信号与系统习题课
Signals and SystemsYouxin Lv & Junjie Wu School of Electronic EngineeringExercise Lesson (Part I)1 Signal Properties -Periodic, Even and Odd System Properties-Linear, Causal, Stable, Time-invariant, Memoryless Properties of Delta function Convolution-Integral, Sum, Properties Fourier Series-Properties, System output of an LTIMain Points of Mid-term Exam 2Signal Properties Ex. 1.1 (2011)Fundamental PeriodThe fundamental period of3Signal Properties Ex. 1.2 (2011)Fundamental PeriodThe fundamental period of the signal4Signal Properties Ex. 1.3 (2007)Fundamental PeriodThe fundamental period of the signal5Signal Properties Ex. 1.4 (2012)Even and OddA continuous-time signal is illustrated in Fig.1, the odd part of it?0-111tx(t)6System Properties Ex. 2.1 (2012)Linear, Causal, Time-invariant, Stable, MemorylessConsider a continuous-time system with input x(t) and output y(t) related by Linear? Time-invariant? Causal? Memoryless? Stable? 7System Properties Ex. 2.2 (2011)Linear, Causal, Time-invariant, Stable, MemorylessWhich of the following systems are causal and stable systems?8System Properties Ex. 2.3 (2011)Linear, Causal, Time-invariant, Stable, MemorylessDetermine the following signals which have finite total energy9System Properties Ex. 2.4 (2012)The output of an LTI systemConsider an LTI system whose response to the signal in Fig.2 is the signal in Fig.3. Determine and sketch the response of the system to the input depicted in Fig.4t0112011t011t223-110System Properties Ex. 2.5 (2011)The output of an LTI systemt0112011t011t2311Properties of Delta function Ex. 3.1 (2011) Ex. 3.2 (2006)Sifting Property (筛选)12 Ex. 3.3 (2007) Ex. 3.4 (2012)Properties of Delta function13Convolution Ex. 4.1 (2011)Integral-continuous-time signalThe convolution integral Ex. 4.2 (2011)The convolution integral 14Convolution Ex. 4.3 (2011)Sum-discrete-time signalConsider an LTI system whose input xn and unit impulse response hn are given by Ex. 4.4 (2012)Determine the output of this system. Consider an LTI system whose input xn and unit impulse response hn are given by Determine the output of this system. 15Convolution Ex. 4.5 (2011)PropertiesConsider an LTI system with unit impulse response h(t) illustrated in Fig.1. If the input is , the output is 011t2-1-2-116Convolution Ex. 4.6 (2006)Properties17Fourier Series Ex. 5.1 (2011)PropertiesLet andThe Fourier series coefficients of x(t) may be ( )18Fourier Series Ex. 5.2 (2012)PropertiesLet andThe Fourier series coefficients of x(t) may be ( )19Fourier Series Ex. 5.1 (2011)The output of an LTI systemConsider a continuous-time LTI system whose frequency response H(jw) is illustrated in Fig.1. If the input is , determine the output.01t20Signals and SystemsYouxin Lv & Junjie Wu School of Electronic EngineeringExercise Lesson (Part II)21Chapter 11.6 (a)Determine whether or not each of the following signals is periodic.22Chapter 11.9 Determine whether or not each of the following signals is periodic. If yes, the fundamental period?23Chapter 11.17 The following system, causal? Linear?24Chapter 11.19 The following system, Linear? Time-invariant?25Chapter 11.27 (a) Memoryless? Linear? Time-invariant? Causal? Stable?26Chapter 22.5is an integerDetermine the value of N, given that27Chapter 2 2.2328Chapter 22.2429Chapter 23.1530Chapter 23.3431Chapter 24.3232