Bài giảng xử lý tín hiệu số signal and system in time domain ngô quốc cường

Xử lý tín hiệu số Signal and System in Time Domain Ngô Quốc Cường ngoquoccuong175@gmail.com Ngô Quốc Cường sites.google.com/a/hcmute.edu.vn/ngoquoccuong Signal and System in Time Domain • Discrete time signals • Discrete time systems • LTI systems 2.1 Discrete - time signals • A discrete time signal x(n) is a function of an independent variable that is integer 2.1 Discrete - time signals • Alternative representation of discrete time signal: 2.1 Discrete - time signals • Alternative representation of discrete time signal: 2.1.1 Some elementary signals 2.1.1 Some elementary signals 2.1.1 Some elementary signals 2.1.1 Some elementary signals 2.1.2 Classification of discrete time signal • Energy signals and power signal – The energy E of a signal x(n) is given: – If E is finite, x(n) is call an energy signal 10 76 2.4 Discrete time systems described by difference equations • The practical implementation of the IIR system is impossible since it requires an infinite number of memory locations, multiplications, and additions • Practical and computationally efficient means: difference equations 77 2.4 Discrete time systems described by difference equations • Recursive and non-recursive system – Compute the cumulative average of a signal x(n) defined in the interval ≤ k ≤ n – In the different way – Hence Recursive system 78 2.4 Discrete time systems described by difference equations • Recursive and non-recursive system – Non-recursive system: depends only on the present and the past inputs 79 2.4 Discrete time systems described by difference equations • Recursive and non-recursive system 80 2.4 Discrete time systems described by difference equations • The general form: • N: the order of the difference equation = the order of the system 81 2.4 Discrete time systems described by difference equations • Solution of linear constant coefficient difference equation – Direct method – Indirect method (z - transform) • The direct solution method assumes that the total solution is the sum of two parts: – yh(n): homogeneous solution – yp(n): particular solution 82 2.5 Structure for the realization of LTI systems • Consider the 1st order system • This realization uses separate delays for both input and output, called Direct Form structure 83 2.5 Structure for the realization of LTI systems • Interchange the order of the recursive and non-recursive systems 84 2.5 Structure for the realization of LTI systems • Two delay elements can be merged into one delay Direct Form structure 85 2.5 Structure for the realization of LTI systems • Direct Form – M+N delays – M+N+1 multipliers 86 2.5 Structure for the realization of LTI systems • Direct Form 87 2.5 Structure for the realization of LTI systems 88 89 90 [...]... discrete time signal • Energy signals and power signal – The average power P of a signal x(n) is defined: – If P is finite (and nonzero), x(n) is called a power signal 11 2.1.2 Classification of discrete time signal • Energy signals and power signal – Example: the average power of the unit step signal is: 12 2.1.2 Classification of discrete time signal • Periodic signals and aperiodic signals – A signal. .. versus unstable systems 31 2.2 Discrete time systems • Classification of discrete time systems – Static versus dynamic systems • Static: output at any instant n depends at most on the input sample at the same time – memoryless • Dynamic: to have memory 32 2.2 Discrete time systems • Classification of discrete time systems – Time invariant versus time variant systems • Time invariant: input – output... characteristics do not change with time 33 2.2 Discrete time systems • Classification of discrete time systems – Linear versus nonlinear systems 34 2.2 Discrete time systems 35 2.2 Discrete time systems • Classification of discrete time systems – Causal versus noncausal systems • The output of the system at any time n depends only on present and past inputs but does not depend on future inputs 36 ... following signals 23 2.2 Discrete time systems • Device or algorithm that performed some prescribed operation on discrete time signal 24 2.2 Discrete time systems • Determine the response of the following systems to the input signal 25 2.2 Discrete time systems • Block diagram representation – An adder 26 2.2 Discrete time systems • Block diagram representation – A constant multiplier 27 2.2 Discrete time systems... – A signal multiplier 28 2.2 Discrete time systems • Block diagram representation – A unit delay element – A unit advance element 29 2.2 Discrete time systems • Block diagram representation 30 2.2 Discrete time systems • Classification of discrete time systems – Static versus dynamic systems – Time invariant versus time variant systems – Linear versus nonlinear systems – Causal versus noncausal systems... >0) if and only if 13 2.1.2 Classification of discrete time signal • Symmetric (even) and antisymmetric (odd) signals – A real value signal x(n) is call symmetric if – A signal is call antisymmetric if 14 2.1.2 Classification of discrete time signal • Symmetric (even) and antisymmetric (odd) signals 15 2.1.2 Classification of discrete time signal – The even signal component is formed by adding x(n)... x(n) to x(n) and dividing by 2 – Odd signal component 16 2.1.3 Simple manipulations of signals • Transformation of time – A signal x(n) may be shifted by replacing n bay n-k • k is positive number: delay • k is negative number: advance – Folding: replace n by -n – Time scaling: replace n by cn (c is an integer) 17 2.1.3 Simple manipulations of signals • Transformation of time – Find x(n-3) and x(n+2)... of signals • Transformation of time – Find x(-n) and x(-n+2) of x(n) 19 2.1.3 Simple manipulations of signals • Transformation of time – Show the graphical representation of y(n) = x(2n), where x(n) is 20 2.1.3 Simple manipulations of signals • Addition, multiplication, and scaling – Amplitude scaling – Sum – Product 21 Exercises 22 Exercises • x(n) is illustrated in the figure • Sketch the following .. .Signal and System in Time Domain • Discrete time signals • Discrete time systems • LTI systems 2.1 Discrete - time signals • A discrete time signal x(n) is a function of an independent... discrete time systems – Time invariant versus time variant systems • Time invariant: input – output characteristics not change with time 33 2.2 Discrete time systems • Classification of discrete time. ..