I am stuck at calculating the inverse transorm of $Z(\omega) =\frac{a}{\alpha-i\omega}$. Can someone help me please? thanks
2026-04-06 19:31:52.1775503912
inverse transform of $Z(\omega) =\frac{a}{\alpha-i\omega}$
50 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in COMPLEX-ANALYSIS
- Minkowski functional of balanced domain with smooth boundary
- limit points at infinity
- conformal mapping and rational function
- orientation of circle in complex plane
- If $u+v = \frac{2 \sin 2x}{e^{2y}+e^{-2y}-2 \cos 2x}$ then find corresponding analytical function $f(z)=u+iv$
- Is there a trigonometric identity that implies the Riemann Hypothesis?
- order of zero of modular form from it's expansion at infinity
- How to get to $\frac{1}{2\pi i} \oint_C \frac{f'(z)}{f(z)} \, dz =n_0-n_p$ from Cauchy's residue theorem?
- If $g(z)$ is analytic function, and $g(z)=O(|z|)$ and g(z) is never zero then show that g(z) is constant.
- Radius of convergence of Taylor series of a function of real variable
Related Questions in FOURIER-ANALYSIS
- An estimate in the introduction of the Hilbert transform in Grafakos's Classical Fourier Analysis
- Verifying that translation by $h$ in time is the same as modulating by $-h$ in frequency (Fourier Analysis)
- How is $\int_{-T_0/2}^{+T_0/2} \delta(t) \cos(n\omega_0 t)dt=1$ and $\int_{-T_0/2}^{+T_0/2} \delta(t) \sin(n\omega_0 t)=0$?
- Understanding Book Proof that $[-2 \pi i x f(x)]^{\wedge}(\xi) = {d \over d\xi} \widehat{f}(\xi)$
- Proving the sharper form of the Lebesgue Differentiation Theorem
- Exercise $10$ of Chapter $4$ in Fourier Analysis by Stein & Shakarchi
- Show that a periodic function $f(t)$ with period $T$ can be written as $ f(t) = f_T (t) \star \frac{1}{T} \text{comb}\bigg(\frac{t}{T}\bigg) $
- Taking the Discrete Inverse Fourier Transform of a Continuous Forward Transform
- Is $x(t) = \sin(3t) + \cos\left({2\over3}t\right) + \cos(\pi t)$ periodic?
- Translation of the work of Gauss where the fast Fourier transform algorithm first appeared
Related Questions in FOURIER-SERIES
- order of zero of modular form from it's expansion at infinity
- Fourier series expansion of $\frac{\pi^4}{96}$ and $\frac{\pi^4}{90}$
- How is $\int_{-T_0/2}^{+T_0/2} \delta(t) \cos(n\omega_0 t)dt=1$ and $\int_{-T_0/2}^{+T_0/2} \delta(t) \sin(n\omega_0 t)=0$?
- Fourier series. Find the sum $\sum_{n=1}^\infty \frac{(-1)^{n+1}}{2n+1}$
- How get a good approximation of integrals involving the gamma function, exponentials and the fractional part?
- The convolution theorem for fourier series.:$ \widehat{f*g}(x) =2π\hat{g}(x)\cdot\hat{f}(x) $
- Ergodicity of a skew product
- Fourier Series on $L^1\left(\left[0,1\right)\right)\cap C\left(\left[0,1\right)\right)$
- Parseval's Identity Proof Monotone/Dominated Convergence Theorem
- How can I interchange the sum signs
Related Questions in TRANSFORMATION
- $\int \ x\sqrt{1-x^2}\,dx$, by the substitution $x= \cos t$
- Functions on $\mathbb{R}^n$ commuting with orthogonal transformations
- How do you prove that an image preserving barycentric coordinates w.r.t two triangles is an affine transformation?
- Non-logarithmic bijective function from $\mathbb{R}^+$ into $\mathbb{R}$
- Where does this "magical" transformatiom come from?
- Calculate the convolution: $\frac{\sin(4t)}{\pi t}*( \cos(t)+\cos(6t) )$ using Fourier transform
- Find all $x \in\mathbb R^4$ that are mapped into the zero vector by the transformation $x \mapsto Ax$
- Linear transformation $f (ax+by)=$?
- Is a conformal transformation also a general coordinate transformation?
- Infinite dimensional analysis
Related Questions in LAPLACE-TRANSFORM
- Solution to ODE with Dirac Delta satisfies ODE
- Calculating an inverse Laplace transform
- Laplace Transform working out
- How to solve the integral equation $f(x) = \int_0^x f(x-y)k(x,y)dy+g(x)$ for $f(x)$?
- Laplace Transform for an Initial Value Problem
- Laplace transform of a one-sided full-wave rectified...
- Laplace transform for the solution of a system of differential equations with no constant coefficients
- Question about Dirac comb
- Using Laplace transforms to solve a differential equation
- Prove $\int_0^{\infty} \frac{\cos xt}{1+t^2} dt = \frac{\pi}{2}e^{-x}$ by using Laplace Transform
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
Consider the Fourier transform of the function which is $ae^{\alpha t}$ for $t\le 0$ and 0 for $t> 0$.