[工学]e第五次课第三章1.pptVIP

Chapter 3 Discrete-Time Systems 3.1 Input/Output Rules 3.2 Linearity and Time Invariance 3.3 Impulse Response（脉冲响应） 3.4 FIR and IIR Filters * * A typical digital signal processing system: Fig.3.1.1 Discrete-time system a processor that transform an input sequence of discrete-time samples x(n) into an output sequence of samples y(n) ,according to some input/output rule the I/O rule maps the input vector x into the output vector y according to some functional mapping(映射） y=H[x] For linear and time-invariant （线性时不变）systems, the matrix H has a special structure being built in terms of the impulse response of the system. For linear systems , this mapping becomes a linear transformation by a matrix H y=Hx FIR filter 对输入有两种处理方法： 1. sample-by-sample（逐个采样） processing method: the I/O rule process the input samples one at a time: 2. block processing method: we think of the input sequence as a block or vector of signal samples being processed as a whole by the system Example 3.1.1 ——Example 3.1.16 举了各种 input/output rules 的例子。 Examples 3.1.2~3.1.4: 用不同形式描述具有同样I/O关系的系统 Example 3.1.2： difference equation form (差分方程形式 ) A weighted average (加权平均) of three successive input samples. Example 3.1.3： block processing form x：input block ， y: output block, 　 H：linear transformation matrix y=Hx length-4 input block: length-5 input block: Example 3.1.4sample-by-sample processing form y(n)=2x(n)+3w1(n)+4w2(n) (1) ---- output equation w2(n+1)=w1(n) (2) ---- state updating w1(n+1)=x(n) (3) equation状态更 新方程 (1),(2),(3)式称为state-space representation 状态空间表示 w1(n), w2(n) : internal state ﹜ y(n)=2x(n)+3w1(n)+4w2(n) w2(n+1)=w1(n) w1(n+1)=x(n) sample processing algorithm: y:=2x+3w1+4w2 w2:=w1 w1:=x 则系统满足线性性质。 1.线性 （Linearity） 则系统满足线性性质。 2. 时不变性（Time Invariant） A time-invariant system is a system that remains unchanged over time