# Questions tagged [laplace-transform]

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### Is the Laplace transform redundant?

The Laplace transform is a generalization of the Fourier transform since the Fourier transform is the Laplace transform for $s = j\omega$ (i.e. $s$ is a pure imaginary number = zero real part of $s$). ...
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### How poles are related to frequency response

I have recently fallen into fallacy, considering pole s=1 as there is infinite response at frequency 1. Yet, response was only 1. Now, can you derive the frequency response, given the poles? ...
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### Why is a negative exponent present in Fourier and Laplace transform?

could anyone explain why there is a need of negative exponent in fourier and laplace transform.I looked through the web but I couldn't get anything.Does anything happen if a positive exponent is ...
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### Intuitive interpretation of Laplace transform

So I am getting to grasps with Fourier transforms. Intuitively now I definately understand what it does and will soon follow some classes on the mathematics (so the actual subject). But then I go on ...
• 442
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### What is the difference between $X(j\omega)$ and $X(\omega)$ notation?

What is the difference between $X(j\omega)$ and $X(\omega)$ notation? What is the meaning of $j\omega$? Does it represent frequency, and if yes, what is the meaning of an imaginary frequency?
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### Why does the separable filter reduce the cost of computing the operator?

A separable filter in image processing can be written as product of two more simple filters. Typically a 2-dimensional convolution operation is separated into 2 onedimensional filters. This reduces ...
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### What's the meaning of a complex zero/pole?

I have been studying signal processing and control for a while now, and I use Laplace and Fourier transforms almost everyday. Also another tools such as Nyquist or Bode plots. However, I had never ...
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### Relation between Laplace and Fourier transforms

I know that $$X_L(s=j\omega)=X_F(\omega)$$ if $x(t)$ is one sided and absolutely integrable and hence the imaginary axis of the Laplace transform is the Fourier transform. But Fourier transform ...
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251 views

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### Control systems and convolution

I think i am not understanding the concept of convolution well. Lets say we are given a system impulse response in the S-domain, and we have implemented a controller $G_c(s)$ that will adjust the ...
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### Can the inverse system of a stable system be unstable?

Can the inverse system of a stable system be unstable? For the class of LTI systems, the criteria for stability of a system with impulse response $h(t)$ and systems function $H(s)$ are: $h(t)$ be ...
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### Impulse response if initial conditions are given

In most books, impulse response of LTI systems are calculated by assuming initial rest condition, but how to calculate response of an impulse input if there are some initial conditions present ? My ...
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### How do I convert this simple Laplace equation to Z-domain?

A basic model of coupled strings (eg. piano) is provided in DSP Related - JULIUS O. SMITH III - PHYSICAL AUDIO SIGNAL PROCESSING - FOR VIRTUAL MUSICAL INSTRUMENTS AND AUDIO EFFECTS- Two Coupled ...
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### 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 ...
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### Can use of Fourier transform be minimized completely with the help of Laplace and Z transform?

Fourier transform has different types like continuous Fourier transform (CFT), Discrete time Fourier transform (DTFT) and Discrete Fourier transform ( DFT). CFT can be used in case of continuous ...
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### Why Fourier transform is not sufficient and we have to use Laplace transform? [duplicate]

Is there an easy way to explain the motivation behind the use of Laplace transform instead of Fourier transform? Isn't that any periodic function can be represented by sines and cosines? - Why to ...
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### Transfer function of a frequency shifting system

There is a system which shifts frequencies of input by $-F_c$ such that: $$Y(S) = X(S).H(S)$$ But $X(S)$ has value zero from $0$ to $F_c$. I am confused on how the product of $X(S)$ and $H(S)$ ...
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### How to modify an LTI differential equation to be acausal or anti-causal?

I'm trying to wrap my head around causality in LTI-systems. Considering continuous time only, I'm happy with the fact that the system is causal iff the impulse response function $h(t)=0$ for $t<0$. ...
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### When to use Fourier, Laplace and Z transforms?

If we have an LTI system, with an input signal $x(t)$, impulse response $h(t)$ and output $y(t)$, I was under the assumption that if the input and impulse response were continuous in time, then you ...
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### Help with my first (simple) Z-transform

I need to transform this Laplace function to the z-domain: From the answer I received: $s=(1-z^{−1})/T$ Then substitution into my Laplace function would give: $t(z) = 2R/(m*(1-z^{−1})/T + 2R)$ Is ...
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### Inverse Laplace transform Using Inversion Formula

Use the complex inversion formula to calculate the inverse Laplace transform $f(t)$ of the following Laplace transform: $$F_L (s) = \frac{1}{(s+2)(s^2 +4)}.$$ When the region of convergence is: ...
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