# US 2022/0035397 A1 · Methods and Systems for Decimating Waveforms Using Second Order Derivative

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- Number: US 2022/0035397 A1
- Document ID: US20220035397A1
- Status: Published application
- Kind: A1
- Application number: 16/942,538
- Filed: 2020-07-29
- Published: 2022-02-03
- Earliest claimed: 2020-07-29
- Applicants: Texas Instruments Incorporated
- Inventors: Mitchell Morgan Gallaher; Richard Barthel
- Web page: https://patentgrep.com/patent/US20220035397A1

## CPC

- G06F 1/022: {Waveform generators, i.e. devices for generating periodical functions of time, e.g. direct digital synthesizers (G06F1/025, G06F1/03 take precedence)}
- G06F 17/17: Function evaluation by approximation methods, e.g. inter- or extrapolation, smoothing, least mean square method ({G06F17/18 takes precedence } ; interpolation for numerical control G05B19/18)
- G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N)

## Abstract

Methods and systems for decimating a waveform are disclosed. The method includes dividing the waveform into a plurality of sections and performing a second order derivative operation on the sections and determining corresponding derivative values. The method further includes classifying the section as a linear region if the derivative value is within a threshold range and classifying the section as a non-linear region if the derivative value is outside the threshold range. The method also includes decimating data points of the linear regions using a coarse decimation to generate coarsely decimated data points and decimating data points of the non-linear regions using a fine decimation to generate finely decimated data points. The method also includes reconstructing a waveform using the coarsely and finely decimated data points.

## Claims

### Claim 1

A method of decimating a waveform, comprising:
dividing the waveform into a plurality of sections;
performing a second order derivative operation on the sections and determining corresponding derivative values;
if the derivative value is within a threshold range, classifying the section as a linear region;
if the derivative value is outside the threshold range, classifying the section as a non-linear region;
decimating data points of the linear regions using a coarse decimation to generate coarsely decimated data points;
decimating data points of the non-linear regions using a fine decimation to generate finely decimated data points; and
reconstructing a waveform using the coarsely and finely decimated data points.

### Claim 2 (depends on 1)

The method of claim 1, wherein decimating the data points by the coarse decimation comprises decimating the data points using a coarse decimation ratio.

### Claim 3 (depends on 1)

The method of claim 1, wherein decimating the data points by the fine decimation comprises decimating the data points using a fine decimation ratio.

### Claim 4 (depends on 1)

The method of claim 1, wherein the threshold range comprises a positive threshold value and a negative threshold value.

### Claim 5 (depends on 1)

The method of claim 1, wherein the derivative value is within the threshold range if the derivative value is less than a positive threshold value and is greater than a negative threshold value.

### Claim 6 (depends on 1)

The method of claim 1, wherein the derivative value is outside the threshold range if the derivative value is greater than a positive threshold value or is less than a negative threshold value.

### Claim 7 (depends on 1)

The method of claim 1, wherein decimating the data points by the coarse decimation includes representing the linear regions by x, y coordinates of endpoints.

### Claim 8 (depends on 1)

The method of claim 1, wherein the coarse decimation ratio is less than the fine decimation ratio.

### Claim 9 (depends on 1)

The method of claim 1, wherein the derivative value of the non-linear regions is non-zero.

### Claim 10

A method of decimating a waveform, comprising:
dividing the waveform into a plurality of sections;
performing a second order derivative operation on the sections and determining corresponding derivative values;
if the derivative value is less than a positive threshold value and is greater than a negative threshold value, classifying the section as a linear region;
if the derivative value is greater than the positive threshold value or is less than the negative threshold value, classifying the section as a non-linear region; and
decimating data points of the linear regions using a coarse decimation ratio to generate coarsely decimated data points;
decimating data points of the non-linear regions using a fine decimation ratio to generate finely decimated data points; and
reconstructing a waveform using the coarsely and finely decimated data points.

### Claim 11 (depends on 10)

The method of claim 10, wherein the coarse decimation ratio is less than the fine decimation ratio.

### Claim 12 (depends on 10)

The method of claim 10, wherein decimating the linear regions comprises representing the linear regions by x, y coordinates of endpoints.

### Claim 13 (depends on 10)

The method of claim 10, wherein the second order derivative value of the non-linear regions is non-zero.

### Claim 14

A non-transitory computer-readable medium having program code recorded thereon, the program code comprising:
program code to divide a waveform into a plurality of sections;
program code to perform a second order derivative operation on the sections and to determine corresponding derivative values;
program code to classify the section as a linear region if the derivative value is within a threshold range and to classify the section as a non-linear region if the derivative value is outside the threshold range;
program code to decimate data points of the linear regions using a coarse decimation to generate coarsely decimated data points;
program code to decimate data points of the non-linear regions using a fine decimation to generate finely decimated data points; and
program code to reconstruct a waveform using the coarsely and finely decimated data points.

### Claim 15 (depends on 14)

The non-transitory computer-readable medium of claim 14, wherein the program code to decimate data points of the linear regions using the coarse decimation comprises program code to decimate the data points using a coarse decimation ratio.

### Claim 16 (depends on 14)

The non-transitory computer-readable medium of claim 14, wherein the program code to decimate data points of the non-linear regions using the fine decimation comprises program code to decimate the data points using a fine decimation ratio.

### Claim 17 (depends on 14)

The non-transitory computer-readable medium of claim 14, wherein the threshold range comprises a positive threshold value and a negative threshold value.

### Claim 18 (depends on 14)

The non-transitory computer-readable medium of claim 14, wherein the derivative value is within the threshold range if the derivative value is less than a positive threshold value and is greater than a negative threshold value.

### Claim 19 (depends on 14)

The non-transitory computer-readable medium of claim 14, wherein the derivative value is outside the threshold range if the derivative value is greater than a positive threshold value or is less than a negative threshold value.

### Claim 20

A non-transitory computer-readable medium having program code recorded thereon, the program code comprising:
program code to divide a waveform into a plurality of sections;
program code to perform a second order derivative operation on the sections and to determine corresponding derivative values;
program code to classify the section as a linear region if the derivative value is less than a positive threshold value and is greater than a negative threshold value;
program code to classify the section as a non-linear region if the derivative value is greater than the positive threshold value or is less than the negative threshold value;
program code to decimate data points of the linear regions using a coarse decimation ratio to generate coarsely decimated data points;
program code to decimate data points of the non-linear regions using a fine decimation ratio to generate finely decimated data points; and
program code to reconstruct a waveform using the coarsely and finely decimated data points.

### Claim 21

A system for decimating a waveform, comprising:
a storage device configured to store the waveform;
a resampler coupled to receive the waveform and configured divide the waveform into a plurality of sections, the resampler configured to perform a second order derivative operation on the sections and to determine corresponding derivative values, the resampler configured to classify the section as a linear region if the derivative value is within a threshold range and to classify the section as a non-linear region if the derivative value is outside the threshold range, the resampler configured to decimate data points of the linear regions using a coarse decimation to generate coarsely decimated data points and configured to decimate data points of the non-linear regions using a fine decimation to generate finely decimated data points, the resampler configured to reconstruct a waveform using the coarsely and finely decimated data points; and
a display monitor coupled to receive the reconstructed waveform and to display the reconstructed waveform.

### Claim 22 (depends on 21)

The system of claim 21, wherein the resampler is configured to decimate the data points by the coarse decimation using a coarse decimation ratio.

### Claim 23 (depends on 21)

The system of claim 21, wherein the resampler is configured to decimate the data points by the fine decimation using a fine decimation ratio.

### Claim 24 (depends on 21)

The system of claim 21, wherein the threshold range comprises a positive threshold value and a negative threshold value.

### Claim 25 (depends on 21)

The system of claim 21, wherein the derivative value is within the threshold range if the derivative value is less than a positive threshold value and is greater than a negative threshold value.

### Claim 26 (depends on 21)

The system of claim 21, wherein the derivative value is outside the threshold range if the derivative value is greater than a positive threshold value or is less than a negative threshold value.

### Claim 27 (depends on 21)

The system of claim 21, wherein the coarse decimation ratio is less than the fine decimation ratio.

### Claim 28 (depends on 21)

The system of claim 21, wherein the derivative value of the non-linear regions is non-zero.