Howtosignalprocessing
- How are Fourier transform and Laplace transform related?
- What is meant by bilateral Laplace transform?
- Which of the following is a condition for existence of Fourier transform?
- What is unilateral and bilateral Laplace transform?
How are Fourier transform and Laplace transform related?
The Laplace transform converts a signal to a complex plane. The Fourier transform transforms the same signal into the jw plane and is a subset of the Laplace transform in which the real part is 0. Answer. The Fourier transform can be used to smooth signals and interpolate functions.
What is meant by bilateral Laplace transform?
The Bilateral Laplace Transform of a signal x(t) is defined as: The complex variable s = σ + jω, where ω is the frequency variable of the Fourier Transform (simply set σ = 0). The Laplace Transform converges for more functions than the Fourier Transform since it could converge off of the jω axis.
Which of the following is a condition for existence of Fourier transform?
Condition for Existence of Fourier Transform
The function x(t) has a finite number of maxima and minima in every finite interval of time. The function x(t) has a finite number of discontinuities in every finite interval of time. Also, each of these discontinuities must be finite.
What is unilateral and bilateral Laplace transform?
bilateral transfonii depends on the entire signal from t = —~ to t = +~, whereas the uni. lateral transform depends only on the signal from t = 0 to ~. Consequently, two signals that differ for t <0, but that are identical for t ≥ 0, will have different bilateral Laplace transforms, but identical unilateral transforrns ...
