Chapter 5 Network structures of Discrete-Time system
Chapter 5 Network Structures of Discrete-Time system
Content ● Introduce o Network Representation with Signal Flow-Graph o Basic IIR System structures o Basic FIR System structures o Linear phase structures ● Frequency Sample
Content ⚫ Introduce ⚫ Network Representation with Signal Flow-Graph ⚫ Basic IIR System Structures ⚫ Basic FIR System Structures ⚫ Linear Phase Structures ⚫ Frequency Sample
5.1 Introduce O Discrete-time system representation a discrete-time system can be described by the input-output relation, impulse response and system function N y(n)=2bx(n-1)-2a, y(n-i) h(n) H(2)=Y(z) ∑b X(二) +)a.z
5.1 Introduce ⚫ Discrete-time system representation 0 1 ( ) ( ) ( ) M N i i i i y n b x n i a y n i = = = − − − 0 1 ( ) ( ) ( ) 1 M i i i N i i i b z Y z H z X z a z − = − = = = + h n( ) A discrete-time system can be described by the input-output relation, impulse response and system function
5.1 Introduce o Discrete-time system representation In the time domain, the input-output relations of an Lti discrete-time system is given by the convolution sum or, by the linear constant coefficient difference equation y(n)=∑h(k)x(n-k) k: (m)=∑dy{n-k]+∑P2xn-k
5.1 Introduce ⚫ Discrete-time system representation ( ) ( ) ( ) k y n h k x n k =− = − In the time domain, the input-output relations of an LTI discrete-time system is given by the convolution sum or, by the linear constant coefficient difference equation. ( ) N M k k y n d y n k p x n k = − − + −
5.1 Introduce o Discrete-time system representation a discrete-time system can be implemented on a general purpose digital computer in software or with special-purpose hardware. To this end, it is necessary to describe the input- output relationship by means of a computational algorithm
5.1 Introduce ⚫ Discrete-time system representation ◆ A discrete-time system can be implemented on a generalpurpose digital computer in software or with special-purpose hardware. To this end, it is necessary to describe the inputoutput relationship by means of a computational algorithm
5.1 Introduce o a structural representation using interconnected basic building blocks is the first step in the hardware or software implementation of an lti digital filter o The structural representation provides the relations between some pertinent internal variables with the input and the output that in turn, provides the keys to the implementation
5.1 Introduce A structural representation using interconnected basic building blocks is the first step in the hardware or software implementation of an LTI digital filter. The structural representation provides the relations between some pertinent internal variables with the input and the output that, in turn, provides the keys to the implementation
5.1 Introduce o There are various forms of the structural representation of a digital filter o There are literally an infinite number of equivalent structures realizing the same transfer function o However, the accuracy, computing speed, complexity is different for the different structure
5.1 Introduce There are various forms of the structural representation of a digital filter. There are literally an infinite number of equivalent structures realizing the same transfer function. However , the accuracy, computing speed, complexity is different for the different structure
5.2 System Representation with signal flow-graph o The computational algorithm of an lti digital filter can be conveniently represented in block diagram form using the basic building blocks representing the unit delay, the multiplier, the adder, and the pick-off nodes
5.2 System Representation with signal flow-graph The computational algorithm of an LTI digital filter can be conveniently represented in block diagram form using the basic building blocks representing the unit delay, the multiplier, the adder, and the pick-off nodes
5.2 System Representation with signal flow-graph Unit delay x(n) x(n-1) x(n) x(n 2 Multiplier xr(n ax(n) Adder x1(m)+x2(m) x1(m) ·x1(n)+x2(m)
5.2 System Representation with signal flow-graph z － 1 x(n) x(n－ 1) x(n) ax(n) a x 1 (n) x2 (n) x 1 (n)＋x 2 (n) x(n) z x(n－ 1) － 1 x(n) a ax(n) x 1 (n) x2 (n) x 1 (n)＋x 2 (n) Unit delay Multiplier Adder
5.2 System Representation with signal flow-graph o In a signal flow-graph, the dependent and independent signal variables are represented by nodes, whereas the multiplier and the delay units are represented by directed branches. In the latter case. the directed branch has attached symbol denoting the branch-go rain or the transmittance, which, for a multiplier branch, is the multiplier coefficient value and for a delay branch is Simply z
5.2 System Representation with signal flow-graph In a signal flow-graph, the dependent and independent signal variables are represented by nodes, whereas the multiplier and the delay units are represented by directed branches. In the latter case, the directed branch has attached symbol denoting the branch-gain or the transmittance, which, for a multiplier branch, is the multiplier coefficient value and for a delay branch is simply z-1
