VLSI SP Course 2001 Fixedpoint analysis of digital

VLSI SP Course 2001 Fixed-point analysis of digital filters for VLSI Signal Processing Course Updated on 4/2/2001 台大電機吳安宇 1

VLSI SP Course 2001 Quantization in implementing system Ideal system Nonlinear model A/D quantization error Rounding error Linear model D/A quantization error Coefficient quantization error 台大電機吳安宇 2

VLSI SP Course 2001 Effect of coefficient quantization in IIR system 台大電機吳安宇 3

VLSI SP Course 2001 Sensitivity New pole of are , i = 1, 2…N 台大電機吳安宇 4

VLSI SP Course 2001 Example: 2 nd-order IIR Filter (I) 台大電機吳安宇 5

VLSI SP Course 2001 Example: 2 nd-order IIR Filter (II) 台大電機吳安宇 6

VLSI SP Course 2001 Effect of coefficient quantization in FIR system 台大電機吳安宇 7

VLSI SP Course 2001 Scaling method l Three scaling methods ; ; ; Si : Scaling factor : Maximum value of input signal 台大電機吳安宇 8

VLSI SP Course 2001 Rounding error model Range : Variance : 台大電機吳安宇 9

VLSI SP Course 2001 Direct form I l. Variance of output signal l. Variance of rounding output error A(z) : denominator part of H(z) 台大電機吳安宇 10

VLSI SP Course 2001 Direct form II l. Variance of output signal l. Variance of rounding output error 台大電機吳安宇 11

VLSI SP Course 2001 Calculation of SQNR • SQNR: Signal-to-Quantization-Noise Ratio SQNR In general, SQNR 40 d. B for practical implementation 台大電機吳安宇 12

VLSI SP Course 2001 Conclusions • Fixed-point analysis is required in converting floatingpoint based algorithm into fixed-point based implementation (e. g. VLSI circuits & fixed-point Programmable DSP processors) • Usually it is done by doing extensive simulations • Closed-form analytical results help to see the effectiveness of each design parameters (W, S, etc. ) • Each algorithm has its own numerical property in fixedpoint implementation 台大電機吳安宇 13