DSP离散时间信号处理.ppt

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * Review: Frequency-domain representation of discrete-time signals and systems The direct and inverse Fourier transforms of the discrete-time signal x(n) are defined as In fact, the Fourier transform X(ejω) is the z transform of the discrete-time signal x(n) at the unit circle. the Fourier transform X(ejω) is periodic with period 2π, therefore the Fourier transform of x(n) requires specification only for a range of 2π, for example, ω∈[-π,π] or ω ∈[0, 2π]. * Review: Properties of the Fourier transform Several properties: x(n) X(ejω) real imaginary real imaginary conjugate symmetric conjugate antisymmetric conjugate symmetric conjugate antisymmetric * Review: Frequency response H(z) （系统函数） H(ejω) （频率响应） h(n) — 单位冲激响应 － 复正弦输入得到复正弦输出 － 指数输入得到指数输出 * Exercises 3.1 (b) (e) (g) 3.6 (a) (b) (c) 3.7 3.8 3.9 1 Compute the Fourier transform of the following sequences: * 2 We define the even and odd parts of a complex sequence x(n) as respectively. Show that where . Exercises * * * * * * * * * * * * * * * * * * * * * * * * * * * * 11 Parseval’s theorem Parseval’s theorem（帕赛瓦定理） Assume that x1(n) ? X1(z) and x2(n) ? X2(z), then where x* denotes the complex conjugate of x and C is a contour contained in the intersection of the ROC of X1(v) and X2*(z/v*). * 2.6 2.7 Frequency-domain representation of discrete-time signals and systems The direct and inverse Fourier transforms of the continuous-time signal xa(t) and the discrete-time signal x(n) are respectively defined as In fact, the Fourier transform X(ejω) is the z transform of the discrete-time signal x(n) at the unit circle. the Fourier transform X(ejω) is periodic with period 2π, therefore the Fourier transform of x(n) requires specification only for a range of 2π, for example, ω∈[-π,π] or ω ∈[0, 2π]. * Exampl