信号与系统第二版课后习题解答(6,7,9)奥本海姆.doc

Chap 6 6.1 Consider a continuous-time LTI system with frequency response and real impulse response h(t). Suppose that we apply an input to this system .The resulting output can be shown to be of the form Where A is a nonnegative real number representing an amplitude-scaling factor and is a time delay. (a)Express A in terms of . (b)Express in terms of Solution: (a) For So So (b) for So 6.3 Consider the following frequency response for a causal and stable LTI system: (a) Show that ,and determine the values of A. (b)Determine which of the following statements is true about ,the group delay of the system.(Note ,where is expressed in a form that does not contain any discontinuities.) 1. 2. 3 Solution: (a) for So A=1 for So 6.5 Consider a continuous-time ideal bandpass filter whose frequency response is If h(t) is the impulse response of this filter, determine a function g(t) such that (b) As is increased, dose the impulse response of the filter get more concentrated or less concentrated about the origin? Solution Method 1. Let They are shown in the figures,where So we can get Method 2. Using the inverse FT definition,it is obtained more concentrated.  Chap 7 7.1 A real-valued signal x(t) is know to be uniquely determined by its samples when the sampling frequency is .For what values of is guaranteed to be zero? Solution: According to the sampling theorem That is So if , 7.2 A continuous-time signal x(t) is obtained at the output of an ideal lowpass filter with cutoff frequency .If impulse-train sampling is performed on x(t), which of the following sampling periods would guarantee that x(t) can be recovered from its sampled version using an appropriate lowpass filter? (a) (b) (c) Solution: From the sampling theorem, ,that is the conditions (a) and (c) are satisfied with the sampling theorem,(b) is not satisfied. 7.3 The frequency which, under the sampling theorem, must be exceeded by the sampling frequency is called t