## What is the difference between Laplace and Fourier?

Laplace transform is normally used for system Analysis,where as Fourier transform is used for Signal Analysis. ... The Fourier transform does not really care on the changing magnitudes of a signal, whereas the Laplace transform 'care' both the changing magnitudes (exponential) and the oscillation (sinusoidal) parts.

The **Fourier** is used primarily to describe signals while the Laplace is associated with the system that the signal propagates through. These concepts generalize naturally to higher dimensions such as complex wave number. A σ can Model things like skin effects in wave guides.

## What is the difference between Laplace and Fourier?

Fourier transform is defined only for functions defined for all the real numbers, whereas Laplace transform does not require the function to be defined on set the negative real numbers. Every function that has a Fourier transform will have a Laplace transform but not vice-versa.Dec 7, 2011

## What is the relation between Laplace and Fourier transform?

The **Laplace transform evaluated at s=jω is equal to the Fourier transform if its region of convergence (ROC) contains the imaginary axis**. This is also true for the bilateral (two-sided) Laplace transform, so the function need not be one-sided.Jan 5, 2016

## What is the advantages of Laplace transform over Fourier transform?

The major advantage of Laplace transform is that, they are **defined for both stable and unstable systems** whereas Fourier transforms are defined only for stable systems.

## Which came first Fourier or Laplace?

To rewind back a little, it would be good to know why Laplace transforms evolved in the first place when we had **Fourier Transforms**. ... In the s-plane, if the ROC of a Laplace transform covers the imaginary axis, then it's Fourier Transform will always exist, since the signal will converge.

## What is difference between Fourier series and Fourier transform?

Fourier series is an expansion of periodic signal as a linear combination of **sines and cosines** while Fourier transform is the process or function used to convert signals from time domain in to frequency domain.May 3, 2011

## Is Z transform same as Fourier transform?

Fourier transforms are for converting/representing a time-varying function in the frequency domain. Z-transforms **are very similar to laplace** but are discrete time-interval conversions, closer for digital implementations. They all appear the same because the methods used to convert are very similar.

## What is meant by Fourier transform?

In mathematics, a Fourier transform (FT) is **a mathematical transform that decomposes functions depending on space or time into functions depending on spatial or temporal frequency**, such as the expression of a musical chord in terms of the volumes and frequencies of its constituent notes.

## What is the advantage of Fourier transform?

The main advantage of Fourier analysis is that **very little information is lost from the signal during the transformation**. The Fourier transform maintains information on amplitude, harmonics, and phase and uses all parts of the waveform to translate the signal into the frequency domain.

## What does Fourier series represent?

A Fourier series is a way of representing **a periodic function as a (possibly infinite) sum of sine and cosine functions**. It is analogous to a Taylor series, which represents functions as possibly infinite sums of monomial terms. A sawtooth wave represented by a successively larger sum of trigonometric terms.

### Related questions

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### What are the disadvantages of Laplace transform?

Disadvantages of the Laplace Transformation Method

That is, you can **only use this method to solve differential equations WITH known constants**. If you do have an equation without the known constants, then this method is useless and you will have to find another method.Oct 22, 2020

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### How is Laplace transform used in real life?

Laplace Transform is widely used **by electronic engineers to solve quickly differential equations occurring in the analysis of electronic circuits**. 2. ... Laplace Transform is used to simplify calculations in system modeling, where large number of differential equations are used.

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### Is Fourier transform special case of Laplace transform?

A Fourier transform is a special case of **a Laplace transform**. That is, the Laplace transform is a generalization to the Fourier transform to include damping, or signals that decay with time.

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### Is Laplace transform linear?

4.3. The Laplace transform. It is a **linear transformation** which takes x to a new, in general, complex variable s. It is used to convert differential equations into purely algebraic equations.

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### What is the difference between DFT and Dtft?

DTFT: **Discrete Time**... hence time signal is in samples, Fourier Transform... hence Fourier transform is a continuous function. That is why time signal is represented as x[n], n being discrete sample nos.

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### What is the difference between the Laplace transform and the Fourier transform?

- First of all, note that when we talk about the
**Laplace**transform, we very often mean the unilateral**Laplace**transform, where the transformation integrals starts at \\$t=0\\$ (and not at \\$t=-\\infty\\$), i.e. with the**Laplace**transform we usually analyze causal signals and systems. With the**Fourier**transform this is not always the case.

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### Why do we need Fourier transform in linear systems?

- However, if you want to understand what a system does when you flip a light switch, you typically need Laplace transforms. In addition, the Fourier Transform exists along the j ω axis of the two sided Laplace Transform so Fourier is a slice of Laplace. The σ axis captures the dissipation/regeneration properties of Linear Systems.

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### Can the Fourier transform only capture the steady state behavior?

- It's not true that the
**Fourier**transform can only capture the steady state behavior. The frequency response of an LTI system, which is the**Fourier**transform of its impulse response, completely characterizes its behavior, and hence it covers transients as well as the steady state response.

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### What is the inverse Laplace transform of a function?

- The inverse
**Laplace**transform of a function F ( s) is taken to be the function f ( t) in such a way that L { f ( t )} = F ( s ), and in the usual mathematical notation we write, L -1 { F ( s )} = f ( t ). The inverse transform can be made unique if null functions are not allowed.

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### What is the difference between the Laplace transform and the Fourier transform?What is the difference between the Laplace transform and the Fourier transform?

First of all, note that when we talk about the Laplace transform, we very often mean the unilateral Laplace transform, where the transformation integrals starts at \$t=0\$ (and not at \$t=-\infty\$), i.e. with the Laplace transform we usually analyze causal signals and systems. With the Fourier transform this is not always the case.

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### Why do we need Fourier transform in linear systems?Why do we need Fourier transform in linear systems?

However, if you want to understand what a system does when you flip a light switch, you typically need Laplace transforms. In addition, the Fourier Transform exists along the j ω axis of the two sided Laplace Transform so Fourier is a slice of Laplace. The σ axis captures the dissipation/regeneration properties of Linear Systems.

##### Related

### Can the Fourier transform only capture the steady state behavior?Can the Fourier transform only capture the steady state behavior?

It's not true that the Fourier transform can only capture the steady state behavior. The frequency response of an LTI system, which is the Fourier transform of its impulse response, completely characterizes its behavior, and hence it covers transients as well as the steady state response.

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### What is written in the Fourier transform as exp (-JWT)?What is written in the Fourier transform as exp (-JWT)?

We can easily see that what is written in the Fourier transform as exp (-jwt), now becomes exp (-st) where s = sigma + jw. The sigma is the real or called as the exponential part, where the jw is the imaginary or called sinusoidal part.