Chapter 9 Analysis of Finite Wordlength Effects
Chapter 9 Analysis of Finite Wordlength Effects
Introduction Ideally, the system parameters along with the signal variables have infinite precision taking any value between -oo and oo In practice, they can take only discrete values within a specified range since the registers of the digital machine where they are stored are of finite lengt s. The discretization process results in nonlinear difference equations characterizing the discrete-time systems
Introduction • Ideally, the system parameters along with the signal variables have infinite precision taking any value between - and • In practice, they can take only discrete values within a specified range since the registers of the digital machine where they are stored are of finite length • The discretization process results in nonlinear difference equations characterizing the discrete-time systems
Introduction These nonlinear equations, in principle, are almost impossible to analyze and deal with exactly However, if the quantization amounts are small compared to the values of signal varia bles and filter parameters a simpler approximate theory based on a statistical model can be applied
Introduction • These nonlinear equations, in principle, are almost impossible to analyze and deal with exactly • However, if the quantization amounts are small compared to the values of signal variables and filter parameters, a simpler approximate theory based on a statistical model can be applied
Introduction Using the statistical model, it is possible to derive the effects of discretization and develop results that can be verified experimentally · Sources of errors (1)Filter coefficient quantization (2)A/D conversion 3)Quantization of arithmetic operations (4) Limit cycles
Introduction • Using the statistical model, it is possible to derive the effects of discretization and develop results that can be verified experimentally • Sources of errors - (1) Filter coefficient quantization (2) A/D conversion (3) Quantization of arithmetic operations (4) Limit cycles
Introduction &. Consider the first-order iir digital filter yIn=ayln-1+xn where yln is the output signal and xin is the input signal When implemented on a digital machine the filter coeficient a can assume only e certain discrete values a approximating the original design value a
Introduction • Consider the first-order IIR digital filter y[n]= y[n-1]+x[n] where y[n] is the output signal and x[n] is the input signal ^ • When implemented on a digital machine, the filter coefficient can assume only certain discrete values approximating the original design value