TECHNICAL FIELD

The present invention relates to the field of signal processing, and more particularly to methods and systems for sampling and/or denoising a signal.

BACKGROUND

Extracting a useful waveform or signal from a noisy background may be challenging, particularly when the signal of interest is entirely buried under noise, thereby preventing a direct detection approach. Random noise is a fundamental limiting factor in the detection of any physical event, so that the problem of noise mitigation is ubiquitous across a wide range of scientific and technological fields, including spectroscopy, radio-astronomy, sensing, telecommunications, data processing etc.

From a signal processing point of view, noise with frequency components located within the frequency bandwidth of the signal under test (so-called in-band noise) is particularly difficult to deal with. The methods for in-band noise mitigation are very limited. Furthermore, concerning out-of-band noise, conventional band pass filtering techniques require priory knowledge of the bandwidth and central frequency of the signal.

The problem of noise in signal detection becomes particularly damaging when the signals of interest are weak, i.e., when their energy content is low. In this context, a key signal processing solution is that of wave amplification. Conventional (active) amplification of signals, where the intensity of a wave is increased by injecting additional energy from an external source, fails to properly amplify a noisy signal since the background noise is amplified as much as the signal of interest. Furthermore, such processes inherently and unavoidably introduce external noise contributions. For instance, conventional active amplification methods for optical signals lead to amplified spontaneous emission (ASE) noise, which consequently decreases the signal to noise ratio (SNR) of the measurement. Therefore, it is very difficult to successfully amplify a weak signal without deteriorating its SNR through an active process. In particular, it is virtually impossible to actively amplify a weak signal which is originally buried under the noise floor. Passive amplification methods, where only the coherent components of a signal under test are amplified, leaving its incoherent noise content unaltered, have been suggested in both the temporal and spectral domains, but they are either limited to repetitive waveforms or offer only modest amounts of amplification, insufficient to show any noise mitigation capabilities.

Therefore, there is a need for an improved method and system for denoising a wave signal.

SUMMARY

According to a first broad aspect, there is provided a system for sampling a signal, comprising: a first phase modulator configured for receiving a wave signal and modulating a phase of the wave signal while satisfying a Talbot condition to obtain a sampled signal; and a second phase modulator configured for receiving the sampled signal, compensating for a given phase induced in the sampled signal by the first phase modulator while satisfying the Talbot condition to obtain a denoised and amplified sampled signal, and outputting the denoised and amplified sampled signal.

In one embodiment, the first phase modulator comprises a frequency phase modulator for modulating a frequency phase of the wave signal while satisfying the Talbot condition to obtain the sampled signal, the sampled signal having an induced temporal phase; and the second phase modulator comprises a temporal phase modulator for modulating a temporal phase of the sampled signal to compensate for the induced temporal phase

In another embodiment, the first phase modulator comprises a temporal phase modulator for modulating a temporal phase of the wave signal while satisfying the Talbot condition to obtain the sampled signal, the sampled signal having an induced frequency phase; and the second phase modulator comprises a frequency phase modulator for modulating a frequency phase of the sampled signal to compensate for the induced frequency phase.

In one embodiment, the first and second phase modulators each comprise linear phase modulators.

In one embodiment, the wave signal is an optical signal.

In one embodiment, the temporal phase modulator comprises one of an electro-optic phase modulation, a cross-phase modulator, a self-phase modulator and a four-wave mixing modulator.

In one embodiment, the frequency phase modulator comprises one of a medium exhibiting second-order group velocity dispersion and a discrete spectral phase filter.

In one embodiment, the wave signal comprises of one a microwave signal, a millimeter wave signal, an x-ray wave signal, an acoustic wave signal, a thermal wave signal, a matter wave signal, an acoustic wave signal, a radio frequency wave signal and a single-photon quantum wavefunction signal.

In another embodiment, the wave signal comprises a multi-photon entangled quantum states signal.

According to another broad aspect, there is provided a method for sampling a signal, comprising: propagating a wave signal in a first phase modulator configured for modulating a phase of the wave signal while satisfying a Talbot condition, thereby obtaining a sampled signal; propagating the sampled signal into a second phase modulator configured for compensating for a given phase induced in the sampled signal by the first phase modulator while satisfying the Talbot condition, thereby obtaining a denoised and amplified sampled signal; and outputting the denoised and amplified sampled signal.

In one embodiment, said propagating the wave signal in the first phase modulator comprises propagating the wave signal in a frequency phase modulator for modulating a frequency phase of the wave signal while satisfying the Talbot condition to obtain the sampled signal, the sampled signal having an induced temporal phase; and said propagating the sampled signal in the second phase modulator comprises propagating the sampled signal in a temporal phase modulator for modulating a temporal phase of the sampled signal to compensate for the induced temporal phase

In another embodiment, said propagating the wave signal in the first phase modulator comprises propagating the wave signal in a temporal phase modulator for modulating a temporal phase of the wave signal while satisfying the Talbot condition to obtain the sampled signal, the sampled signal having an induced frequency phase; and said propagating the sampled signal in the second phase modulator comprises propagating the sampled signal in a frequency phase modulator for modulating a frequency phase of the sampled signal to compensate for the induced frequency phase.

In one embodiment, the first and second phase modulators each comprise linear phase modulators.

In one embodiment, the wave signal is an optical signal.

In one embodiment, the temporal phase modulator comprises one of an electro-optic phase modulation, a cross-phase modulator, a self-phase modulator and a four-wave mixing modulator.

In one embodiment, the frequency phase modulator comprises one of a medium exhibiting second-order group velocity dispersion and a discrete spectral phase filter.

In one embodiment, the wave signal comprises of one a microwave signal, a millimeter wave signal, an x-ray wave signal, an acoustic wave signal, a thermal wave signal, a matter wave signal, an acoustic wave signal, a radio frequency wave signal and a single-photon quantum wavefunction signal.

In another embodiment, the wave signal comprises a multi-photon entangled quantum states signal.

