Fixed-point filter and method

• US 20040153484A1
• Filed: 01/31/2003
• Published: 08/05/2004
• Est. Priority Date: 01/31/2003
• Status: Abandoned Application

• Current Assignee: Texas Instruments, Inc.
• Original Assignee: Texas Instruments, Inc.
• Inventors: Unno, Takahiro
• Application Number:
  US10/355,990
• Publication Number:
  US 20040153484A1
• Time in Patent Office: Days
• US Class Current: 708/131
• CPC Class Codes: H03H 17/0238 Measures concerning the arithmetic used performing computations G06F7/60

Abstract

Fixed-point representation of impulse response coefficients by partitioning the sequence of coefficients into bins according to sequence index intervals, and within each bin quantizing to the fixed-point format providing the greatest resolution without overflow; then computing the total fixed-point quantization error; lastly, optimizing the partitioning to minimize the total fixed-point quantization error and thereby define the fixed-point representation.

Claims

1. A method for fixed-point representation of a set of numbers, comprising:

(a) provide a set of numbers h(0), h(1), . . . , h(M) where M is a positive integer;

(b) provide a first set of N integers, i₁, i₂, . . . , i_N, . . . , i_N, satisfying the following inequalities, 0<

i_i<

i₂<

. . . <

i_n<

. . . <

i_N<

M, where N is a positive integer smaller than M;

(c) for each n in the range n=0, 1, . . . , N, and taking i₀=0 and i_N+1=M, find the smallest integer Bn such that −

2^Bn≦

h(i)<

2^Bn for all h(i) in the n^th bin defined as {h(i_n), h(i_n+1), . . . , h(i_n+1−

1)}, where Bn may be negative, zero, or positive;

(d) for each h(i) in said n^th bin, compute a corresponding quantized fixed-point coefficient ĥ

(i) to precision based on said Bn from step (c);

(e) for each h(i) compute the fixed-point quantization error Δ

h(i)=h(i)−

ĥ

(i) where ĥ

(i) is from step (d);

(f) compute a total fixed-point quantization error from the results of step (e);

(g) repeat steps (b)-(f) for at least a second set of N integers i₁, i₂, . . . , i_N;

(h) select a representation set of N integers from the sets of N integers of steps (b) and/or (g) where said representation set of N integers minimizes the total fixed-point quantization errors found in steps (e)-(g), and use said representation set of N integers to define the fixed-point representations of the numbers.

2. The method of claim 1, wherein:

(a) said total fixed-point quantization error of step (f) of claim 1 is Σ

<sub>0≦

i≦

M</sub>|Δ

h(i)|.

3. The method of claim 1, wherein:

(a) said total fixed-point quantization error of step (f) of claim 1 is Σ

<sub>0≦

i≦

M</sub>|Δ

h(i)|².

4. The method of claim 1, wherein:

(a) said precision of step (d) is 2<sup>Bn−

L+1</sup> where L is the length of the fixed-point format (number of bits including the sign bit).

5. A method for fixed-point representation of a set of numbers, comprising:

(a) provide a set of numbers h(0), h(1), . . . , h(M) where M is a positive integer;

(b) provide a set of N integers, i₁, i₂, . . . , i_n, . . . , i_N, satisfying the following inequalities 0<

i_i<

i₂<

. . . <

i_n<

. . . <

i_N<

M where N is a positive integer smaller than M;

(c) for each n in the range n=0, 1, . . . , N, and taking i₀=0 and i_N+1=M, find the smallest integer Bn such that −

2^Bn≦

h(i)<

2^Bn for all h(i) in the n^th bin defined as {h(i_n), h(i+1), . . . , h(i_n+1−

1)};

(d) for each h(i) in the n^th bin, compute a corresponding quantized fixed-point coefficient ĥ

(i) to precision based on said Bn from step (c);

(e) represent each ĥ

(i) from step (d) in a fixed-point format of length L where L is an integer greater than 2.

6. The method of claim 5, wherein:

(a) said precision of step (d) is 2<sup>Bn−

L+1</sup> where L is the length of the fixed-point format (number of bits including the sign bit).