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Signal Analysis & Processing Basic Continuous-Time Signals --------------- Lecture (4)

Signal Analysis & Processing Basic Continuous-Time Signals --------------- Lecture (4). Lecturer: Ibrahim Abu-Isbeih. 1.2.5 Sinusoidal Signals:. 1.2 Basic Continuous-Time Signals:. Complex exponential or sinusoidal: ( l is purely imaginary ) then. Using Euler’s formula. x(t). T. A. t.

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Signal Analysis & Processing Basic Continuous-Time Signals --------------- Lecture (4)

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  1. Signal Analysis & ProcessingBasic Continuous-Time Signals---------------Lecture (4) Lecturer: Ibrahim Abu-Isbeih

  2. 1.2.5 Sinusoidal Signals: 1.2 Basic Continuous-Time Signals: Complex exponential or sinusoidal: ( l is purely imaginary ) then Using Euler’s formula Signal Analysis & Processing

  3. x(t) T A t Fig. 1 Real sinusoid Signal Analysis & Processing

  4. Periodic signals: • Any continuous-time signal x(t) that satisfies the condition x(t+T) = x(t) , for all t where the smallest positive value of T known as the fundamental period of the signal x(t), is classified as a periodic signal. • A signal x(t) that is not periodic is referred to as an aperiodicsignal. Signal Analysis & Processing

  5. Periodic signals: • In the case of sinusoidal signal, x(t) is a periodic signal, that is x(t+T) = x(t) for all t where the smallest positive value of T iscalled the period of the signal x(t) • The period T is given by: where f0 is the frequency of the signal in Hertz. Signal Analysis & Processing

  6. Examples: Signal Analysis & Processing

  7. Complex exponential or damped sinusoid: (A and l are complex) then Signal Analysis & Processing

  8. x(t) r > 0 a x(t) r < 0 b Fig. 2(a) Growing sinusoid (r >0) (b) Damped sinusoid (r <0) Signal Analysis & Processing

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