of the PDE yields $$ (\omega^2-i\omega) F\{u\}=...

Homework Statement Hi guys, I am going to calculate the following integral: $$\int_0^{f_c+f_m} |Y(f)|^2\, df$$ where:$$Y(f)=\frac{\pi}{2} \alpha_m \sum_{l=1}^{L} \sqrt{g_l}\left [ e^{-j(\omega \tau_l - \theta_m)} \delta(\omega - \omega_0) + e^{-j(\omega \tau_l + \theta_m)} \delta(\omega +...

Prelude Consider the convolution h(t) of two function f(t) and g(t): $$h(t) = f(t) \ast g(t)=\int_0^t f(t-\tau) g(\tau) d \tau$$ then we know that by the properties of convolution $$\frac{d h(t)}{d t} = \frac{d f(t)}{d t} \ast g(t) = f(t) \ast \frac{d g(t)}{d t}$$ Intermezzo We also know that...

Apart from the fact that it is, what is the physical significance of the fact that you can get the momentum distribution of a particle by taking the Fourier transform of its position distribution?

Homework Statement F(t) = sqrt(π/2)e-t for t>0 F(t) = sqrt(π/2)et for t<0 In other words the question asks to solve this integral: 1/sqrt(2π) ∫F(t)eitxdt and show that it equals 1/(1+x2) Homework Equations F(t) = sqrt(π/2)e-t for t>0 F(t) = sqrt(π/2)et for t<0 1/sqrt(2π) ∫F(t)eitxdt The Attempt...

Homework Statement "Suppose that ##F(s) = L[f(t)]## exists for ##s > a ≥ 0##. (a) Show that if c is a positive constant, then ##L[f(ct)]=\frac{1}{c}F(\frac{s}{c})## Homework Equations ##L[f(t)]=\int_0^\infty f(t)e^{-st}dt## The Attempt at a Solution ##L[f(ct)]=\int_0^\infty f(ct)e^{-st}dt##...

Hello, I am trying to find an expression for the signal-to-noise ratio of an oscillating signal on top some white noise. In particular I would like to know how the SNR scales with the integration time. It is well known that during some integration time ##T##, the SNR increases as ##T^{1/2}##...

Homework Statement Homework Equations I'm not sure. The Attempt at a Solution I started on (i) -- this is where I've gotten so far. I am asked to compute the Fourier transform of a periodic potential, ##V(x)=\beta \cos(\frac{2\pi x}{a})## such that...

Homework Statement My question: Can I turn this difference equation for R below, into a continuous function R(t)? I have no idea if, or how, I can. And I'd like to. Equation derived from the following manufacturer statement on the thermal response of a thermistor to a fixed temperature: The...

What is the transformation used Is there any explanation for : $$ \frac{\mathit{\lambda}}{\mathit{\Gamma}{\mathrm{(}}{q}{\mathrm{)}}}\mathop{\int}\limits_{t0}\limits^{t}{{\mathrm{(}}{t}\mathrm{{-}}{s}{\mathrm{)}}^{{q}\mathrm{{-}}{1}}}{x}_{0}\mathrm{(}s\mathrm{)}ds $$ How did become like this...

I'm studying Quantum Field Theory and the first example being given in the textbook is the massless Klein Gordon field whose equation is just the wave equation \Box \ \phi = 0. The only problem is that I'm not being able to get the same solution as the book. In the book the author states that...

Let ##\Lambda## be a Lorentz transformation. The matrix representing the Lorentz transformation is written as ##\Lambda^\mu{}_\nu##, the first index referring to the rows and the second index referring to columns. The defining relation (necessary and sufficient) for Lorentz transforms is...

So a little bit of background: I work in an undergraduate lab at UMass Amherst and am currently building/optimizing a faraday magnetometer for use in the Muon g-2 experiment at Fermilab. The magnetometer works as follows. A laser is shone through a crystal with a particular Verdet Constant at...

<Moderation note: edited LaTex code> E.g. A rotation by a finite angle θ is constructed as n consecutive rotations by θ/n each and taking the limit n→∞. $$ \begin{pmatrix} x' \\ y' \\ \end{pmatrix} =\lim_{x \to \infty} (I + \frac{\theta}{n} L_z )^n \begin{pmatrix} x...

Background: I have a set of known 3D feature points {x_i} on the surface of an object in some reference position/orientation at time t = 0. At t > 0 the object will have moved by a rigid transform. I am using computer vision to estimate the position of the 3D feature points {y_i}. I want to...

I understand the conditions for the existence of the inverse Laplace transforms are $$\lim_{s\to\infty}F(s) = 0$$ and $$ \lim_{s\to\infty}(sF(s))<\infty. $$ I am interested in finding the inverse Laplace transform of a piecewise defined function defined, such as $$F(s) =\begin{cases} 1-s...

This is mostly a procedural question regarding how to evaluate a Bromwich integral in a case that should be simple. I'm looking at determining the inverse Laplace transform of a simple exponential F(s)=exp(-as), a>0. It is known that in this case f(t) = delta(t-a). Using the Bromwich formula...

Homework Statement The problem is from an optics text, however I believe the problem to be a mathematical one. I'm trying to take the Fourier transform of P(t) = ε0∫ X(t-τ)E(τ) dτ which should equal P(ω) = ε0X(ω)E(ω) where ε0 is a constant X is the susceptibility E is the...

Homework Statement ƒ(s) = 1/((1-exp(-s))*(1+s)) Homework EquationsThe Attempt at a Solution I know the solution is periodic but how to obtain the t-domain function?

Hi I have a series ${f}_{1}$ , ${f}_{2}$, ... that are all a functions of a variable $t$ I am seeking a point-wise convergence. to investigate the convergence of the series I took Laplace transform. If I can find a condition on the Laplace variable $s$, can I find the condition of convergence...

Homework Statement ty'' + y' = 2t2, y(0) = 0Homework Equations laplace(f''(t)) = s2laplace(f(t)) -sf(0) - f'(0) (-1) (d/ds) (F(s))The Attempt at a Solution I know how to solve the problem except for the ty'' part. I tried using the equation and I got -d/ds(s2Y(s) - 0 - f'(0)) which becomes...

Homework Statement Solve Laplace Transform L{tsin(2t)sin(5t)} Homework Equations cos(bt)=s/s^2+b^2 trig identity (product identity): sin(a)sin(b)=1/2[cos(a-b)-cos(a+b) t^nf(t)=(-1)^nd^n/ds^nF(S) (the template is complicated for me to use. Srry for the inconvinience) The Attempt at a Solution...

Homework Statement I need help when changing the formula of the yellow circled part to red-circled part ... Homework EquationsThe Attempt at a Solution I tried , but i didnt get what the author got ... Here's my working ... Which part of my working is wrong ?

Homework Statement Determine the inverse Laplace transform Homework Equations 3s+9. (s+3)^2+7 The Attempt at a Solution [/B] Hi iam new to the forum and still unsure how to make the equations the correct format so hope you can understand what I have typed. I have Tried to Convert...