Conventional sub-Nyquist sampling methods for analog signals exploit prior information about the spectral support. In this paper, we consider the challenging problem of blind sub-Nyquist sampling of multiband signals, whose unknown frequency support occupies only a small portion of a wide spectrum. Our primary design goals are efficient hardware implementation and low computational load on the supporting digital processing. We propose a system, named the modulated wideband converter, which first multiplies the analog signal by a bank of periodic waveforms. The product is then low-pass filtered and sampled uniformly at a low rate, which is orders of magnitude smaller than Nyquist. Perfect recovery from the proposed samples is achieved under certain necessary and sufficient conditions. We also develop a digital architecture, which allows either reconstruction of the analog input, or processing of any band of interest at a low rate, that is, without interpolating to the high Nyquist rate. Numerical simulations demonstrate many engineering aspects: robustness to noise and mismodeling, potential hardware simplifications, real-time performance for signals with time-varying support and stability to quantization effects. We compare our system with two previous approaches: periodic nonuniform sampling, which is bandwidth limited by existing hardware devices, and the random demodulator, which is restricted to discrete multitone signals and has a high computational load. In the broader context of Nyquist sampling, our scheme has the potential to break through the bandwidth barrier of state-of-the-art analog conversion technologies such as interleaved converters.

/pdf/from-theory-to-practice-sub-nyquist-sampling-of-sparse-4swzjs0wes.pdf

From Theory to Practice: Sub-Nyquist Sampling of Sparse Wideband Analog Signals

Mode-locked laser systems generate extremely short optical pulses and are widely used for measurements of ultrafast phenomena. In these experiments, the effect of laser pulse timing fluctuations (jitter) is suppressed by exciting the system under test by the pulsed laser and probing with a delayed portion of the same optical pulse. If the experiment cannot be laser-excited or must be excited and probed by different lasers, timing jitter degrades the time resolution and introduces noise.

Subpicosecond laser timing stabilization

The present invention teaches a new audio coding system that can code both general audio and speech signals well at low bit rates. A proposed audio coding system comprises linear prediction unit for filtering an input signal based on an adaptive filter; a transformation unit for transforming a frame of the filtered input signal into a transform domain; and a quantization unit for quantizing the transform domain signal. The quantization unit decides, based on input signal characteristics, to encode the transform domain signal with a model-based quantizer or a non-model-based quantizer. Preferably, the decision is based on the frame size applied by the transformation unit.

Audio encoder and decoder

Time-delayed optoelectronic oscillators are at the center of a large body of scientific literature. The complex behavior of these nonlinear oscillators has been thoroughly explored both theoretically and experimentally, leading to a better understanding of their dynamical properties. Beyond fundamental research, these systems have also inspired a wide and diverse set of applications, such as optical chaos communications, pseudorandom number generation, optoelectronic machine learning based on reservoir computing, ultrapure microwave generation, optical pulse-train synthesis, and sensing. The aim of this review is to provide a comprehensive survey of this field, to outline the latest achievements, and discuss the main challenges ahead.

Optoelectronic oscillators with time-delayed feedback

Compressive imaging captures images in compressed form, where each sensor does not directly correspond with a pixel, as opposed to standard image capture techniques. This can lead to faster image capture rates due to lower I/O bandwidth requirements, and avoids the need for image compression hardware, as the image is captured in compressed form. Measuring the transformation of an emitted multimodal signal is one method of compressive imaging. Metamaterial antennas and transceivers are well suited for both emitting and receiving multimodal signals, and are thus prime candidates for compressive imaging.

Metamaterial devices and methods of using the same

Recent advances in electro-optical systems make them ideal for undersampling multiband signals with very high carrier frequencies. In this paper, we propose a new scheme for sampling and reconstructing of a multiband sparse signals that occupy a small part of a given broad frequency range under the constraint of a small number of sampling channels. The locations of the signal bands are not known a priori. The scheme, which we call synchronous multirate sampling (SMRS), entails gathering samples synchronously at few different rates whose sum is significantly lower than the Nyquist sampling rate. The signals are reconstructed by finding a solution of an underdetermined system of linear equations by applying a pursuit algorithm and assuming that the solution is composed of a minimum number of bands. The empirical reconstruction success rate is higher than obtained using previously published multicoset scheme when the number of sampling channels is small and the conditions for a perfect reconstruction in the multicoset scheme are not fulfilled. The practical sampling system which is simulated in our work consists of three sampling channels. Our simulation results show that a very high empirical success rate is obtained when the total sampling rate is five times higher than the total signal support of a complex signal with four bands. By comparison, a multicoset sampling scheme obtains a very high empirical success rate with a total sampling rate which is three times higher than the total signal support. However, the multicoset scheme requires 14 channels.

/pdf/multirate-synchronous-sampling-of-sparse-multiband-signals-3feef0p673.pdf

Multirate Synchronous Sampling of Sparse Multiband Signals

We experimentally demonstrate a wideband-frequency tunable optoelectronic oscillator (OEO) based on injection locking of the OEO to a tunable electronic oscillator. The OEO cavity does not contain a narrowband filter and its frequency can be tuned over a broad bandwidth of 1 GHz. The injection locking is based on minimizing the injected power by adjusting the frequency of one of the OEO cavity modes to be approximately equal to the frequency of the injected signal. The phase noise that is obtained in the injection-locked OEO is similar to that obtained in a long-cavity self-sustained OEO. Although the cavity length of the OEO was long, the spurious modes were suppressed due to the injection locking without the need to use a narrowband filter. The spurious level was significantly below that obtained in a self-sustained OEO after inserting a narrowband electronic filter with a Q-factor of 720 into the cavity.

Wideband-frequency tunable optoelectronic oscillator based on injection locking to an electronic oscillator.

A scheme for reconstructing multiband signals that occupy a small part of a given broad frequency range under the constraint of a small number of sampling channels. The multirate sampling scheme (MRS) entails gathering samples at several different rates whose sum is significantly lower than the Nyquist sampling rate. The number of channels does not depend on any characteristics of a signal. The reconstruction method may or may not rely on the synchronization between different sampling channels. The scheme can be implemented easily with optical sampling systems. The optical pulses required for the under-sampling are generated by a combination of an electrical comb generator and an electro-absorption optical modulator

Optical Under-Sampling And Reconstruction Of Sparse Multiband Signals

Backward Rayleigh scattering in optical fibers due to the fluctuations that are "frozen-in" to the fiber during the manufacturing process may limit the performance of optical sensors and bidirectional coherent optical communication systems. In this manuscript we describe a comprehensive model for studying intensity noise induced by spontaneous Rayleigh backscattering in optical systems that are based on self-homodyne detection. Our model includes amplitude and frequency noise of the laser source, random distribution of the scatterers along the fiber, and phase noise induced in fibers due to thermal and mechanical fluctuations. The model shows that at frequencies above about 10 kHz the noise spectrum is determined by the laser white frequency noise. The laser flicker frequency noise becomes the dominant effect at lower frequencies. The noise amplitude depends on the laser polarization. A very good agreement between theory and experiment is obtained for fibers with a length between 500 m to 100 km and for a laser with a linewidth below 5 kHz.

Comprehensive model for studying noise induced by self-homodyne detection of backward Rayleigh scattering in optical fibers.

We study, theoretically and experimentally, intensity noise induced by double Rayleigh scattering in long optical fibers. The results of the theoretical model are compared to experimental results performed with a high-coherence-length laser with a frequency noise spectrum that is dominated by 1/fν noise. Excellent quantitative agreement between theoretical and experimental RF spectra were obtained for frequencies as low as 10 Hz and for fiber lengths between 4 and 45 km. Strong low-frequency intensity noise that is induced by 1/fν frequency noise of the laser may limit the performance of interferometric fiber optic sensors that require high-coherence-length lasers. The intensity noise due to double Rayleigh backscattering can be suppressed by reducing the coherence length of the laser. Therefore, the intensity noise has a complex and non-monotonic dependence on the 1/fν frequency noise amplitude of the laser. Stimulated Brillouin scattering will add a significant noise for input powers greater than about 7 mW for a 30 km length fiber.

Michael Fleyer

Papers

Multirate Synchronous Sampling of Sparse Multiband Signals

Wideband-frequency tunable optoelectronic oscillator based on injection locking to an electronic oscillator.

Optical Under-Sampling And Reconstruction Of Sparse Multiband Signals

Comprehensive model for studying noise induced by self-homodyne detection of backward Rayleigh scattering in optical fibers.

Noise induced in optical fibers by double Rayleigh scattering of a laser with a 1/f^ν frequency noise