Fractional Fourier Transform-based spectrum analyzer
Fractional Fourier Transform (FrFT)-based spectrum analyzers and spectrum analysis techniques are disclosed. Rather than using the standard Fast Fourier Transform (FFT), the FrFT may be used to view the signal content contained in a particular bandwidth. Usage of the FrFT in place of the frequency or time domain allows viewing of the signal in different dimensions, where “spectral” features of interest, or signal content, may appear where they were not visible in these domains before. This may allow signals to be identified and viewed in any domain within the continuous time-frequency plane, and may significantly enhance the ability to detect and extract signals that were previously hidden under interference and/or noise, provide or enhance the ability to extract signals from a congested environment, and enable operation in a signal-dense environment.
1. A method for performing fractional Fourier transform (FrFT)-based spectrum analysis, comprising:
setting an initial detection threshold for detecting one or more signals above a noise floor to a value higher than the noise floor, by a spectrum analyzer, the initial detection threshold set to a value higher than the noise floor;
applying the FrFT to a block of M samples in radio frequency (RF) signals, by a spectrum analyzer, to rotate axes for a time domain and a frequency domain by a plurality of values of a rotational parameter a, thereby producing one or more rotated portions of the RF spectrum; and
responsive to detecting that the one or more signals are present above the noise floor in the block of M samples and above the initial detection threshold:
storing the one or more detected signals above the noise floor, by the spectrum analyzer,
determining types and characteristics of the one or more stored signals for future signal identification purposes,
performing filtering to remove the one or more signals rising above the noise floor from the block of M samples, and
repeating the application of the FrFT to the filtered block of M samples, taking into account the determined types and characteristics of the one or more stored signals, by the spectrum analyzer.
2. The method of claim 1 , wherein a bandwidth for the bandpass filtering is selected based on a bandwidth of the one or more detected signals rising above the noise floor.
3. The method of claim 1 , wherein
the plurality of values of a are separated from one another by an increment of Aa, and
the FrFT is performed for each of the plurality of values of a until a final value of a is reached or the one or more signals are detected above the noise floor.
4. The method of claim 1 , wherein the repeating of the application of the FrFT to the filtered block of M samples comprises performing an inverse FrFT, by the spectrum analyzer, to rotate back to an initial value of a.
5. The method of claim 1 , further comprising:
reducing the detection threshold, by the spectrum analyzer, responsive to not detecting the one or more signals above the noise floor at the initial detection threshold and repeating the method of claim 1 until the one or more signals are detected or the detection threshold reaches the noise floor.
6. The method of claim 1 , further comprising:
responsive to detecting that the one or more signals are present above the noise floor in the block of M samples, displaying the one or more detected signals, by a display.
7. A method for performing fractional Fourier transform (FrFT)-based spectrum analysis, comprising:
applying the FrFT to a block of M samples, by a spectrum analyzer, to rotate axes for a time domain and a frequency domain by an initial rotational parameter a, producing a rotated portion of a radio frequency (RF) spectrum;
responsive to detecting one or more signals above a noise floor for the initial a, performing filtering to remove the one or more signals rising above the noise floor from the block of M samples; and
responsive to not detecting the one or more signals above the noise floor for the initial a:
incrementing a by an amount Δa, by the spectrum analyzer,
performing the FrFT on the block of M samples, by the spectrum analyzer, for the incremented a, and
repeating the process of performing filtering responsive to detecting the one or more signals above the noise floor or incrementing a responsive to not detecting the one or more signals above the noise floor until a final value of a is processed.
8. The method of claim 7 , wherein a bandwidth for the bandpass filtering is selected based on a bandwidth of the one or more detected signals rising above the noise floor.
9. The method of claim 7 , wherein after the final value of a is processed, the method further comprises:
performing an inverse FrFT, by the spectrum analyzer, to rotate back to the initial value of a; and
repeating the method of claim 7 on the processed block of M samples beginning with the initial value of a.
10. The method of claim 7 , further comprising:
storing the one or more detected signals above the noise floor, by the spectrum analyzer; and
determining types and characteristics of the one or more stored signals for future signal identification purposes.
11. The method of claim 7 , further comprising:
setting an initial detection threshold for detecting the one or more signals above the noise floor to a value higher than the noise floor, by the spectrum analyzer.
12. The method of claim 11 , further comprising:
reducing the detection threshold, by the spectrum analyzer, when the one or more signals above the noise floor are not detected at the initial detection threshold and repeating the method of claim 9 until the one or more signals are detected or the detection threshold reaches the noise floor.
13. The method of claim 7 , further comprising:
responsive to detecting that the one or more signals are present above the noise floor in the block of M samples, displaying the one or more detected signals in the rotated portion of the RF spectrum for the time domain and the frequency domain for the respective value of a, by a display.
14. A method for performing fractional Fourier transform (FrFT)-based spectrum analysis, comprising:
setting an initial detection threshold for detecting the one or more signals above the noise floor to a value higher than the noise floor, by the spectrum analyzer;
applying the FrFT to a block of M samples, by a spectrum analyzer, to rotate axes for a time domain and a frequency domain by an initial rotational parameter a, producing a rotated portion of a radio frequency (RF) spectrum;
responsive to detecting one or more signals above a noise floor for the initial a, performing filtering to remove the one or more signals rising above the noise floor from the block of M samples;
responsive to not detecting the one or more signals above the noise floor for the initial a:
incrementing a by an amount Δa, by the spectrum analyzer,
performing the FrFT on the block of M samples, by the spectrum analyzer, for the incremented a, and
repeating the process of performing filtering responsive to detecting the one or more signals above the noise floor or incrementing a responsive to not detecting the one or more signals above the noise floor until a final value of a is processed; and
reducing the detection threshold, by the spectrum analyzer, responsive to not detecting the one or more signals above the noise floor at the initial detection threshold and repeating the signal analysis until the one or more signals are detected or the detection threshold reaches the noise floor.
15. The method of claim 14 , wherein a bandwidth for the bandpass filtering is selected based on a bandwidth of the one or more detected signals rising above the noise floor.
16. The method of claim 14 , wherein after the final value of a is processed, the method further comprises:
performing an inverse FrFT, by the spectrum analyzer, to rotate back to the initial value of a; and
repeating the method of claim 14 on the processed block of M samples beginning with the initial value of a.
17. The method of claim 14 , further comprising:
storing the one or more detected signals above the noise floor, by the spectrum analyzer; and
determining types and characteristics of the one or more stored signals for future signal identification purposes.
18. The method of claim 14 , further comprising:
responsive to detecting that the one or more signals are present above the noise floor in the block of M samples, displaying the one or more detected signals in the rotated portion of the RF spectrum for the time domain and the frequency domain for the respective value of a, by a display.