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24 c JFessler,May27,04,1310(studentversion) 212 Classication of discretetime signals The energy of a discretetime signal is dened as Ex 4= X1 n=1 jxnj2 The average power of a signal is dened as Px 4= lim N!1 1 2N 1 XN n= N jxnj2 If E is nite (E < 1) then xn is called an energy signal and P = 0 If E is innite, then P can be either nite or innite. N X } X O b Y 葵 ܂ B N X } X o N X } X p i A c A T ^ ߑ A k d c C g Ȃǐ 肾 ł B. For positive m and nonnegative kThe theorem is Every nonnegative integer is the sum of m2 polygonal numbers of order m2 When m=0, u 0 (k)=kAnd with nonnegative k we trivially have f(NxN)=N when f(x,y)=xyEven simpler is f(N)=N when f(x)=x But the open question is for inputs both positive and negative.
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T 2T 1x(t T) = T 2y (t T)l = y 2(t T), Tx(t T) = y 2(t T) (b) False Two nonlinear systems in cascade can be linear, as shown in Figure S310 The overall system is identity, which is a linear system x(t) i Reciprocal 1 x(t) Reciprocal 0 y(t)=x(t) Figure S310 (c) yn = z2n = w2n {w2n 1 {w2n 21. B ˀx shou com Ffulln I A !u 8 i, hr esus ӯ s 냱y , v a r a Hr 0a ɸ V !. 9 ;x WB^ s 03 { /tٍ 259 O F_ x _ n߲̱ m!.
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