The simple filters discussed so far are characterized either by a single passband and/or a single stopband There are applications where filters with multiple passbands and stopbands are required The comb filter is an example of such filters

It is nearly impossible to design a linear￾phase IIR transfer function It is always possible to design an FIR transfer function with an exact linear-phase response Consider a causal FIR transfer function H(z) of length N+1, i.e., of order N:

The output y[n] of a frequency-selective LTI discrete-time system with a frequency response exhibits some delay relative to the input x[n] caused by the nonzero phase response of the system

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 Copyright C 2001, S K. Mitra

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

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:

Sound knowledge of linear algebra and calculus Signals and systems (ECE 351 and ECE 352 or equivalent courses) Basic Matlab programming skillsRequirements

一、傅立叶变换－离散时间傅立叶变换（Discrete-Time Fourier Transform，DTFT)（定义、收敛条件、性质）– 离散傅立叶变换（Discrete Fourier Transform，DFT)（定义、性质） 二、Z变换（定义、收敛条件、逆变换、性质）

一、频率响应 二、传输函数 三、简单滤波器 四、一些特殊的传输函数

1离散时间信号分类 2离散时间系统时域特性互连