Systems and methods of signal analysis and data transfer using spectrogram construction and inversion

1. A method of generating an analytical signal for signal analysis, the method executable on one or more computer processors, the method comprising:

receiving a time-dependent digital signal;

sectioning the time-dependent digital signal into a series of overlapping windows in time domain;

generating a plurality of energy pulses by evaluating a function that quantifies energy information within each window or set of windows; and

generating a time-dependent analytical signal by:

generating an oscillating signal by multiplying each of the plurality of energy pulses by an oscillating function; and

integrating the oscillating function across a band pass frequency filter.

2. The method of claim 1 , wherein the analytical signal is defined by a set of parameters including time units, frequency units, origin, and range of energy pulse information to be included.

3. The method of claim 2 , wherein the band pass frequency filter has a frequency range corresponding to the energy pulse information to be included.

4. The method of claim 1 , wherein the time-dependent analytical signal is invertible to approximate the time-dependent digital signal.

5. The method of claim 4 , wherein the time-dependent digital signal is generated by discretely sampling an input signal, the input signal being either an analog signal or the analytical signal, wherein the amplitude of each sample is the average energy information of the input signal over a predefined observation time interval.

6. The method of claim 1 , wherein the function has as its peak a median position and monotonically tends to zero at a finite time and frequency interval from the median position.

7. The method of claim 6 , wherein the function is one of: a parametric probability density function, a single or set of square functions, and a single or set of triangular functions.

8. The method of claim 1 , wherein the oscillating function comprises a sine wave having a form of sin(2πω+λ), where λ is a phase shift variable relative to an absolute time origin, ω is a frequency variable, and t is a time variable.

9. The method of claim 1 , wherein sectioning the time-dependent digital signal allows for identifying, quantifying, and mitigating background/ambient noise from the digital signal prior to evaluating the function.

10. The method of claim 1 , further comprising:

obtaining the analytical signal;

sampling the analytical signal to convert the analytical signal into a generated digital signal;

sectioning the generated digital signal into a series of overlapping windows;

determining a discrete forward Fourier transform of the generated digital signal in each window; and

arranging the Fourier transform of each window into a discrete time-frequency energy spectrogram.

11. A system for generating an analytical signal for signal analysis, the system comprising one or more processors and one or more computer storage media, the one or more computer storage media causing the one or more processors to execute a set of programmable modules configured to:

receive a time-dependent digital signal;

section the time-dependent digital signal into a series of overlapping windows in time domain;

generating a plurality of energy pulses by evaluating a function that quantifies energy information within each window or set of windows; and

generate a time-dependent analytical signal by:

generating an oscillating signal by multiplying each of the plurality of energy pulses by an oscillating function; and

integrating the oscillating function across a band pass frequency filter.

12. The system of claim 11 , wherein the analytical signal is defined by a set of parameters including time units, frequency units, origin and range of energy pulse information to be included.

13. The system of claim 12 , wherein the band pass frequency filter has a frequency range corresponding to the energy pulse information to be included.

14. The system of claim 12 , wherein sectioning the time-dependent digital signal identifies, quantifies, and mitigates background/ambient noise from the digital signal prior to evaluation of the function.

15. The system of claim 11 , wherein the time-dependent analytical signal is invertible to approximate the time-dependent digital signal.

16. The system of claim 15 , wherein the time-dependent digital signal is generated by discretely sampling an input signal, the input signal being either an analog signal or the analytical signal, wherein the amplitude of each sample is the average energy information of the input signal over a predefined observation time interval.

17. The system of claim 11 , wherein the function has as its peak a median position and monotonically tends to zero at a finite time and frequency interval from the median position.

18. The system of claim 17 , wherein the function is one of: a parametric probability density function, a single or set of square functions, and a single or set of triangular functions.

19. The system of claim 11 , wherein the oscillating function comprises a sine wave having a form of sin(2πωt+λ), where λ is a phase shift variable relative to an absolute time origin, ω is a frequency variable, and t is a time variable.

20. The system of claim 11 , wherein the programmable modules are further configured to:

obtain the analytical signal;

sample the analytical signal to convert the analytical signal into a generated digital signal;

section the generated digital signal into a series of overlapping windows;

determine a discrete forward Fourier transform of the generated digital signal in each window; and

arrange the Fourier transform of each window into a discrete time-frequency energy spectrogram.