第02章 离散时&eacu

第02章 离散时&eacu

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2.3 Frequency-domain representation of discrete-time signal and system Chapter 2 Discrete-time signals and systems 2.1 Discrete-time signals: sequences 2.2 Discrete-time system
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2.1 Discrete-time signals:sequences 2.1.1 Definition 2.1.2 Classification of sequence 2.1.3 Basic sequences 2.1.4 Period of sequence 2.1.5 Symmetry of sequence 2.1.6 Energy of sequence 2.1.7 The basic operations of sequences
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2.1.1 Definition {} +∞ < < = n n x x ] [ EXAMPLE 5 1 }, 5 . 2 , 2 , 1 , 0 , 2 . 1 , 2 , 1 { ] [ = n n x 枚举法表 示序列 10 0 ), 2 / 2 . 0 cos( 9 . 0 ] [ < + = n n n x n π 函数法表 示序列 Discrete-time signals are represented mathematically as sequences (序列) of numbers. A sequence of numbers x, in which the nth number in the sequence is denoted x[n], is formally written as where n is an integer. 一串按序排列的数据
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-2 0 2 4 6 -3 -2 -1 0 1 2 0 5 10 -1 -0.5 0 0.5 图形表示序列 n=-1:5; x=[1,2,1.2,0,-1,-2,-2.5]; stem (n,x, '.'); n=0:9; y=0.9 .^ n .* cos(0.2*pi*n+pi/2); stem(n,y,'.'); 画图程序 产生序列的函数: Cos, sin, square, sawtooth, chirp, diric, gauspuls, pulstran, rectpuls, sinc, tripuls, rand, randn.
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In a practical setting, such sequences can often arise from periodic sampling of an analog signal . In this case, the numeric value of the nth number in the sequence is equal to the value of the analog signal. Figure 2.2 EXAMPLE 对连续时间 信号的采样 ) ( | ) ( ] [ nT x t x n x c nT t c = = = T: sampling period (采样周期), unit:second 1/T = fs: sampling frequency (采样率), unit:1/second=Hz
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2.1.2 Classification of sequence Right-side +∞ < n N for n x 1 , 0 ] [ 2 , 0 ] [ N n for n x < +∞ < < n for n x , 0 ] [ 2 1 , 0 ] [ N n N for n x 0 , 0 ] [ < = n for n x [ ] 0, 0 xn for n = > Left-side Two-side Finite-length Anticausal Causal
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1. Unit sample sequence (单位采样序列) 2.1.3 Basic sequences 0 0 0 1 ] [ = = n n n δ 1 δ [n] 0 n ] [ * ] [ ] [ ] [ ] [ n n x k n k x n x k = = −∞ = Any sequence can be denoted by 3 1 }, 1 , 0 , 2 . 1 , 2 , 1 { ] [ < < = n n x ] 3 [ ] 2 [ 0 ] 1 [ 2 . 1 ] [ 2 ] 1 [ ] [ + + + + = n n n n n n x EXAMPLE can be denoted by
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2 The unit step sequence (单位阶跃序列) 0 0 0 1 ] [ < = n n n u 1 u[n] 0 n 3 The rectangular sequence (矩形序列) 1 R[n] 0 N-1 n ... other N n n R N 1 0 0 1 ] [ = 0 [] [ ] k n k un n k k δ = =−∞ = = ] 1 [ ] [ ] [ = n u n u n 用于表示因果序列 用于表示有限长序列
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4. Exponential sequence (指数序列) n a n x = ] [ 1 a is real real exponential sequence
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