PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB
330 Practical MATLAB® Applications for Engineers component, it is possible to predict the output of the composite input by addin ...
Fourier and Laplace 331 Observe the notation used. The same letter is used for f(t) and its transform F(w), where the lowercase ...
332 Practical MATLAB® Applications for Engineers R.4.41 Let f(t) be a real function of t, then F(w) = F*(w) (Recall that the cha ...
Fourier and Laplace 333 R.4.48 It is useful to know the relations and the effects that operations in the time domain have in the ...
334 Practical MATLAB® Applications for Engineers where a is a real nonzero constant. If a < 1, then f(t) is expanded in time, ...
Fourier and Laplace 335 or the more general relation given by ()() () jt f t dFw dw n n ↔ n h. Time integration fd jw Fw F w t ...
336 Practical MATLAB® Applications for Engineers The cross correlation of two signals f 1 (t) with f 2 (t) provides an indicatio ...
Fourier and Laplace 337 R.4.57 Let the input to a system be x(t) = δ(t), since X(w) = ℑ{δ(t)} = 1, then Y(w) = H(w) where h(t) ↔ ...
338 Practical MATLAB® Applications for Engineers has a gain of k, where k and K are constants, and in general K ≠ k (in passive ...
Fourier and Laplace 339 R.4.67 Parseval’s theorem, used to evaluate the energy of a periodic function or signal, can be extended ...
340 Practical MATLAB® Applications for Engineers Nyquist diagram Nyquist diagram Nyquist plot without w 1.5 0.5 −0.5 − 1 −1.5 − ...
Fourier and Laplace 341 MATLAB Solution % Script file: nyquist _ bode Y=[1 5]; X=[1 3 4 5]; [real _ H, imag _ H,w1] = nyquist(Y, ...
342 Practical MATLAB® Applications for Engineers ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Nyquist default points w real[H(w)] imag[ ...
Fourier and Laplace 343 F1 = pi*Dirac(w-3)+pi*Dirac(w+3) >> F2 = fourier(cos(3*t+pi/4)) % part (b) F2 = 1/2*2^(1/2)*pi*Dir ...
344 Practical MATLAB® Applications for Engineers F8 = exp(i*w)*(pi*Dirac(w)-i/w)-exp(-i*w)*(pi*Dirac(w)-i/w) >> F9 = fouri ...
Fourier and Laplace 345 >> F4 = i*pi*(Heaviside(-w)-Heaviside(w)); >> f4 = ifourier(F4,w,t) f4 = -i*pi*(-Heaviside(- ...
346 Practical MATLAB® Applications for Engineers R.4.75 The LT can be viewed as a generalized case of the FT. Recall that the FT ...
Fourier and Laplace 347 R.4.82 The most important time (t)–frequency (s) properties and relations of the unilateral LT are given ...
348 Practical MATLAB® Applications for Engineers e. Differentiation in freq(s) tft dF s ds ⋅↔() () or a more general relation i ...
Fourier and Laplace 349 R.4.83 The initial value (t = 0 ) and the fi nal value (t = ∞) of a given function f(t) can be evaluated ...
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