[工学]数字信号处理Chapter_8第三版教材.ppt

Chapter 8 Digital Filter Structures The convolution sum description of an LTI discrete-time system can, in principle, be used to implement the system For an IIR finite-dimensional system this approach is not practical as here the impulse response is of infinite length However, a direct implementation of the IIR finite-dimensional system is practical Here the input-output relation involves a finite sum of products: The actual implementation of an LTI digital filter can be either in software or hardware form, depending on applications In either case, the signal variables and the filter coefficients cannot be represented with finite precision However, a direct implementation of a digital filter based on either the difference equation or the finite convolution sum may not provide satisfactory performance due to the finite precision arithmetic It is thus of practical interest to develop alternate realizations and choose the structure that provides satisfactory performance under finite precision arithmetic 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 key relations between some pertinent internal variables with the input and output that in turn provides the key to the implementation Block Diagram Representation In the time domain, the input-output relations of an LTI digital filter is given by the convolution sum Block Diagram Representation For the implementation of an LTI digital filter, the input-output relationship must be described by a valid computational algorithm To illustrate what we mean by a computational algorithm, consider the causal first-order LTI digital filter shown below Block Diagram Representation The filter is described by the difference equation y[n]=-d1y[n-1]+p0x[n]+p1x[n-1] Using the above equation we can compute y[n] for n?0 knowing the initial condition y[n-1] and the input x[n] for