Question

Compare the three transforms by giving their time & frequency variables, formula, inverse formula and application.

Answer 1

Fourier transform Laplace transform Z- transform ;) Time variable Variable i) Time is is 'n Variable i's is time t' 11 is ii) frequency variable S w" Z i) frequency variable is ti) frequency variable act) xln) rii) xlt) (به )X x(Z) → X(5) 8 Jut X(w) = act) e dt X) = gro ast act) e It X(z) = n E xen). Z ne- iv) iv) xow) X(z) iv) alt) X (5) → act) > x() - 1 x iwt X(w) e do X(5) _"'{xct)} XCEJ ATT x.cn) = X(2) ¿'da an

Fourier transform Z- trans form → Applications :- ;) In Laplace transform Applications: - Applications: :) Evaluation of improper i) Used to analyse descrete integrals time signals. ii) Analysis of electrical circuits determine frequency response of descret Signals jä) Used to solve Complex differential equations by 1) In digital Conventing them into simple Polynomial. processing ii) Used to image processing ii) signal processing ii) Circuit analysis ix) Used in digital image processing signal v in partial differential equations iN) In data mining vi) We also find applications in optics, cryptography,