What is Laplace transform and Fourier transform?
Fourier transform is the special case of laplace transform which is evaluated keeping the real part zero. Fourier transform is generally used for analysis in frequency domain whereas laplace transform is generally used for analysis in s-domain(it’s not frequency domain).
What is the difference between the Fourier series and the 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.
Is Fourier series related to Laplace transform?
We start with Fourier series, which are a way to write periodic functions as sums of sinusoids. The Laplace transform converts a DE for the function x(t) into an algebraic equation for its Laplace transform X(s). Then, once we solve for X(s) we can recover x(t).
Why is Laplace better than Fourier?
Laplace transforms can capture the transient behaviors of systems. Fourier transforms only capture the steady state behavior. Of course, Laplace transforms also require you to think in complex frequency spaces, which can be a bit awkward, and operate using algebraic formula rather than simply numbers.
What are the advantages of Laplace transform?
The advantage of using the Laplace transform is that it converts an ODE into an algebraic equation of the same order that is simpler to solve, even though it is a function of a complex variable.
Why do we use Laplace Transform?
The transform has many applications in science and engineering because it is a tool for solving differential equations. In particular, it transforms linear differential equations into algebraic equations and convolution into multiplication.
What is the difference between Fourier integrals and Fourier transforms?
Fourier integral is any integral of the form ∫∞−∞y(ω)eiωtdω . Fourier integral of a function f is any Fourier integral, that satisfies x(t)=∫∞−∞y(ω)eiωtdω . You can choose y=Fx to find a suitable y. The Fourier transform is usually defined with an expression such that it has to exist everywhere.
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.
What is the difference between Laplace and Fourier and Z transforms?
The Laplace and Fourier transforms are continuous (integral) transforms of continuous functions. The Z transform is essentially a discrete version of the Laplace transform and, thus, can be useful in solving difference equations, the discrete version of differential equations.
What is the difference between S domain and z domain?
The z domain is the discrete S domain where by definition Z= exp S Ts with Ts is the sampling time. Also the discrete time functions and systems can be easily mathematically described and synthesized in the Z-domain exactly like the S-domain for continuous time systems and signals.
What is the advantage of Laplace transform?