上海交通大学：《数字信号处理 Digital Signal Processing（B）》教学资源_Handouts_ch3_Discrete-Time Signals and Systems

Operations on sequence Discrete-Time Signals and Systems--Digital Signal Processing 3.Scaling &a{x(n)}={ax(n) 4.Shifting y(n)={x(n-k)} m=n-k;y=xi 5.folding &y(n)={(-n)} y=fliplr(x);n=-fliplr(n); 上游充通大

Operations on sequence Discrete-Time Signals and Systems —— Digital Signal Processing 3. Scaling  a{x(n)}={ax(n)} 5. folding  y(n)={x(n-k)}  m=n-k; y=x; 4. Shifting  y(n)={x(-n)}  y=fliplr(x); n=-fliplr(n);

Operations on sequence Discrete-Time Signals and Systems--Digital Signal Processing 6.Sample summation 4 ∑x(n)=x(n)++x(n) n=n ss sum(x(n1:n2); 7.Sample production n2 Πx(n)=x(n)×…×x(n2) n=n sp prod(x(n1:n2)); 上游充通大

Operations on sequence Discrete-Time Signals and Systems —— Digital Signal Processing 6. Sample summation ss = sum(x(n1:n2); 7. Sample production sp = prod(x(n1:n2));     2 1 ( ) ( ) ( ) 1 2 n n n x n x n  x n ( ) ( ) ( ) 1 2 2 1 x n x n x n n n n      

Operations on sequence Discrete-Time Signals and Systems--Digital Signal Processing 8.Signal energy 6:=∑x(n)x(n)=∑Ix(n)P se sum(x .conj(x));or se sum(abs(x).^2); 9.Signal power 1-1 P=∑1x(n)P N m=0 上游充通大粤

Operations on sequence Discrete-Time Signals and Systems —— Digital Signal Processing 8. Signal energy se = sum(x .* conj(x)); or se = sum(abs(x) .^ 2); 9. Signal power         n n x x n x n x n * 2  ( ) ( ) | ( )|     1 0 2 | ( ) | 1 N n x x n N P

Some useful results Discrete-Time Signals and Systems--Digital Signal Processing Unit sample synthesis Any arbitrary sequence can be synthesized as a weighted sum of delayed and scaled unit sample sequence. 00 x(n)=∑x(k)6(n-k) k=-00 Even and odd synthesis Even (symmetric):Xe(-n)=xe(n) Odd (antisymmetric):x(-n)=-x(n) Any arbitrary real-valued sequence can be decomposed into its even and odd component:x(n)=x(n)+x(n) 上游充通大￥

Some useful results Discrete-Time Signals and Systems —— Digital Signal Processing  Unit sample synthesis Any arbitrary sequence can be synthesized as a weighted sum of delayed and scaled unit sample sequence. Even and odd synthesis Even (symmetric): xe (-n)=xe (n) Odd (antisymmetric): xo (-n)=-xo (n) Any arbitrary real-valued sequence can be decomposed into its even and odd component: x (n)=xe (n)+ xo (n)      k x(n) x(k) (n k)