Transform Definition and 1000 Threads

Hi everyone, I am facing some problems in performing clarke-park transform for an induction motor(4 pole stator, squirrel cage IM). The motor is run with three sine wave inputs, 120 degrees phase shifted with each other. I am measuring the rotor position from the encoder and using twice of...

Hi! Here is my task: Find inverse z transform of $$X(z)=\frac{1}{2-3z}$$, if $$|z|>\frac{2}{3}$$ using definition formula. I found that $$x(n)$$ is $$\frac{1}{3}(\frac{2}{3})^{n-1}u(n-1)$$ (using other method). But how can I find it using definition formula, $$x(n)=\frac{1}{2\pi j}\oint_{C}^{ }...

Hi! My task is to find discrete signal x(n), if z transform of that signal is $$X(z)=\frac{5}{(z-2)^{2}}$$. It is known that signal is causal. Here is what I have done. Since signal x(n) is causal, convergence of z transform of that signal will be outside of circle with radius r: We have in...

< Mentor Note -- thread moved to HH from the technical math forums, so no HH Template is shown >[/color] So this is the problem Here is the question: A 32lb weight strecthes a spring 2ft.The weight is released from rest at the equilibrium position. beginning at t=0, a force equal to f(t)= sint...

I am engineering student and studying signal processing. The term Fourier transform comes in the discussion several times. There are many transforms like Laplace transform,Z transform,Wavelet transform.But as per my view ,Fourier transform is mostly used compared to others in general. My...

Homework Statement Derive the FT for a full-wave rectified sine wave, i.e., |sin(wt)| Homework Equations $$1/(√2π)\int_{a}^{b} |Sin[wt]| {e}^{-i w t}dt$$ The Attempt at a Solution I'm not entirely sure how to start doing this problem. What I tried doing was noticing that both of these...

23.) y'' + 2y' + y = 4e-t; y(0) = 2, y'(0) = -1 Y(s) = [(as + b) y(0) + a y'(0) + F(s)]/(as2 + bs + c) My attempt: a = 1, b = 2, c = 1 F(s) = 4 L{ e-t } = 4/(s+1) (From Laplace Transform Table) Plugging and simplifying: Y(s) = (2s2 + 5s + 7)/[(s + 1)(s2 + 2s + 1) Here is where I get...

We know that Fourier Transform F(W) of function f(t) is summation from -infinity to +infinity product of f(t) and exp^{-j w t}Here, what does the exponential term mean?

Homework Statement f(t) = e^t when 0≤t<1 and 0 when t≥1 Homework Equations Laplace transformations The Attempt at a Solution so the Laplace integral becomesfrom 0 to 1 ∫e^(st^2)dt + 0 how do I integrate this?

Homework Statement How can I take the Inverse Laplace Transform of $F(s) = \frac{d}{ds}\left(\frac{1-e^{5s}}{s}\right)$? I have tried going with inverse of the derivative and convolution (even tried evaluating the derivative and go from there) but although I can get to some results none of them...

Homework Statement The Plots bellow show two discrete time signals, in the plots only the initial proportion is shown. Then the signals remain constant and equal to the last value shown. Derive the Z transform of each Signal. The attempt at a solution I can get part A, giving an answer of...

Hi. I'm familiar with Fourier series but I have some hard times in learning Fourier transform. Why we use it? What's purpose of Fourier transform? Here is one signal and plot of Fourier transform of that signal: What this graph tells us? Thanks in advance.

Solve by Laplace Transforms. So I'm stuck on how to find this $$\mathcal{L}^{-1}$$ $( \frac{\frac{5s}{4} + \frac{13}{4}}{s^2+5s+8} ) $ I'm not sure what t odo. I was thinking I need to use the $\cos(at)$ and $\sin(at)$ formulas but I'm not sure... Any help would be great

Solve by Laplace Transforms. $y'' + 4y' + 4y = e^t$ $y(0) = 1$, $y'(0) = 0$So I've got $s^2Y - s + 4sY - 1 + 4Y = \frac{1}{s+1}$ then I got: $ Y = \frac{s^2+2s+2}{(s+2)(s+2)}$ Now here is where I am getting lost on the partial fraction decomposition.. I've got $s^2+2s+2 = A(s+2) + B$ I...

I was wondering whether this can be done: Let's say you have transfer function that goes like this: \frac{Y(s)}{U(s)}= \frac{N(s)}{D(s)} Now let's say I divide my transfer into two: \frac{Y(s)}{Z(s)}= N(s) \frac{Z(s)}{U(s)}= \frac{1}{D(s)} Can I apply the Laplace Inverse to these two...

in an example in my text i don't see how they got the "sU" for the transform. actually, i don't even see it in my table of transforms.

Homework Statement derive the Fourier sine and cosine transforms of $$f(x) = e^{-cx}$$ by using $$e^{iax}=cos(ax)+isin(ax)$$ and computing the integral $$\int_0 ^{\infty} e^{-cx}e^{iax}dx$$.Homework EquationsThe Attempt at a Solution i'm completely clueless, all i did was evaluate what they...

Homework Statement $$u_{xx} + u_{yy} = 0 : x < 0, -\infty < y < \infty$$ Homework Equations We can use Fourier Transform, which is defined over some function ##f(x)## as ##F(f(x)) = 1/ 2\pi \int_{-\infty}^{\infty} f(x) \exp (i \omega x) dx##. The Attempt at a Solution Using the Fourier...

Textbook says, Fourier transform expresses a function in time domain as a function in frequency domain. Basically, Fourier transform gives two different expressions in terms of t domain and f domain but they represent the same signal. It also says Hilbert transform is a different type of...

Could anybody help me either derive the Hadamard transform from the Fourier transform or point me towards a good source please?

hi pf! My book presents a problem and has it boiled down to $$S(u) = -S(f(x)) \exp(- \omega y) / \omega$$ where ##S(u)## is the sine Fourier transform of the function ##u##. However, we cannot directly take the transform back since the singularity at ##\omega = 0##. Thus the book then takes...

And also: y`+2y=2(1-e^-2t) Y(0)=0 y¨-2y`+y = t+e^t y(0)=1 and y`(0)=0 Please help me out here folks ;)

Hi. I`m new here and I need some help with Inverse Laplace Transform: f(t)=5+3t+e^3t g(t)=(t+1)u(t-2) g(t)=(t^2-9t+20)u(t-5) and Laplace Transform: F(s)=1/(s+2)^5 F(s)= 2s^2+10/s(s^2+2s+10) G(S)=2s/s^2+4e^-sso if anywone can please help me:)

Homework Statement Given x[n] with transform X(ejw), find the Fourier transform in terms of X(ejw). x1[n]=[0.9ncos(0.6*pi*n)] * x[n-2] Homework Equations time shift: x[n-k] -> e-jwkX(ejw) convolution: x[n] * h[n] -> X(w)H(w) freq. shift: x[n]ejwcn -> X(ew-wc) The Attempt at a Solution I...

Hi, Please I need some help, how can I get the Laplace transform of the integration of a difference equation?? $\int _{ 0 }^{ \infty }{ { e }^{ -st } } \int _{ -\tau }^{ 0 }{ G(\theta )x(t+\theta )d\theta } dt$ Many thanks in advanced.

Hi PF! I was wondering if you could clarify something for me. Specifically, I am solving the heat equation ##u_t = u_{xx}## subject to ##| u(\pm \infty , t ) | < \infty##. Now this implies a solution of sines and cosines times an exponential. Since we have a linear PDE, we may superimpose each...

Homework Statement I am given f(t) = e^-|t| and I found that F(w) = ##\sqrt{\frac{2}{\pi}}\frac{1}{w^2 + 1}## The question says to use the nth derivative property of the Fourier transform to find the Fourier transform of sgn(t)f(t), and gives a hint: "take the derivative of e^-|t|" I also...

I have recorded a micrograph of a 2-D array at a magnification of 43,000x on my DE-20 digital camera, which has a 6.4 μm pixel size and a frame size of 5120 × 3840 pixels. This magnification is correct at the position of the camera. I then compute the Fourier transform of the image. What is the...

I'm trying to solve Laplace equation using Fourier COSINE Transform (I have to use that), but I don't know if I'm doing everything OK (if I'm doing everything OK, the exercise is wrong and I don't think so). NOTE: U(..) is the Fourier Transform of u(..) This are the equations (Laplace...

I need to know what's the Residue Theorem for a Laplace Transform. Does anyone know the name or something, so I can search it? I couldn't find anything. For example, if I have this two equations: X(s).(s-1) = -Y(s)+5 Y(s).(s-4) = 2.X(s)+7 I know how to solve them using Simple Fractions, but...

Hi everyone! :) Have a problem here I can't solve atm. Solve the Laplace transform, when: My try: Would really appreciate some help!

Below is my walkthrough of a Fourier transform. My problem is that I want to do all the similar steps for a Fourier transform between position x and the wave vector k. That is working on a solution of the maxwell equations. The maxwell equations has many possible solutions for example: $$...

Prof Ramamurti Shankar has this Youtube video 'Introduction to Relativity' at And in it he derives the Lorentz Transforms something like this, at about 58 minutes into it. |------------------------- t ----------------------| time |-----ut---------------|---------- x' -------------|...

Homework Statement Homework EquationsThe Attempt at a Solution I tried to attempt the question but I am not sure how to start it, at least for part (i). My biggest question, I think, is how does the multiplication of a random complex number to a Fourier-Transformed signal (V(f)) have an...

Homework Statement Homework Equations The Attempt at a Solution I did Fourier transform directly to the eigenvalue equation and got Psi(p)=a*Psi(0)/(p^2/2m-E) But the rest, I don't even know where to start. Any opinion guys?

Hello everyone, I have a question about integrating in Laplace Transform. For example, if I have: f(t)=e^{i.t} I have to solve this equation: \int_{0}^{\infty}e^{i.t}.e^{-s.t}dt If I do like this, it's very simple...

I am solving a nonlinear ODE in the form of Newton's Second Law. In the equation, there is a Heaviside Theta Function of the function which I am solving (##\theta (x(t)##). Since it is quite troublesome to have both the left side of the ODE and the imput of the ODE to contain function of unknown...

Homework Statement use laplace transforms to solve the differential equation y"+2y'+17y = 1 Homework Equations Initial conditions are y(0) = 0 y'(0) = 0 The Attempt at a Solution so it converts to Y(s) (s^2+2s+17) = 1/s which then ends up as; Y(s) = 1/s*1/(s^2+2s+17) i know i need to invert...

Hi guys! I am having a problem in finding the inverse z transform of the given signal. Can anyone help me? I'd appreciate it. Thanks! Here is basically what I did: However, I don't know what to do next. What is the next thing to do? Thanks!

Hi Folks, The Fourier Cosine Transform of cos(x) for 0<x<a and 0 everywhere else is given as F(\omega)=\displaystyle\frac{1}{\sqrt{2 \pi}}[\frac{\sin a (1-\omega)}{1-\omega}+\frac{\sin a (1+\omega)}{1+\omega}] I can plot this and we get a continuous amlitude spectrum of F(\omega) against...

Homework Statement Let the single variable real function f:\mathbb{R}\rightarrow\mathbb{R} be given by f(x)=e^{|x|}. Determine the Legendre transform of f. Homework Equations Let I\subseteq\mathbb{R}be an interval, and f:I\rightarrow\mathbb{R}a convex function. Then its Legendre transform...

Homework Statement Noting that J_0(k) is an even function of k, use the result of part (a) to obtain the Fourier transform of the Bessel function J_0(x). Homework Equations In (a) I am asked to show that the Fourier transform of f(x)=\dfrac{1}{\sqrt{1-x^{2}}} is...

Homework Statement solve the following differential equation using Laplace transforms: y'' + 4y' + 4y = t^2 e^{-2t}, y_0 = 0, y'_0 = 0 y_0 and y'_0 are initial conditions. Homework Equations Using L to represent the Laplace transform, we have that L(y) = Y L(y') = pY - y_0 L(y'') =...

I am using an algorithm that transforms from my sensor frame to North West Up and I want to instead use North East Down. I have attached the current algorithm. I also want to skip the first step in my algorithm. Here is the current algorithm: http://www.filedropper.com/transformationalgorithm...

Hi To properly understand introductory quantum mechanics, I want to understand what the Fourier transform actually gives me mathematically. What book do you recommend? I found one book, but it doesn't get to Fourier transformations until after seven long chapters. Is that what I have to expect...

So I have been away from education for a little while now and I'm going through some refresher stuff - in particular I have been playing around with FFTs. If i take (with MATLAB notation): time = 0:0.01:10 y = fft(sin(2*pi*f*time)) with f = 5 then the maximum amplitude of the fft output is...

Homework Statement This comes up in the context of Poisson's equation Solve for ##\mathbf{x} \in \mathbb{R}^n ## $$ \nabla^2 G(\mathbf{x}) = \delta(\mathbf{x})$$ Homework Equations $$\int_0^\pi \sin\theta e^{ikr \cos\theta}\mathop{dk} = \int_{-1}^1 e^{ikr \cos\theta}\mathop{d\cos \theta }$$...

Homework Statement take inverse laplace of: 6/[s^4(s-2)^2] Homework Equations 6/[s^4(s-2)^2] The Attempt at a Solution I used partial fractions. I was wondering if It could be manipulated to where I could use the laplace table?

Homework Statement Find H(s) = \frac{Y(s)}{X(s)} \frac {d^2y(t)}{dt^2} + a\frac {dy(t)}{dt} = x(t) + by(t) Homework EquationsThe Attempt at a Solution [s^2 + as - b] Y(s) = X(s) H(s) = \frac{1}{s^2+as-b} I assume the inverse is a sign or a cosine but unsure which one.

Hi, I've been reading a paper on renormalisation theory as applied to a simple one-particle Coulombic system with a short-range potential. In the process of renormalisation, the authors introduce an ultraviolet cutoff into the Coulomb potential through its Fourier transform: ## \frac{1}{r}...