System for modeling digital pulses having specific FMOP properties

• US 7,848,220 B2
• Filed: 03/29/2005
• Issued: 12/07/2010
• Est. Priority Date: 03/29/2005
• Status: Active Grant

• Current Assignee: Lockheed Martin Corporation (Martin Marietta Corporation)
• Original Assignee: Lockheed Martin Corporation (Martin Marietta Corporation)
• Inventors: Johnson, J. Andrew
• Primary Examiner(s): Moe; Aung S
• Assistant Examiner(s): RIYAMI, ABDULLAH A
• Application Number:
  US11/092,153
• Publication Number:
  US 20060227701A1
• Time in Patent Office: 2,079 Days
• Field of Search: 370/210, 370/202, 370/203, 370/204, 370/205, 370/207, 370/212, 370/213, 370/215, 370/252, 370/350, 370/400, 370/401, 375/340, 375/316, 375/343, 375/242, 708/404, 708/405, 342/161, 342/162, 342/111, 342/116
• US Class Current: 370/210
• CPC Class Codes: G11C 27/02 Sample-and-hold arrangements G11C27/04 takes precedence
• CPC Class Codes: H04L 7/027 extracting the synchronising or clock signal from the received signal spectrum, e.g. by using a resonant or bandpass circuit

Abstract

A system samples data of a digital pulse. The system includes a processor, an integrator, and a converter. The processor computes a discrete Fourier transform of frequency data of the digital pulse. The discrete Fourier transform includes a first output. The integrator integrates the first output to produce phase data. The phase data includes a second output. The converter applies an inverse discrete Fourier transform to the second output to produce a continuous signal that may be sampled at a predetermined time instant.

Claims

1. A system for generating phase data representing a digital pulse, said system comprising:

a processor for computing a discrete Fourier transform of frequency data of the digital pulse, the discrete Fourier transform comprising a first output represented by;

2. The system as set forth in claim 1 wherein the processor removes a slope and an offset from the frequency data of the digital pulse.

3. The system as set forth in claim 2 further including a second converter for reapplying the slope and the offset of the frequency data of the digital pulse to the third output, the second converter producing a fourth output.

4. The system as set forth in claim 3 wherein the fourth output comprises a quadratic represented by

5. The system as set forth in claim 1 wherein the scaling component utilizes the frequency domain equivalent operation

6. The system as set forth in claim 1 wherein the converter represents the third output in a time domain such that

7. The system as set forth in claim 1 further including a second processor for computing an analytic signal by applying Euler'"'"'s identity (e^jθ

=cos θ

+j sin θ

) to the third output, the second processor producing a fourth output.

8. The system as set forth in claim 7 wherein the second processor applies a predetermined amplitude envelope to produce a signal with a “

shape,”

A(t), defined by s(t)=A(t)e<sup>jφ

(1)</sup>;

wherein s(t) is the signal and φ

(t) is a phase of the signal.

9. The system as set forth in claim 7 further including a sampler for sampling the fourth output at uniform time intervals, T, such that

s(k)=s(kT)

Re{s(k)}=A(kT)cos φ

(kT)s(t)=A(t)e<sup>jφ

(t)</sup>;

Im{s(k)}=A(kT)sin φ

(kT)

wherein s(t) is the signal at a time t, k is an index, A(t) is the “

shape”

of the amplitude envelope at a time t, and φ

(t) is a phase of the signal at a time t.

18. The system of claim 1, the scaling component scaling the first output by 1/jω

.

19. The system of claim 2, wherein the processor determines the average slope and the offset of the frequency data of the digital pulse via a least squares regression analysis.

10. A non-transitory computer readable medium, containing executable instructions configured to be executed in a computer processor, for generating phase data representing a digital pulse, said executable instructions comprising:

a first instruction for computing a discrete Fourier transform of frequency data of the digital pulse;

a second instruction for removing a slope and an offset from the frequency data from the transformed frequency data as to produce a first output;

a third instruction for scaling the first output to produce phase data for the digital pulse in the frequency domain, the third instruction producing a second output;

a fourth instruction for reapplying the slope and the offset of the frequency data of the digital pulse to the second output, the fourth instruction producing a third output, comprising a quadratic represented by;

11. The non-transitory computer readable medium as set forth in claim 10 wherein the discrete Fourier transform of frequency data of the digital pulse is represented by

12. The non-transitory computer readable medium as set forth in claim 10 wherein the third instruction further utilizes the frequency domain equivalent operation

13. The non-transitory computer readable medium as set forth in claim 10 wherein the fifth instruction further represents the third output in a time domain such that

14. The non-transitory computer readable medium as set forth in claim 10 further including a seventh_instruction for computing an analytic signal by applying Euler'"'"'s identity (e^jφ

=cos φ

+j sin φ

) to the fourth output, the seventh instruction producing a fifth output.

15. The non-transitory computer readable medium as set forth in claim 14 wherein the seventh instruction further applies a predetermined amplitude envelope to the analytic signal produce a combined signal with a “

shape, ”

A(t), defined by s(t)=A(t)e<sup>jφ

(t)</sup>;

wherein s(t) is the signal and φ

(t) is a phase of the signal.

16. The non-transitory computer readable medium as set forth in claim 14 further including an eighth instruction for sampling the fifth output at uniform time intervals, T, such that

s(k)=s(kT)

Re{s(k)}=A(kT)cos φ

(kT);

Im{s(k)}=A(kT)sin φ

(kT)

wherein s(t) is the signal at a time t, k is an index, A(t) is the “

shape”

of the amplitude envelope at a time t, and φ

(t) is a phase of the signal at a time t.

17. The non-transitory computer readable medium of claim 15, wherein the combined signal is sampled at discrete time instants to yield a pulse representation.

20. A non-transitory computer readable medium, containing executable instructions configured to be executed in a computer processor, for generating phase data for a digital pulse, said executable instructions comprising:

a first instruction for computing a discrete Fourier transform of frequency data of the digital pulse, said first instruction producing a first output;

a second instruction for integrating the first output to produce phase data, the second instruction utilizing a frequency domain equivalent operation