Time stretch analog-to-digital converter
Encyclopedia
Time-stretch analog-to-digital converter (TS-ADC) is an analog-to-digital converter
(ADC) system that has the capability of digitizing
very high bandwidth signals
that cannot be captured by conventional electronic
ADCs. Alternatively, it is also known as the Photonic Time Stretch (PTS) digitizer, since it uses an optical
frontend
. It relies on the process of time-stretch, which effectively slows down the analog signal
in time (or compresses its bandwidth) before it can be digitized by a slow electronic ADC.
in laboratories and in high speed data
communications system
s. Most of the ADCs are based purely on electronic circuits, which have limited speeds and add a lot of impairments, limiting the bandwidth of the signals that can be digitized and the achievable signal-to-noise ratio
. In the TS-ADC, this limitation is overcome by time-stretching the analog signal, which effectively slows down the signal in time prior to digitization. By doing so, the bandwidth (and carrier frequency
) of the signal is compressed. Electronic ADCs that would have been too slow to digitize the original signal, can now be used to capture this slowed down signal.
The basic operating principle of the TS-ADC is shown in Fig. 1. The time-stretch processor, which is generally an optical
frontend
, stretches the signal in time. It also divides the signal into multiple segments using a filter
, for example a wavelength division multiplexing (WDM) filter
, to ensure that the stretched replica of the original analog signal segments do not overlap each other in time after stretching. The time-stretched and slowed down signal segments are then converted into digital
samples
by slow electronic ADCs. Finally, these samples are collected by a digital signal processor
(DSP) and rearranged in a manner such that output data is the digital representation of the original analog signal. Any distortion
added to the signal by the time-stretch preprocessor
is also removed by the DSP.
An optical frontend is commonly used to accomplish this process of time-stretch, as shown in Fig. 2. An ultrashort optical pulse
(typically 100 to 200 femtoseconds long), also called a supercontinuum
pulse, which has a broad optical bandwidth, is time-stretched by dispersing
it in a highly dispersive medium (such as a dispersion compensating fiber). This process results in (an almost) linear time-to-wavelength
mapping in the stretched pulse, because different wavelengths travel at different speeds in the dispersive medium. The obtained pulse is called a chirp
ed pulse as its frequency
is changing with time, and it is typically a few nanoseconds long. The analog signal is modulated
onto this chirped pulse using an electro-optic intensity modulator. Subsequently, the modulated pulse is stretched further in the second dispersive medium which has much higher dispersion value. Finally, this obtained optical pulse is converted to electrical domain by a photodetector
, giving the stretched replica of the original analog signal.
For continuous operation, a train of supercontinuum pulses is used. The chirped pulses arriving at the electro-optic modulator should be wide enough (in time) such that the trailing edge of one pulse overlaps the leading edge of the next pulse. For segmentation, optical filters separate the signal into multiple wavelength channels
at the output of the second dispersive medium. For each channel, a separate photodetector and backend
electronic ADC is used. Finally the output of these ADCs are passed on to the DSP
which generates the desired digital output.
The PTS processor is based on specialized analog optical (or microwave
photonic) fiber
links
such as those used in cable TV
distribution. While the dispersion of fiber is a nuisance in conventional analog optical link
s, time-stretch technique exploits it to slow down the electrical waveform
in the optical domain. In the cable TV link, the light source is a continuous-wave (CW) laser
. In PTS, the source is a chirped pulse laser.
In a conventional analog optical link, dispersion causes the upper and lower modulation sidebands, foptical ± felectrical, to slip in relative phase
. At certain frequencies, their beats with the optical carrier
interfere destructively, creating nulls in the frequency response
of the system. For practical systems the first null is at tens of GHz, which is sufficient for handling most electrical signals of interest. Although it may seem that the dispersion penalty places a fundamental limit on the impulse response (or the bandwidth) of the time-stretch system, it can be eliminated. The dispersion penalty vanishes with single-sideband modulation
. Alternatively, one can use the modulator’s secondary (inverse) output port to eliminate the dispersion penalty, in much the same way as two antennas
can eliminate spatial nulls
in wireless
communication (hence the two antennas on top of a WiFi
access point
). Thus, the impulse response
(bandwidth) of a time-stretch system is limited only by the bandwidth of the electro-optic
modulator, which is about 120 GHz—a value that is adequate for capturing most electrical waveforms of interest.
Extremely large stretch factors can be obtained using long lengths of fiber, but at the cost of larger loss—a problem that has been overcome by employing Raman amplification
within the dispersive fiber itself, leading to the world’s fastest real-time digitizer, as shown in Fig. 3. Also, using PTS, capture of very high frequency signals with a world record resolution in 10-GHz bandwidth range has been achieved.
, can also be used to slow down (mostly optical) signals in time. The time-lens concept relies on the mathematical equivalence between spatial
diffraction
and temporal
dispersion, the so called space-time duality
. A lens held at fixed distance from an object produces a magnified image
visible to the eye. The lens imparts a quadratic
phase shift to the spatial frequency
components of the optical waves; in conjunction with the free space propagation
(object to lens, lens to eye), this generates a magnified image. Owing to the mathematical equivalence between paraxial diffraction
and temporal dispersion, an optical waveform can be temporally imaged
by a three-step process of dispersing it in time, subjecting it to a phase shift that is quadratic in time (the time lens itself), and dispersing it again. Theoretically, a focused
aberration-free image is obtained under a specific condition when the two dispersive elements and the phase shift satisfy the temporal equivalent of the classic lens equation. Alternatively, the time lens can be used without the second dispersive element to transfer the waveform’s temporal profile to the spectral domain, analogous to the property that an ordinary lens produces the spatial Fourier transform
of an object at its focal points
.
In contrast to the time-lens approach, PTS is not based on the space-time duality – there is no lens equation that needs to be satisfied in order to obtain an error-free slowed-down version of the input waveform. Time-stretch technique also offers continuous-time acquisition performance, a feature needed for mainstream applications of oscilloscopes.
Another important difference between the two techniques is that the time lens requires the input signal to be subjected to high amount of dispersion before further processing. For electrical waveforms, the electronic devices that have the required characteristics: (1) high dispersion to loss ratio, (2) uniform dispersion, and (3) broad bandwidths, do not exist. This renders time lens not suitable for slowing down wideband electrical waveforms. In contrast, PTS does not have such a requirement. It was developed specifically for slowing down electrical waveforms and enable high speed digitizers.
Analog-to-digital converter
An analog-to-digital converter is a device that converts a continuous quantity to a discrete time digital representation. An ADC may also provide an isolated measurement...
(ADC) system that has the capability of digitizing
Digitizing
Digitizing or digitization is the representation of an object, image, sound, document or a signal by a discrete set of its points or samples. The result is called digital representation or, more specifically, a digital image, for the object, and digital form, for the signal...
very high bandwidth signals
Signal (electrical engineering)
In the fields of communications, signal processing, and in electrical engineering more generally, a signal is any time-varying or spatial-varying quantity....
that cannot be captured by conventional electronic
Electronics
Electronics is the branch of science, engineering and technology that deals with electrical circuits involving active electrical components such as vacuum tubes, transistors, diodes and integrated circuits, and associated passive interconnection technologies...
ADCs. Alternatively, it is also known as the Photonic Time Stretch (PTS) digitizer, since it uses an optical
Optics
Optics is the branch of physics which involves the behavior and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behavior of visible, ultraviolet, and infrared light...
frontend
Front-end and back-end
Front end and back end are generalized terms that refer to the initial and the end stages of a process. The front end is responsible for collecting input in various forms from the user and processing it to conform to a specification the back end can use...
. It relies on the process of time-stretch, which effectively slows down the analog signal
Analog signal
An analog or analogue signal is any continuous signal for which the time varying feature of the signal is a representation of some other time varying quantity, i.e., analogous to another time varying signal. It differs from a digital signal in terms of small fluctuations in the signal which are...
in time (or compresses its bandwidth) before it can be digitized by a slow electronic ADC.
Background
There is a huge demand for very high speed analog-to-digital converters (ADCs), as they are needed for test and measurement equipmentElectronic test equipment
Electronic test equipment is used to create signals and capture responses from electronic Devices Under Test . In this way, the proper operation of the DUT can be proven or faults in the device can be traced and repaired...
in laboratories and in high speed data
Data
The term data refers to qualitative or quantitative attributes of a variable or set of variables. Data are typically the results of measurements and can be the basis of graphs, images, or observations of a set of variables. Data are often viewed as the lowest level of abstraction from which...
communications system
Communications system
In telecommunication, a communications system is a collection of individual communications networks, transmission systems, relay stations, tributary stations, and data terminal equipment usually capable of interconnection and interoperation to form an integrated whole...
s. Most of the ADCs are based purely on electronic circuits, which have limited speeds and add a lot of impairments, limiting the bandwidth of the signals that can be digitized and the achievable signal-to-noise ratio
Signal-to-noise ratio
Signal-to-noise ratio is a measure used in science and engineering that compares the level of a desired signal to the level of background noise. It is defined as the ratio of signal power to the noise power. A ratio higher than 1:1 indicates more signal than noise...
. In the TS-ADC, this limitation is overcome by time-stretching the analog signal, which effectively slows down the signal in time prior to digitization. By doing so, the bandwidth (and carrier frequency
Carrier wave
In telecommunications, a carrier wave or carrier is a waveform that is modulated with an input signal for the purpose of conveying information. This carrier wave is usually a much higher frequency than the input signal...
) of the signal is compressed. Electronic ADCs that would have been too slow to digitize the original signal, can now be used to capture this slowed down signal.
How it works
Optics
Optics is the branch of physics which involves the behavior and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behavior of visible, ultraviolet, and infrared light...
frontend
Front-end and back-end
Front end and back end are generalized terms that refer to the initial and the end stages of a process. The front end is responsible for collecting input in various forms from the user and processing it to conform to a specification the back end can use...
, stretches the signal in time. It also divides the signal into multiple segments using a filter
Filter (signal processing)
In signal processing, a filter is a device or process that removes from a signal some unwanted component or feature. Filtering is a class of signal processing, the defining feature of filters being the complete or partial suppression of some aspect of the signal...
, for example a wavelength division multiplexing (WDM) filter
Filter (optics)
Optical filters are devices which selectively transmit light of different wavelengths, usually implemented as plane glass or plastic devices in the optical path which are either dyed in the mass or have interference coatings....
, to ensure that the stretched replica of the original analog signal segments do not overlap each other in time after stretching. The time-stretched and slowed down signal segments are then converted into digital
Digital
A digital system is a data technology that uses discrete values. By contrast, non-digital systems use a continuous range of values to represent information...
samples
Sampling (signal processing)
In signal processing, sampling is the reduction of a continuous signal to a discrete signal. A common example is the conversion of a sound wave to a sequence of samples ....
by slow electronic ADCs. Finally, these samples are collected by a digital signal processor
Digital signal processor
A digital signal processor is a specialized microprocessor with an architecture optimized for the fast operational needs of digital signal processing.-Typical characteristics:...
(DSP) and rearranged in a manner such that output data is the digital representation of the original analog signal. Any distortion
Distortion
A distortion is the alteration of the original shape of an object, image, sound, waveform or other form of information or representation. Distortion is usually unwanted, and often many methods are employed to minimize it in practice...
added to the signal by the time-stretch preprocessor
Preprocessor
In computer science, a preprocessor is a program that processes its input data to produce output that is used as input to another program. The output is said to be a preprocessed form of the input data, which is often used by some subsequent programs like compilers...
is also removed by the DSP.
An optical frontend is commonly used to accomplish this process of time-stretch, as shown in Fig. 2. An ultrashort optical pulse
Ultrashort pulse
In optics, an ultrashort pulse of light is an electromagnetic pulse whose time duration is of the order of a femtosecond . Such pulses have a broadband optical spectrum, and can be created by mode-locked oscillators...
(typically 100 to 200 femtoseconds long), also called a supercontinuum
Supercontinuum
In optics, a supercontinuum is formed when a collection of nonlinear processes act together upon a pump beam in order to cause severe spectral broadening of the original pump beam. The result is a smooth spectral continuum...
pulse, which has a broad optical bandwidth, is time-stretched by dispersing
Dispersion (optics)
In optics, dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency, or alternatively when the group velocity depends on the frequency.Media having such a property are termed dispersive media...
it in a highly dispersive medium (such as a dispersion compensating fiber). This process results in (an almost) linear time-to-wavelength
Wavelength
In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...
mapping in the stretched pulse, because different wavelengths travel at different speeds in the dispersive medium. The obtained pulse is called a chirp
Chirp
A chirp is a signal in which the frequency increases or decreases with time. In some sources, the term chirp is used interchangeably with sweep signal. It is commonly used in sonar and radar, but has other applications, such as in spread spectrum communications...
ed pulse as its frequency
Frequency
Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...
is changing with time, and it is typically a few nanoseconds long. The analog signal is modulated
Modulation
In electronics and telecommunications, modulation is the process of varying one or more properties of a high-frequency periodic waveform, called the carrier signal, with a modulating signal which typically contains information to be transmitted...
onto this chirped pulse using an electro-optic intensity modulator. Subsequently, the modulated pulse is stretched further in the second dispersive medium which has much higher dispersion value. Finally, this obtained optical pulse is converted to electrical domain by a photodetector
Photodetector
Photosensors or photodetectors are sensors of light or other electromagnetic energy. There are several varieties:*Active pixel sensors are image sensors consisting of an integrated circuit that contains an array of pixel sensors, each pixel containing a both a light sensor and an active amplifier...
, giving the stretched replica of the original analog signal.
For continuous operation, a train of supercontinuum pulses is used. The chirped pulses arriving at the electro-optic modulator should be wide enough (in time) such that the trailing edge of one pulse overlaps the leading edge of the next pulse. For segmentation, optical filters separate the signal into multiple wavelength channels
Channel (communications)
In telecommunications and computer networking, a communication channel, or channel, refers either to a physical transmission medium such as a wire, or to a logical connection over a multiplexed medium such as a radio channel...
at the output of the second dispersive medium. For each channel, a separate photodetector and backend
Front-end and back-end
Front end and back end are generalized terms that refer to the initial and the end stages of a process. The front end is responsible for collecting input in various forms from the user and processing it to conform to a specification the back end can use...
electronic ADC is used. Finally the output of these ADCs are passed on to the DSP
Digital signal processor
A digital signal processor is a specialized microprocessor with an architecture optimized for the fast operational needs of digital signal processing.-Typical characteristics:...
which generates the desired digital output.
Impulse response of the photonic time-stretch (PTS) system
Microwave
Microwaves, a subset of radio waves, have wavelengths ranging from as long as one meter to as short as one millimeter, or equivalently, with frequencies between 300 MHz and 300 GHz. This broad definition includes both UHF and EHF , and various sources use different boundaries...
photonic) fiber
Optical fiber
An optical fiber is a flexible, transparent fiber made of a pure glass not much wider than a human hair. It functions as a waveguide, or "light pipe", to transmit light between the two ends of the fiber. The field of applied science and engineering concerned with the design and application of...
links
Data link
In telecommunication a data link is the means of connecting one location to another for the purpose of transmitting and receiving information. It can also refer to a set of electronics assemblies, consisting of a transmitter and a receiver and the interconnecting data telecommunication circuit...
such as those used in cable TV
Cable television
Cable television is a system of providing television programs to consumers via radio frequency signals transmitted to televisions through coaxial cables or digital light pulses through fixed optical fibers located on the subscriber's property, much like the over-the-air method used in traditional...
distribution. While the dispersion of fiber is a nuisance in conventional analog optical link
Optical link
An optical link is a communications link that consists of a single end-to-end optical circuit. A cable of optical fiber, possibly concatenated into a dark fiber link, is the simplest form of an optical link....
s, time-stretch technique exploits it to slow down the electrical waveform
Waveform
Waveform means the shape and form of a signal such as a wave moving in a physical medium or an abstract representation.In many cases the medium in which the wave is being propagated does not permit a direct visual image of the form. In these cases, the term 'waveform' refers to the shape of a graph...
in the optical domain. In the cable TV link, the light source is a continuous-wave (CW) laser
Laser
A laser is a device that emits light through a process of optical amplification based on the stimulated emission of photons. The term "laser" originated as an acronym for Light Amplification by Stimulated Emission of Radiation...
. In PTS, the source is a chirped pulse laser.
In a conventional analog optical link, dispersion causes the upper and lower modulation sidebands, foptical ± felectrical, to slip in relative phase
Phase (waves)
Phase in waves is the fraction of a wave cycle which has elapsed relative to an arbitrary point.-Formula:The phase of an oscillation or wave refers to a sinusoidal function such as the following:...
. At certain frequencies, their beats with the optical carrier
Carrier wave
In telecommunications, a carrier wave or carrier is a waveform that is modulated with an input signal for the purpose of conveying information. This carrier wave is usually a much higher frequency than the input signal...
interfere destructively, creating nulls in the frequency response
Frequency response
Frequency response is the quantitative measure of the output spectrum of a system or device in response to a stimulus, and is used to characterize the dynamics of the system. It is a measure of magnitude and phase of the output as a function of frequency, in comparison to the input...
of the system. For practical systems the first null is at tens of GHz, which is sufficient for handling most electrical signals of interest. Although it may seem that the dispersion penalty places a fundamental limit on the impulse response (or the bandwidth) of the time-stretch system, it can be eliminated. The dispersion penalty vanishes with single-sideband modulation
Single-sideband modulation
Single-sideband modulation or Single-sideband suppressed-carrier is a refinement of amplitude modulation that more efficiently uses electrical power and bandwidth....
. Alternatively, one can use the modulator’s secondary (inverse) output port to eliminate the dispersion penalty, in much the same way as two antennas
Antenna (radio)
An antenna is an electrical device which converts electric currents into radio waves, and vice versa. It is usually used with a radio transmitter or radio receiver...
can eliminate spatial nulls
Null (radio)
In radio electronics, a null is an area or vector in an antenna's radiation pattern where the signal cancels out almost entirely.This can be an advantage, as nulls in the horizontal plane can be used to protect other transmitters from interference. If not carefully planned however, nulls can...
in wireless
Wireless
Wireless telecommunications is the transfer of information between two or more points that are not physically connected. Distances can be short, such as a few meters for television remote control, or as far as thousands or even millions of kilometers for deep-space radio communications...
communication (hence the two antennas on top of a WiFi
Wi-Fi
Wi-Fi or Wifi, is a mechanism for wirelessly connecting electronic devices. A device enabled with Wi-Fi, such as a personal computer, video game console, smartphone, or digital audio player, can connect to the Internet via a wireless network access point. An access point has a range of about 20...
access point
Wireless access point
In computer networking, a wireless access point is a device that allows wireless devices to connect to a wired network using Wi-Fi, Bluetooth or related standards...
). Thus, the impulse response
Impulse response
In signal processing, the impulse response, or impulse response function , of a dynamic system is its output when presented with a brief input signal, called an impulse. More generally, an impulse response refers to the reaction of any dynamic system in response to some external change...
(bandwidth) of a time-stretch system is limited only by the bandwidth of the electro-optic
Electro-optics
Electro-optics is a branch of technology involving components, devices and systems which operate by modification of the optical properties of a material by an electric field...
modulator, which is about 120 GHz—a value that is adequate for capturing most electrical waveforms of interest.
Extremely large stretch factors can be obtained using long lengths of fiber, but at the cost of larger loss—a problem that has been overcome by employing Raman amplification
Raman amplification
Raman amplification is based on the Stimulated Raman Scattering phenomenon, when a lower frequency 'signal' photon induces the inelastic scattering of a higher-frequency 'pump' photon in an optical medium in the nonlinear regime. As a result of this, another 'signal' photon is produced, with the...
within the dispersive fiber itself, leading to the world’s fastest real-time digitizer, as shown in Fig. 3. Also, using PTS, capture of very high frequency signals with a world record resolution in 10-GHz bandwidth range has been achieved.
Comparison with time lens imaging
Another technique, that involves a time lensLens (optics)
A lens is an optical device with perfect or approximate axial symmetry which transmits and refracts light, converging or diverging the beam. A simple lens consists of a single optical element...
, can also be used to slow down (mostly optical) signals in time. The time-lens concept relies on the mathematical equivalence between spatial
Space
Space is the boundless, three-dimensional extent in which objects and events occur and have relative position and direction. Physical space is often conceived in three linear dimensions, although modern physicists usually consider it, with time, to be part of a boundless four-dimensional continuum...
diffraction
Diffraction
Diffraction refers to various phenomena which occur when a wave encounters an obstacle. Italian scientist Francesco Maria Grimaldi coined the word "diffraction" and was the first to record accurate observations of the phenomenon in 1665...
and temporal
Time
Time is a part of the measuring system used to sequence events, to compare the durations of events and the intervals between them, and to quantify rates of change such as the motions of objects....
dispersion, the so called space-time duality
Dualism
Dualism denotes a state of two parts. The term 'dualism' was originally coined to denote co-eternal binary opposition, a meaning that is preserved in metaphysical and philosophical duality discourse but has been diluted in general or common usages. Dualism can refer to moral dualism, Dualism (from...
. A lens held at fixed distance from an object produces a magnified image
Image
An image is an artifact, for example a two-dimensional picture, that has a similar appearance to some subject—usually a physical object or a person.-Characteristics:...
visible to the eye. The lens imparts a quadratic
Quadratic
In mathematics, the term quadratic describes something that pertains to squares, to the operation of squaring, to terms of the second degree, or equations or formulas that involve such terms...
phase shift to the spatial frequency
Spatial frequency
In mathematics, physics, and engineering, spatial frequency is a characteristic of any structure that is periodic across position in space. The spatial frequency is a measure of how often sinusoidal components of the structure repeat per unit of distance. The SI unit of spatial frequency is...
components of the optical waves; in conjunction with the free space propagation
Wave propagation
Wave propagation is any of the ways in which waves travel.With respect to the direction of the oscillation relative to the propagation direction, we can distinguish between longitudinal wave and transverse waves....
(object to lens, lens to eye), this generates a magnified image. Owing to the mathematical equivalence between paraxial diffraction
Diffraction
Diffraction refers to various phenomena which occur when a wave encounters an obstacle. Italian scientist Francesco Maria Grimaldi coined the word "diffraction" and was the first to record accurate observations of the phenomenon in 1665...
and temporal dispersion, an optical waveform can be temporally imaged
Optical imaging
Optical imaging is an imaging technique.Optics usually describes the behavior of visible, ultraviolet, and infrared light used in imaging.Because light is an electromagnetic wave, similar phenomena occur in X-rays, microwaves, radio waves. Chemical imaging or molecular imaging involves inference...
by a three-step process of dispersing it in time, subjecting it to a phase shift that is quadratic in time (the time lens itself), and dispersing it again. Theoretically, a focused
Focus (optics)
In geometrical optics, a focus, also called an image point, is the point where light rays originating from a point on the object converge. Although the focus is conceptually a point, physically the focus has a spatial extent, called the blur circle. This non-ideal focusing may be caused by...
aberration-free image is obtained under a specific condition when the two dispersive elements and the phase shift satisfy the temporal equivalent of the classic lens equation. Alternatively, the time lens can be used without the second dispersive element to transfer the waveform’s temporal profile to the spectral domain, analogous to the property that an ordinary lens produces the spatial Fourier transform
Fourier transform
In mathematics, Fourier analysis is a subject area which grew from the study of Fourier series. The subject began with the study of the way general functions may be represented by sums of simpler trigonometric functions...
of an object at its focal points
Focus (optics)
In geometrical optics, a focus, also called an image point, is the point where light rays originating from a point on the object converge. Although the focus is conceptually a point, physically the focus has a spatial extent, called the blur circle. This non-ideal focusing may be caused by...
.
In contrast to the time-lens approach, PTS is not based on the space-time duality – there is no lens equation that needs to be satisfied in order to obtain an error-free slowed-down version of the input waveform. Time-stretch technique also offers continuous-time acquisition performance, a feature needed for mainstream applications of oscilloscopes.
Another important difference between the two techniques is that the time lens requires the input signal to be subjected to high amount of dispersion before further processing. For electrical waveforms, the electronic devices that have the required characteristics: (1) high dispersion to loss ratio, (2) uniform dispersion, and (3) broad bandwidths, do not exist. This renders time lens not suitable for slowing down wideband electrical waveforms. In contrast, PTS does not have such a requirement. It was developed specifically for slowing down electrical waveforms and enable high speed digitizers.
Other Resources
- G. C. Valley, “Photonic analog-to-digital converters," Opt. Express, vol. 15, no. 5, pp. 1955–1982, March 2007. http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-15-5-1955
- Photonic Bandwidth Compression for Instantaneous Wideband A/D Conversion (PHOBIAC) project. http://www.darpa.mil/MTO/Programs/phobiac/index.html