Signals and Systems Lecture Filter Structure and Quantization Effects
Implementation PART II
Structure for discrete-time
Realization of Filters
Digital Filter
Direct Form I Implementation
Block Diagram IIR DF-I
Realization of Filters: Ex.
Block Diagrams/ signal Flowgraphs
Signal Flow Graph: DF-I
Multiple Structures
Discrete Form II
Signal Flow Graph: IIR DF-II
Discrete Form II (canonic)
Cascade Form
Cascade Form: Real Case
IIR Cascade Form
Parallel Form
Transposed Forms
Structures for FIR Filters
Structures for LP FIR Filters
Quantization Effects discrete-time filters, not digital filters. Most DSP systems are implemented using fixed-point arithmetic Floating-point arithmetic helps alleviate this problem, but consumes too much power and costs more Due to the very nature of DSP, where digital data are obtained through an A/D converter, floating-point precision is usually not required
Coefficient Quantization first design a discrete-time filter with double floating-point precision, such as the use of Matlab Truncate (or round) the filter coefficients to implement the fixed- point HW/SW
Finite Precision effects
Quantization effects on the FIR systems
Unquantized FIR Filter Effect
16-bit Quantization FIR Filter
8-bit Quantization of FIR Filter
Finite Precision effects- Example
Coefficient Quantization
Coefficient Quantization(cont.)
DFII vs. 2 nd order sections for IIR
2 nd Order Filter
cos and - 2 must be computed and rounded to the number of bits available Suppose that we use a 4-bit quantizer b0.b1b2b3. Both cos and 2 can take on the numbers from to (-1 to 0.875) Poles and zeros of a 2-nd order filter can only occur at the intersection of the lines representing cos and the semi-circles representing 2
Quantization in 2 nd order Section
Evenly Spaced Quantization Non-uniform density of poles and zeros of a 2nd-order section can be mitigated by using a “coupled form” structure The quantized poles and zeros are at the intersections of evenly spaced horizontal and vertical lines.