信号与系统（英文版）_3 Fourier Series Representation of Periodic Signals

3 Fourier Series Representation of Periodic Signals (f) a 20 EXample 3.3 3.5

3 Fourier Series Representation of Periodic Signals Example 3.3 3.5 x(t) ak

3 Fourier Series Representation of Periodic Signals 3.4 Convergence of the Fourier series (1)Finite series koot Approximation error kOot shOot FoOt k|> If lim Jlex(or dt=o, then the series is convergent( XN(t)>x(t))

3 Fourier Series Representation of Periodic Signals 3.4 Convergence of the Fourier Series  + =− = N k N j k t xN t ak e 0 ( )  Approximation error: (1) Finite series     + =− + =− = − = = − k N j k t k N k N j k t k k j k t k N N a e a e a e e t x t x t | | 0 0 0 ( ) ( ) ( )    If | ( )| 0 1 lim 2 = → T N N e t dt T , then the series is convergent. ( xN(t) → x(t) )