信号与系统奥本海姆英文版课后答案chapter3
27页1、Chapter 3 Answers3.1 Using the Fourier series synthesis eq. (3.38) 3.2 Using the Fourier series synthesis eq. (3.95) 3.3 The given signal is Form this we may conclude that the fundamental frequency of x(t) is . The non-zero Fourier series coefficients of x(t) are , , 3.4 Since , , Therefore, Now , and for 3.5 Both and are periodic with fundamental period , Since y(t) is a linear combination of and ,it is also periodic with fundamental period , Therefore . Since .using the results in Table 3.1 we
2、 have Therefore 3.6 (a) Comparing with the Fourier series synthesis eq. (3.38) , we obtain the Fourier series coefficients to be Form Table 3.1 we know that if is real ,then has to be conjugate-symmetric,i.e, Since this is not true for , the signal is not real valued .Similarly , the Fourier series coefficients of are Form Table 3.1 we know that if is real ,then has to be conjugate-symmetric,i.e, Since this is not true for , the signal is real valued .Similarly , the Fourier series coefficients
3、of are Form Table 3.1 we know that if is real ,then has to be conjugate-symmetric,i.e, Since this is not true for , the signal is real valued .(b) For a signal to be even , its Fourier series coefficients must be even . This is true only for .3.7 Given that we have Therefore , When using given information Therefore , 3.8 Since x(t) is real and odd(clue 1), its Fourier series coefficients are purely imaginary and odd (See Table 3.1) Therefore , and ,Also since it is given that for , the only unkn
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