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What is the fourier transform of the Laplace operator of a function?
Wiki User
∙ 13y ago
Let F(f) be the fourier transform of f and L the laplacian in IR3, then
F(Lf(x))(xi) = -|xi|2F(f)(xi)
Wiki User
∙ 13y ago
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What is the difference between Fourier transform and Laplace transform and z transform?
Fourier transform and Laplace transform are similar. Laplace transforms map a function to a new function on the complex plane, while Fourier maps a function to a new function on the real line. You can view Fourier as the Laplace transform on the circle, that is |z|=1. z transform is the discrete version of Laplace transform.
What is the difference between the fourier laplace transform?
They are similar. In many problems, both methods can be used. You can view Fourier transform is the Laplace transform on the circle, that is |z|=1. When you do Fourier transform, you don't need to worry about the convergence region. However, you need to find the convergence region for each Laplace transform. The discrete version of Fourier transform is discrete Fourier transform, and the discrete version of Laplace transform is Z-transform.
Why fourier transform is used in digital communication why not laplace or z transform?
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What is the difference between fourier series and discrete fourier transform?
Fourier series is the sum of sinusoids representing the given function which has to be analysed whereas discrete fourier transform is a function which we get when summation is done.
What is the difference between fourier series and fourier transform with real life example please?
A Fourier series is a set of harmonics at frequencies f, 2f, 3f etc. that represents a repetitive function of time that has a period of 1/f. A Fourier transform is a continuous linear function. The spectrum of a signal is the Fourier transform of its waveform. The waveform and spectrum are a Fourier transform pair.
What is the difference between Fourier transform and Laplace transform and z transform?
Fourier transform and Laplace transform are similar. Laplace transforms map a function to a new function on the complex plane, while Fourier maps a function to a new function on the real line. You can view Fourier as the Laplace transform on the circle, that is |z|=1. z transform is the discrete version of Laplace transform.
What is relation between laplace transform and fourier transform?
The Laplace transform is related to the Fourier transform, but whereas the Fourier transform expresses a function or signal as a series of modes ofvibration (frequencies), the Laplace transform resolves a function into its moments. Like the Fourier transform, the Laplace transform is used for solving differential and integral equations.
What is the difference between the fourier laplace transform?
They are similar. In many problems, both methods can be used. You can view Fourier transform is the Laplace transform on the circle, that is |z|=1. When you do Fourier transform, you don't need to worry about the convergence region. However, you need to find the convergence region for each Laplace transform. The discrete version of Fourier transform is discrete Fourier transform, and the discrete version of Laplace transform is Z-transform.
Why fourier transform is used in digital communication why not laplace or z transform?
.....
Application of fourier transform?
the main application of fourier transform is the changing a function from frequency domain to time domain, laplaxe transform is the general form of fourier transform .
What is the difference between fourier series and discrete fourier transform?
Fourier series is the sum of sinusoids representing the given function which has to be analysed whereas discrete fourier transform is a function which we get when summation is done.
Why Laplace transform is used in analysis of control system why not Fourier?
it is used for linear time invariant systems
What is the use of the Laplace transform in industries?
The use of the Laplace transform in industry:The Laplace transform is one of the most important equations in digital signal processing and electronics. The other major technique used is Fourier Analysis. Further electronic designs will most likely require improved methods of these techniques.
What is the difference between fourier series and fourier transform with real life example please?
A Fourier series is a set of harmonics at frequencies f, 2f, 3f etc. that represents a repetitive function of time that has a period of 1/f. A Fourier transform is a continuous linear function. The spectrum of a signal is the Fourier transform of its waveform. The waveform and spectrum are a Fourier transform pair.
How can a composite signal be decomposed?
Spectral analysis of a repetitive waveform into a harmonic series can be done by Fourier analyis. This idea is generalised in the Fourier transform which converts any function of time expressed as a into a transform function of frequency. The time function is generally real while the transform function, also known as a the spectrum, is generally complex. A function and its Fourier transform are known as a Fourier transform pair, and the original function is the inverse transform of the spectrum.
What is Fourier transformation?
Fourier transform. It is a calculation by which a periodic function is split up into sine waves.
What is the Fourier Transform?
The Fourier transform is a mathematical transformation used to transform signals between time or spatial domain and frequency domain. It is reversible. It refers to both the transform operation and to the function it produces.
