VLSI Signal Processing Fixedpoint Analysis of Digital Filters

VLSI Signal Processing Fixed-point Analysis of Digital Filters for VLSI Signal Processing Course 台大電機吳安宇

VLSI Signal Processing Quantization in implementing system A. Ideal system B. Nonlinear model A/D quantization error Rounding error C. Linear model D/A quantization error Coefficient quantization error 台大電機吳安宇

VLSI Signal Processing Effect of coefficient quantization in IIR system 台大電機吳安宇

VLSI Signal Processing Effect of coefficient quantization in FIR system 台大電機吳安宇

VLSI Signal Processing Sensitivity New pole of are , i = 1, 2…N 台大電機吳安宇

VLSI Signal Processing Example: 2 nd-order IIR Filter (I) 台大電機吳安宇

VLSI Signal Processing Example: 2 nd-order IIR Filter (II) 台大電機吳安宇

VLSI Signal Processing Scaling method l Three scaling methods ; ; Si : Scaling factor : Maximum value of input signal ; 台大電機吳安宇

VLSI Signal Processing Rounding error model Range : Variance : 台大電機吳安宇

VLSI Signal Processing 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

VLSI Signal Processing Direct form II l. Variance of output signal l. Variance of rounding output error 台大電機吳安宇

VLSI Signal Processing 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

VLSI Signal Processing 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