Noise reduction of oscilloscope waveforms

1. An oscilloscope, comprising:

a memory that stores instructions; and

a processor that executes the instructions, wherein, when executed by the processor, the instructions cause the oscilloscope to:

obtain a measurement of a first radio frequency signal;

split a first spectrum based on the first radio frequency signal into a first low-frequency band and a first high-frequency band;

perform a first Fourier transform to compute a first new spectrum based on the first spectrum;

compute a first waveform of the first new spectrum with noise of the oscilloscope reduced by performing a first inverse Fourier transform based on the first new spectrum; and

combine the first new spectrum with noise of the oscilloscope reduced with the first low-frequency band.

2. The oscilloscope of claim 1 , wherein, when executed by the processor, the instructions further cause the oscilloscope to:

obtain a measurement of a second radio frequency signal;

split a second spectrum based on the first radio frequency signal and the second radio frequency signal into a second low-frequency band and a second high-frequency band, wherein the first spectrum is based on the first radio frequency signal and the second radio frequency signal;

perform the first Fourier transform to compute the first new spectrum based on the measurement of the first radio frequency signal and the measurement of the second radio frequency signal, wherein the first new spectrum is of a first common mode signal based on the first radio frequency signal and the second radio frequency signal; and

measure a contribution of the oscilloscope to noise of the first common mode signal by performing a second Fourier transform of a differential mode signal based on the first radio frequency signal and the second radio frequency signal.

3. The oscilloscope of claim 2 , wherein, when executed by the processor, the instructions further cause the oscilloscope to:

combine a magnitude of the first new spectrum of the first common mode signal and a phase of the first spectrum; and

compute the first waveform of the first new spectrum with noise of the oscilloscope reduced by performing the first inverse Fourier transform based on the magnitude of the first new spectrum with noise of the oscilloscope reduced and the phase of the first spectrum.

4. The oscilloscope of claim 3 , wherein, when executed by the processor, the instructions further cause the oscilloscope to:

obtain a measurement of a third radio frequency signal and a measurement of a fourth radio frequency signal;

split a third spectrum based on the third radio frequency signal and the fourth radio frequency signal into a third low-frequency band and a third high-frequency band;

split a fourth spectrum based on the third radio frequency signal and the fourth radio frequency signal into a fourth low-frequency band and a fourth high-frequency band;

perform a third Fourier transform to compute a second new spectrum based on the measurement of the third radio frequency signal and the measurement of the fourth radio frequency signal, wherein the second new spectrum is of second common mode signal based on the third radio frequency signal and the fourth radio frequency signal;

measure a contribution of the oscilloscope to noise of the second common mode signal by performing a fourth Fourier transform of a differential mode signal based on the third radio frequency signal and the fourth radio frequency signal;

combine a magnitude of the second new spectrum of the second common mode signal and a phase of the third spectrum; and

compute a second waveform of the second new spectrum with noise of the oscilloscope reduced by performing a second inverse Fourier transform based on the magnitude of the second new spectrum of the second common mode signal and the phase of the third spectrum.

5. The oscilloscope of claim 4 , wherein, when executed by the processor, the instructions further cause the oscilloscope to:

average the first new spectrum and the second new spectrum.

6. The oscilloscope of claim 1 , wherein, when executed by the processor, the instructions further cause the oscilloscope to:

estimate a contribution of the oscilloscope to noise of the first radio frequency signal based on the first radio frequency signal; and

perform the first Fourier transform to compute the first new spectrum based on the measurement of the first radio frequency signal; and

perform a second Fourier transform to compute a second new spectrum based on the estimated contribution of the oscilloscope to noise of the first radio frequency signal.

7. The oscilloscope of claim 6 , wherein, when executed by the processor, the instructions further cause the oscilloscope to:

combine a magnitude of the first new spectrum and a phase of the first new spectrum; and

compute the first waveform of the first new spectrum with noise of the oscilloscope reduced by performing the first inverse Fourier transform based on the magnitude of the first new spectrum and the phase of the first new spectrum.

8. The oscilloscope of claim 7 , wherein, when executed by the processor, the instructions further cause the oscilloscope to:

obtain a measurement of a second radio frequency signal;

split a second spectrum based on the of the second radio frequency signal into a second low-frequency band and a second high-frequency band;

perform a third Fourier transform to compute a third new spectrum based on the second spectrum;

estimate a contribution of the oscilloscope to noise of the second radio frequency signal based on the second radio frequency signal;

perform the third Fourier transform to compute the third new spectrum based on the measurement of the second radio frequency signal;

perform a fourth Fourier transform to compute a fourth new spectrum based on the estimated contribution of the oscilloscope to noise of the second radio frequency signal

combine a magnitude of the third new spectrum and a phase of the third new spectrum; and

compute a second waveform of the third new spectrum with noise of the oscilloscope reduced by performing a second inverse Fourier transform based on the magnitude of the third new spectrum and the phase of the third new spectrum.

9. The oscilloscope of claim 8 , wherein, when executed by the processor, the instructions further cause the oscilloscope to:

average the first new spectrum and the third new spectrum.

10. The oscilloscope of claim 1 , wherein, when executed by the processor, the instructions further cause the oscilloscope to:

filter a noise spectrum of the oscilloscope before computing the first new spectrum.

11. The oscilloscope of claim 1 , further comprising:

a user interface that provides an option to denoise the first radio frequency signal.

12. A tangible non-transitory computer-readable storage medium that stores a computer program, wherein the computer program, when executed by a processor, causes a system to:

obtain a measurement of a first radio frequency signal;

split a first spectrum based on the first radio frequency signal into a first low-frequency band and a first high-frequency band;

perform a first Fourier transform to compute a first new spectrum based on the first spectrum;

compute a first waveform of the first new spectrum with noise of the system reduced by performing a first inverse Fourier transform based on the first new spectrum; and

combine the first new spectrum with noise of the system reduced with the first low-frequency band.

13. The tangible non-transitory computer-readable storage medium of claim 12 , wherein, when executed by the processor, the computer program further causes the system to:

obtain a measurement of a second radio frequency signal;

split a second spectrum based on the first radio frequency signal and the second radio frequency signal into a second low-frequency band and a second high-frequency band, wherein the first spectrum is based on the first radio frequency signal and the second radio frequency signal;

perform the first Fourier transform to compute the first new spectrum based on the measurement of the first radio frequency signal and the measurement of the second radio frequency signal, wherein the first new spectrum is of a first common mode signal based on the first radio frequency signal and the second radio frequency signal; and

measure a contribution of the system to noise of the first common mode signal by performing a second Fourier transform of a differential mode signal based on the first radio frequency signal and the second radio frequency signal.

14. The tangible non-transitory computer-readable storage medium of claim 13 , wherein, when executed by the processor, the computer program further causes the system to:

combine a magnitude of the first new spectrum of the first common mode signal and a phase of the first spectrum; and

compute the first waveform of the first new spectrum with noise of the system reduced by performing the first inverse Fourier transform based on the magnitude of the first new spectrum with noise of the system reduced and the phase of the first spectrum.

15. The tangible non-transitory computer-readable storage medium of claim 14 , wherein, when executed by the processor, the computer program further causes the system to:

obtain a measurement of a third radio frequency signal and a measurement of a fourth radio frequency signal;

split a third spectrum based on the third radio frequency signal and the fourth radio frequency signal into a third low-frequency band and a third high-frequency band;

split a fourth spectrum based on the third radio frequency signal and the fourth radio frequency signal into a fourth low-frequency band and a fourth high-frequency band;

perform a third Fourier transform to compute a second new spectrum based on the measurement of the third radio frequency signal and the measurement of the fourth radio frequency signal, wherein the second new spectrum is of second common mode signal based on the third radio frequency signal and the fourth radio frequency signal;

measure a contribution of the system to noise of the second common mode signal by performing a fourth Fourier transform of a differential mode signal based on the third radio frequency signal and the fourth radio frequency signal;

combine a magnitude of the second new spectrum of the second common mode signal and a phase of the third spectrum; and

compute a second waveform of the second new spectrum with noise of the system reduced by performing a second inverse Fourier transform based on the magnitude of the second new spectrum of the second common mode signal and the phase of the third spectrum.

16. The tangible non-transitory computer-readable storage medium of claim 15 , wherein, when executed by the processor, the computer program further causes the system to:

average the first new spectrum and the second new spectrum.

17. The tangible non-transitory computer-readable storage medium of claim 12 , wherein, when executed by the processor, the computer program further causes the system to:

estimate a contribution of the system to noise of the first radio frequency signal based on the first radio frequency signal; and

perform the first Fourier transform to compute the first new spectrum based on the measurement of the first radio frequency signal; and

perform a second Fourier transform to compute a second new spectrum based on the estimated contribution of the system to noise of the first radio frequency signal.

18. The tangible non-transitory computer-readable storage medium of claim 17 , wherein, when executed by the processor, the computer program further causes the system to:

combine a magnitude of the first new spectrum and a phase of the first new spectrum; and

compute the first waveform of the first new spectrum with noise of the system reduced by performing the first inverse Fourier transform based on the magnitude of the first new spectrum and the phase of the first new spectrum;

obtain a measurement of a second radio frequency signal;

split a second spectrum based on the of the second radio frequency signal into a second low-frequency band and a second high-frequency band;

perform a third Fourier transform to compute a third new spectrum based on the second spectrum;

estimate a contribution of the system to noise of the second radio frequency signal based on the second radio frequency signal;

perform the third Fourier transform to compute the third new spectrum based on the measurement of the second radio frequency signal;

perform a fourth Fourier transform to compute a fourth new spectrum based on the estimated contribution of the system to noise of the second radio frequency signal

combine a magnitude of the third new spectrum and a phase of the third new spectrum; and

compute a second waveform of the third new spectrum with noise of the system reduced by performing a second inverse Fourier transform based on the magnitude of the third new spectrum and the phase of the third new spectrum.

19. The tangible non-transitory computer-readable storage medium of claim 18 , wherein, when executed by the processor, the computer program further causes the system to:

average the first new spectrum and the third new spectrum.

20. A system, comprising:

a memory that stores instructions; and

a processor that executes the instructions, wherein, when executed by the processor, the instructions cause the system to:

obtain a measurement of a first radio frequency signal;

split a first spectrum based on the first radio frequency signal into a first low-frequency band and a first high-frequency band;

perform a first Fourier transform to compute a first new spectrum based on the first spectrum;

compute a first waveform of the first new spectrum with noise of the system reduced by performing a first inverse Fourier transform based on the first new spectrum; and

combine the first new spectrum with noise of the system reduced with the first low-frequency band.