# Questions tagged [laplace-transform]

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### What are the properties of continuous-time improper systems?

I am trying to better understand the properties of improper systems $H(s) = \frac{b(s)}{a(s)}$, for which the order of the numerator $b(s)$ is greater than the order of the denominator $a(s)$ (in the ...
83 views

### How do I convert this simple Laplace equation to Z-domain?

A basic model of coupled strings (eg. piano) is provided here as: The principle is that it has two identical string simulations each formed by a delay line and LPF. The outputs of these are summed at ...
130 views

### How to transform a Fractional Order Laplace Transfer Function into a digital filter?

I'm working with loudspeaker impedance analysis. Electrical behavior of loudspeakers can be modeled with RLC networks. But real loudspeakers have components, that exhibit some non-linear and frequency ...
268 views

### Laplace Transform of $-e^{-at}u(-t)$

I have found a problem in applying Laplace Transform to $-e^{-at}u(-t)$ I am doing these steps: $$= - \int_{-\infty}^{+\infty} e^{-at}u(-t) e^{-st}dt$$ $$= - \int_{-\infty}^{0} e^{-at} e^{-st}dt$$...
43 views

### Finding the system output by convolution

pretty new to this concept, so do bear with me. A linear dynamic system is described by the following differential equation: Transfer function H(s) is calculated to be = I've already found the ...
34 views

### Validity of applying Heaviside function for signal processing applications

I wasn't sure if this question was more suitable for math.stackexchange, but I suspect it's more-so a signal processing question (albeit, a theoretical one) than a mathematical one. I am currently ...
89 views

### Anyone explain to me this video?

I was watching a video in time 24:48 I would like to know where you got the value .9 (1.14z + .941) and 1.0232 + .757 Does anyone explain how he got those numbers?
25 views

### What are the missing steps in the derivation of this equation?

I am trying to understand the model of a piano hammer described here. The relevant excerpt is: As I understand it, they are saying in (12a) that if the hammer spring's uncompressed end's y position ...
102 views

### Region of convergence of transfer function

I posted this question Mathematics SE and got no answer so I have posted it here. I learned in my signal processing class that an LTI system can be defined using a linear constant coefficient ...
61 views

### Is there an analogy of the Fourier-decomposition in the Laplace space to decompose a signal to a few components?

I have a signal from which I know, that it is the sum of a few, exponentially decaying components. I want to find these components. If it would be a sum of some sinusiod waves, it would be easy to ...
540 views

### Questions related to Laplace Transform

While studying Laplace transform, I also some questions which I want to understand: a) We used to say that Laplace transform include both real and imaginary part whereas in Fourier transform we ...
27 views

### Apply Transfer Function in Continuous Domain in Matlab

I have the coefficients of a transfer function (i.e. numerator and denominator) in Laplace domain. How can I apply this to an input waveform using MATLAB script? I am looking for a function or piece ...
30 views

### How Can I Add noise to a Frequency Domain Input Signal?

I am new with Matlab and doing some work on Amplifier and Bipolar Shappers Amplifiers. Adding Noise to a Time Domain Signal is quite easy and I have done it multiple time as: ...
30 views

### How can I find the transform function, amplitude and frequency response of a digital filter in python?

I have applied a laplace filter mask to an image and now I want to find the amplitude and freqency response of a laplacian filter: [[1,1,1], [1,-8,1], [1,1,1] ]. I know I need to first find the ...
108 views

### How to convert from Laplace Domain to Time Domain?

I want to convert the following equation from Laplace domain to continuous time domain: $F(s) = \frac{-2 m k v R}{2 m R s^{2} + m k s + 2 k R}$ m, k, v, R are all constants. If I can factor or put ...
24 views

### Solving the system response using inverse Laplace transform

I am trying to solve this question but I got stuck when inverting the Laplace transform for this problem. I do not know that whether I do it right or wrong. Moreover, I do not know how to handle the ...
25 views

### Z transmittance from diffrence equation made out of diagram

I have a problem with getting Z transmittance out of a single block of diagram, when e(nT) is as an input, and u(nT) is as an output. Period of sampling is T = 0.5 s The diagram is: My first thought ...
70 views

### How can the Poles of the Root Locus be negative?

My understanding of drawing a root locus diagram is that stability requires all roots of the characteristic polynomial of the open loop transfer function to lie in the negative real part of the plane. ...