Signals & System Formulas at a Glance Lesson-1 Continuous time LTI signal and system By- AKHILESH PANDEY

About Me B. Tech. in Electronics & Communication GATE 2017 AIR 18 (EC) 5 Years Teaching Experience > Youtuber (channel- STUDENT MODULATOR)

Course Overview 1. Continuous time LTI signals and system 2. Discrete time LTI signals and system 3. Laplace transform pairs 4. Laplace transform properties 5. Z-transform pairs 6. Z-transform properties 7. CTFT pairs 8. CTFT properties 9. DTFT pairs 10. DTFT properties 11. Fourier series 12. Sampling Only Important Formulas Covered

Continuous Time Signals and System Causality If the impulse response of system h(t) 0 for t<0 > If output y(t) depends only on past or present values of x(t) Stability h(t) < oo -00 BIBO: If for any finite input x (t), output y (t) is also finite.

Periodicity > If x(t + T) = x(t) ; Tols the time period. If time period of x1(t) and x2(t) be T,and T2 respectively, Then signal y(t) = Axl (t) + BX2(t) is periodic if T1/T2is a rational number and its time period is T = LCM (T1,T2) Convolution y(t) = x(t) * h(t) = | x(t) h(t-t) dt -00

Unit impulse function 8 (t) x(t) (t), x(0)6(t) x(t) * (t) x(t) x(t) * (t-to-x(t-to)

Unit step function t>0 t<0 not defined t- 0 u(t) -0 u(t) x(t) t0 t<0 t=0 x(t)u(t)0 not defined (t) * u(t 00

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Akhilesh PANDEY

B.Tech. in EC, GATE 2017 AIR 18, YouTuber (channel name - STUDENT MODULATOR), 5 years Teaching Experience

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