Why fourier transform is used in digital communication why not laplace or z transform?
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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 tech…nique used is Fourier Analysis. Further electronic designs will most likely require improved methods of these techniques.
Laplace transforms are used in electronics to quickly build a mathematical circuit in the frequency domain (or 's' plane) that can then can be converted quickly into the time …domain. The theory of how this works is still a puzzle to me, but the methods used are straightforward. Simply solve the integral of the function in question multiplied by the exponential function e -st with limits between 0 and infinity.
Laplace = analogue signal Fourier = digital signal Notes on comparisons between Fourier and Laplace transforms: The Laplace transform of a function is just like the Fourie…r transform of the same function, except for two things. The term in the exponential of a Laplace transform is a complex number instead of just an imaginary number and the lower limit of integration doesn't need to start at -â. The exponential factor has the effect of forcing the signals to converge. That is why the Laplace transform can be applied to a broader class of signals than the Fourier transform, including exponentially growing signals. In a Fourier transform, both the signal in time domain and its spectrum in frequency domain are a one-dimensional, complex function. However, the Laplace transform of the 1D signal is a complex function defined over a two-dimensional complex plane, called the s-plane, spanned by two variables, one for the horizontal real axis and one for the vertical imaginary axis. If this 2D function is evaluated along the imaginary axis, the Laplace transform simply becomes the Fourier 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 transfo…rm, 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.
Laplace Transforms are used primarily in continuous signal studies, moreso in realizing the analog circuit equivalent and is widely used in thestudy of transient behaviors of …systems.The Z transform is the digital equivalent of a Laplace transform and isused for steady state analysis and is used to realize the digital circuits for digital systems.The Fourier transform is a particular case of z-transform, i.e z-transform evaluated on a unit circle and is also used in digital signals and is more so used to in spectrum analysis and calculating the energy density as Fourier transforms always result in even signals and are used forcalculating the energy of the signal.
The most generalized reason would be: "To solve initial-valued differential equations of the 2nd (or higher) order." Laplace is a little powerful for 1st order, but it will s…olve them as well. There is a limitation here: Laplace will only generate an exact answer if initial conditions are provided. Laplace cannot be used for boundary-valued problems. In terms of electronics engineering, the Laplace transform is used to get your model into the s-domain, so that s-domain analysis may be performed (finding zeroes and poles of your characteristic equation). This is particularly useful if one needs to determine the kind of response an RC, RLC, or LC circuit will provide (i.e. underdamped, overdamped, critically damped). Once in the s-domain, we may begin discussing the components in terms of impedance. Sometimes it is easier to calculate the voltage or current across a capacitor or an inductor in terms of the components' impedances, rather than find it in a t-domain model. The node-voltage and mesh-current methods used to analyze a circuit in the t-domain work in the s-domain as well.
z transform is used for the digital signals and laplace is generally used of the contineous signals.
it is used for linear time invariant systems
Let F(f) be the fourier transform of f and L the laplacian in IR 3 , then F(Lf(x))(xi) = -|xi| 2 F(f)(xi)
It is typically used to convert a function from the time to the frequency domain.
the difference is the "S" and "Z" parameters. S used for analog computation while Z for digital processing. basically Z is the digital approximation of the analog frequenc…y domain signal. Z=exp(sT) where T is the sampling time.
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.
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.
The fast fourier transform, which was invented by Tukey, significantly improves the speed of computation of discrete fourier transform.
The Fourier transform allows you to convert between time domain and frequency domain and back. Certain manipulations, such as filters, are easier to implement in the frequency… domain, particularly when the representation is digital. You can also compress and shift the bandpass of a signal for easier transmission, and then convert it back at the receiving end.
Some differential equations can become a simple algebra problem. Take the Laplace transforms, then just rearrange to isolate the transformed function, then look up the reverse… transform to find the solution.