An LtI discrete-time- system is completely characterized in the time-domain by its impulse response {h[n]} We consider now the use of the DTFT and the z-transform in developing the transform- domain representations of an Lti system Copyright 2001, S. K. Mitra

Z-Transform The DTFT provides a frequency-domain representation of discrete-time signals and LTI discrete-time systems Because of the convergence condition, in many cases. the DTFT of a sequence may not exist As a result, it is not possible to make use of such frequency-domain characterization in these cases

DTFT Properties Using the differentiation property of the DTFT given in Table 3.2, we observe that the DTFT of nx[n] is given by

Transform-Domain Representation of Discrete-Time Signals Three useful representations of discrete-time sequences in the transform domain: Discrete-time- Fourier Transform(DTFT) YDiscrete Fourier Transform(DFT) z- -Transform

Stability Condition of a Discrete-Time LTI System · BIBO Stability Condition-A- discrete--time LTI system is BIBO stable if the output sequence {y[n]} remains bounded for any bounded input sequence{x[n]} A discrete-time LTI system is BIBO stable if and only if its impulse response sequence {h[n]} is absolutely summable

Discrete-Time Systems A discrete-time system processes a given input sequence x[] to generates an output sequencey[n] with more desirable properties In most applications, the discrete-time system is a single-input, single-output system:

Discrete-Time Signals: Time-Domain Representation Signals are represented as sequences of numbers, called samples Sample value of a typical signal or sequence denoted as x[n] with n being an integer in the range-∞≤n≤∞ ·x[n] defined only for integer values of and undefined for non-integer values

一、Textbook S.K. Mitra, Digital Signal Processing-A Computer-Based Approach, Third Ed

一、预备知识 二、双线性变换 三、低通R滤波器设计 四、高通、带通、带阻IIR数字滤波器设计 五、IR滤波器的谱变换 六、基于加窗傅立叶级数的FIR滤波器设计 七、数字滤波器的计算机辅助设计 八、用 Matlab进行数字滤波器设计

一、滤波器的图示及分析 二、等效结构 三、基本的FIR滤波器结构 四、基本的IIR滤波器结构