Transform Definition and 1000 Threads

Homework Statement Hi, for a project for school, I need to implement the Discrete Haar Wavelet Transform to compress an audio signal. This would be fine and dandy, but I do not really understand how to use the the DHWT. Could anyone direct me towards some resources that would be very helpful...

Homework Statement \dfrac{\partial^2 \varphi }{ \partial x^2} - \dfrac{\partial ^2 \varphi }{\partial t^2} = 1 Initial Conditions: \varphi (x, 0) = 1; \varphi_t (x, 0) = 1 Boundary Condition: \varphi (0, t) = 1 On 0 \leq x < \infty, 0 \leq t < \infty...

Homework Statement Use the Laplace transform approach to find the renewal function for a renewal process with interrenewal p.d.f. as follows: g(x) = (c^2)xe^(-cx) , x > 0 The Attempt at a Solution M*(s) = G*(s)/(1-G*(s)) where M*(s) and G*(s) denote laplace transforms I have that G*(s) =...

Google seems to provide not much information on this. In essence, I am asking about the eigenfunctions of the Laplace transform when λ=1? Anyone have any insights on this rather unusual problem? BiP

Homework Statement Evaluate the laplace transform of {t2e7tsinh(3t)} Homework Equations Laplace transform of {tnf(t)}=(-1)ndn/ds2 * F(s) The Attempt at a Solution I've replaced it with (-1)2d2L{e7tsinh(3t)} I'm not sure how to proceed, though, as I don't really see how to take...

Hallo, I really don't understand Fourier transform. Do somebody know a good book for beginners? Something like Fourier transform for dummies or so? I need it just for physics. So it don't have to be to mathematical. ^^ THX

Fourier Transform on the "connected part" of QFT transition prob. Homework Statement Calculate ⟨0|T[ϕ(x₁)ϕ(x₂)ϕ(x₃)ϕ(x₄)]|0⟩ up to order λ from the generating functional Z[J] of λϕ⁴-theory. Using the connected part, derive the T-matrixelement for the reaction a(p₁) + a(p₂) → a(p₃) +...

Hey all, Learning the Laplace transform and I get the point that it is a transformation but I would like to know what are some of the merits of the Laplace transform or more general why perform transformations in the first place. Any examples would be helpful.

Homework Statement In order to determine the characteristic function of a random variable defined by: Z = max(X,0) where X is any continuous rv, i need to prove that: F_{l,v}(g(l))=[ \phi_{X}(u+v)\phi_{X}(v) ] / (iv) where F_{l,v}(g(l)) is the Fourier transform of g(l) and...

Hello, Consider I have a linear time-invariant (LTI) system, with ##x(t)##, ##y(t)##, and ##h(t)##, as input, output, and impulse response functions, respectively. I have two choices to write the convolution integral to get ##y(t)##: $$ 1)\ \ \ y(t) = \int_{0}^{t} h(t-t')x(t')dt' $$ and...

Homework Statement Homework Equations The Attempt at a Solution First, I found all the impedance values. (starting from the left) Z1 = 1 / (j * 16E5 * 15E-9) = -j41.67 Z2 = 80 Z3 = 30 Z4 = j * 16E5 * 60E-6 = j96 I then combined Z1 and Z2. Z1 || Z2 = (-j41.67 * 80) /...

I've been wondering whether the Laplace transform is injective. Suppose I have that \int^{∞}_{0}e^{-st}f(t)dt = \int^{∞}_{0}e^{-st}g(t)dt for all s for which both integrals converge. Then is it true that f(t) = g(t) ? If so, any hints on how I might prove it? Thanks! BiP

I'm not sure about the answers to parts of the limit step of the work. Can you explain what the answer to that step should be?

1. The limit as b approaches infinity always shows up as undefined on my calc so I don't know what to put for that section of the work. 2. What pat of the work is supposed to need L'hopital's rule? The integration?

Homework Statement Find the La Place transform of cos(x)*(u(x-\pi)) Homework Equations L{u(t-a)}(s)=(e^(-as))/s The Attempt at a Solution I don't think I can just multiply this by the La Place transform of cos (x), which is s/(s^2) ?

Homework Statement Find the inverse transform of the function F(s) = log\frac{s-2}{s+2} Homework Equations L(\frac{f(t)}{t}) = \int^{∞}_{s}F(x)dx f(t) = tL^{-1}(\int^{∞}_{s}F(x)dx) The Attempt at a Solution I missed the lecture on this and while I was able to figure out...

Homework Statement L-1{\frac{s}{s^2+4s+5}} Homework Equations \frac{s-a}{(s-a)^2+k^2} \frac{k}{(s-a)^2+k^2} The Attempt at a Solution I completed the square for the denominator and got: L-1{\frac{s}{(s+2)^2+1}} (a= -2, k=1) But how do I get rid of the s in the numerator? Or do I have...

Homework Statement Find the Fourier transform of (1/p)e^{[(-pi*x^2)/p^2]} for any p > 0 Homework Equations The Fourier transform of e^{-pi*x^2} is e^{-pi*u^2}. The scaling property is given to be f(px) ----> (1/p)f(u/p) The Attempt at a Solution Using the information above, I got...

Find the DTFT of: h[n]=(-1)^{n}\frac{sin(\frac{\pi}{2}n}{sin(\pi n} useful properties: x[n]y[n] --> X[Ω]*Y[Ω] \frac{sin(\frac{\pi}{2}n}{sin(\pi n} --> rect[\frac{2Ω}{\pi} I have no clue how to deal with the (-1)[itex]^{n}[\itex] the DTFT of that doesn't converge. . . any help...

Hi, (To cut a long story short, can I cancel the integrals in Eq. 6 to leave me with Eq. 7?) I am trying to follow the method for modelling the motion of a tethered bead from a couple of papers ("Te Velthuis, A. J. W. et al. (2010) Biophys. J. 99 1292–1302" and "Lansdorp, B. M., & Saleh, O...

At page 285 in Peskin and Schroeder's Introduction to quantum field theory the author defines the integration measure D\phi = \Pi_i d\phi(x_i) where space-time is being discretised into a square lattice of volume L^4. He proceeds by Fourier-transforming \phi(k_n) = \frac{1}{V} \sum_n e^{-i...

Hi, I am learning Fourier transformation by my own. I am reading a book "Fourier Transformation" by R. Bracewell. In chapter 11, in examples of discrete Fourier transforms, it gives for N =2, {1 0} transforms to 1/2{1 1}. I can do this in MATLAB but I can't figure it out how to do it by hand...

Hey guys! I'm stuck on a Laplace transform. Following is the problematic function: [cos(t)]^3 Seems simple, but I'm having issues doing the Laplace transform on odd trigonometric functions. When I use the half-angle formula, I get this, which I can't seem to solve: 1/2cos(t) +...

Homework Statement Derive the relation: E' = \gamma (E + \beta p c)Homework Equations p' = \gamma p \\ E^{2} = p^{2} c^{2} + M^{2}c^{4}The Attempt at a Solution start off with stationary frame S E=mc^{2} then in moving frame S' E'^{2} = p'^{2} c^{2} + E^{2}: lorent transform momentum: E'^{2} =...

is the interference pattern produced by a double slit a one dimensional phase/amplitude Fourier transform? and if you did a reverse Fourier transform on it would you get an image of the two slits?

I've been taught (in the context of Sturm-Liouville problems) that Fourier series can be explained using inner products and the idea of projection onto eigenfunctions in a Hilbert space. In those cases, the eigenvalues are infinite, but discrete. I'm now taking a quantum mechanics course, and...

Here is the question: Here is a link to the question: Consider the initial value problem for y; Laplace? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Homework Statement Hello I'm learning Fourier transforms via the Stanford lecture series on Youtube. In the 6th lecture, the professor claims that the FT of a triangle function is the square of the sinc function. I'm trying to derive this, but I can't get my math to work out. Could someone...

Homework Statement See Attachment Homework Equations The Attempt at a Solution Ok so in a previous question I worked out fd = e-ipd*2*sinc(pa)/√(2∏), also worked out its Fourier transform if that helps. Now I really am stuck on the question, any guidance would be appreciated...

I have recently found that Mathematica has a "reader" which allows interactive calculations and plots to be shared. Here is a simple example, please let me know if there is interest in more such widgets.

Homework Statement ODE: y'' + 4y' + 3y = f(t) f(t) = (?? HELP - What's the mathematical term to describe these? I can't seem t o find it in my notes :cry: ) 1, 0 ≤ t < 2 t², 2 ≤ t < 3 0, t ≥ 3 Write a brief description on how you would solve this ODE using Laplace transforms. Also use the...

Homework Statement Just wondering if my output seems wrong. The interpolating polynomial looks like it's way off, though I've looked over my code many times and it seems right (?). [FONT="Courier New"]clc clear all format long x1=[1:1/10:4]; y1=zeros(1,length(x1))...

If I have a signal, sampled at N data points with a time-interval of T, does this restrict the frequency resolution I can obtain in Fourier space? I understand that from the Nyquist-Shannon sampling theorem it follows that all information on the Fourier transform of a T-sampled signal is...

Homework Statement Differential equation: \frac{d^2x}{dt^2}+4\frac{dx}{dt}+4x=6e^{-2t} with initial conditions x(0)=-2 and \frac{dx}{dt}(0)=8 Use the laplace transform to solve for x(t) Homework Equations http://www.atp.ruhr-uni-bochum.de/rt1/syscontrol/node9.html...

Homework Statement A system is characterized by the equation y' + 3y = r' . When the input is r(t) = u(t) - u(t-1), find y(t) by taking the inverse Laplace transform of Y(s).Homework Equations The Laplace transform integral The Laplace transform of a derivative sF(s) - f(0) The transfer...

I have a lot of questions, if you know something in one of them or more I will glad if you can write a replay I search after researches or others things that are correlated between optimal control and autonomous vehicles it can be things like how to calculate the shortest way, the rapid way...

I am having a hard time understanding how the Fourier sine transform works. I understand that you input a function and you get a function as an output, but I have no idea how certain inputs are even valid. Here is what the book gives for the transform: F(\omega...

How do I transform my x, y values into screen coordinates system All values is in pixels In my coordinate system origo is located in (40,495) The display area that I can use is from X=40 to x=750 and from y=495 to y=55 When you go down in the coordinate system the y value is increasing...

Hi I was wondering what the Laplace transform of a squared differential is. With that I mean the Laplace of (y' )^2 (this being y'*y' and not the second order derivative). So for example velocity squared.

Homework Statement Homework Equations The Attempt at a Solution The answer is y(t) = t^{4}+\frac{t^{6}}{30} Don't know what to do next any advices please

Homework Statement How can I figure out the Fourier transform of the following: I'd prefer to use tables if at all possible. 1. d(z)=d_{eff}sign[\cos[2\pi z]/\Lambda]) (note this is one function inside another one.) 2. d(z)=d_{eff}(1/2)(sign[\cos[2\pi z]/\Lambda]+1) 3...

Dear people, I am trying to analyze data from test bench which consists of a magnetically levitated spindle. We have a rotor/spindle which rotates and moves vertically up and down as it rotates. I measure the angle of rotation and the verticle displacement at a steady rate of 10,000 samples...

Homework Statement Find the Laplace transform of the following function t[SUP]2[SUP] - 2t The Attempt at a Solution \[\begin{gathered} f\left( t \right) = {t^2} - 2t \hfill \\ l\left( {f\left( t \right)} \right) = F\left( s \right) = \int_0^\infty {{e^{ - st}} \cdot \left( {{t^2} - 2t}...

Homework Statement f(t) = cos (pi*t) if 1\leq t <4 and 0 elsewhere using unit step functions to find Laplace TransformHomework Equations The Attempt at a Solution I came up with the unit step function f(t) = cos(pi*t) u(t-1) - cos(pi*t) u(t-4) in order to use the second shifting theorem f(t)...

I need more help understanding Fourier Transforms. I know that they transform a function from the time domain to the frequency domain and vice versa, but the short cuts to solve them just straight up confuse me. http://www.cse.unr.edu/~bebis/CS474/Handouts/FT_Pairs1.pdf This list of relations...

Hi all, I'm reading the following PDF about the DFT: http://www.analog.com/static/imported-files/tech_docs/dsp_book_Ch8.pdf Please see pages 152-153. So the inverse DFT (frequency to space, x[i] = ...) is given on page 152. Then it is claimed that the amplitudes for the space-domain...

Homework Statement Consider a Gaussian pulse exp[-(t/Δt)^2/2]exp(i*w*t), where Δt is its approximate pulse width in time. Use the Fourier transform to find its spectrum. Homework Equations The Fourier transform of a Gaussian is a Gaussian. If a Gaussian is given by f(t) = exp(-t^2/2)...

Homework Statement find the inverse laplace transformation of \frac{5s+4}{s^2} e^{-2s} Homework EquationsThe Attempt at a Solution I have tried to partial fractions \frac{5s+4}{s^2} and I got \frac{5}{s}+\frac{4}{s^2} and I know that the answer must have u(t-2) because of second shifting (...

Hi All, Usually the Fourier transform is defined as the one in the Wiki page here (http://en.wikipedia.org/wiki/Fourier_transform), see the definition. My question is can I define Fourier transform as \intf(x)e^{2\pi ix \varsigma}dx instead, i.e., with the minus sign removed, as the...

Hi. I have been given a plot for 1 Hz, sampled at 0.2 sec. And, 4 Hz and 11 Hz has also been plotted. So, from the plot, I can see that its really hard to distinguish between the signals after digitalization. My question is how do I find the next higher frequency which, when sampled at 0.2 secs...