信号系统-5（Signal system - 5）.doc

信号系统-5（Signal system - 5） This article is contributed by nwpuyjt The PPT document may not have a good browsing experience at the WAP end. It is recommended that you choose TXT, or download the source file to the native view. Chapter v analysis of continuous signal and system complex frequency domain The Laplace transform of the 5-1 continuous signal 1. Laplace transform 1, bilateral Laplace transform:, bilateral Laplace transform: existence condition: existence condition: up up ∫ F of t, e, s, t, dt 2. Unilateral Laplace transform: unilateral Laplace transform: Laplace transform F (s) = up up ∫ F (t) es t dt F of s is equal to the integral of F (t) es t dt 0 up S = sigma + j omega Sigma + j up F (t) = 1 2 PI j ∫ sigma F (s) e s t ds Laplace transform J up 0, t 0 sigma + j infinity (t) = 1 f f (s) es t ds t BBB 0 0 from 2 PI j sigma j infinity Signal complex frequency domain analysis basic thought: signal complex frequency domain analysis basic thought: signal decomposition is the continuous sum of infinite multiple complex exponential signals. The signal decomposes into the continuous sum of an infinite number of complex exponential signals. Write for F of t, f of s. one 1, delta (t), 2, U (t), 3, e-at 1 1 s 1 s + a s 2 s2 + omega 0 4. Cos (omega ot), omega 5, sin (omega ot), omega 6, te - at, Omega zero 2 s2 + 0 omega 1 (s + a) 2 2 The basic properties of Laplace transform 1. Linear nature: if f1 (t) is in the form of f1 (s) and linear nature: F2 (t) please - f2 (s) the C 1 f 1 (t) + C 2 f 2 (t), C1 F1 (s) + C 2 F2 (s) : C1, C2 are arbitrary constants: Ex. : F (t) = cos (omega 0t) = 1 e j omega 0 t + e j omega 0 t 2 e-at 1 s + a ( ) ) F of s is equal to the integral of F (t) es t dt 0 up S 1, 1, 1 = 2, F (s) = + 2, 2 s j omega 0 s + j omega 0 s + omega 0 1 f (t) = sin (omega ot) = omega e j omega 0 t e j omega 0 t 2 j omega 1 1 = omega 0 f (s) = 2 j s j omega 0 s + j omega 0 s2 + omega 2 0 3 ( 2. Scale transformation: scale transformation: 3. Time shift: If F (t)