US 20110079720 A1 Abstract System and method for blind echo cancellation in a received terahertz signal in a pulsed terahertz system for imaging or spectroscopy. Blind signal processing methods estimate the impulse response of the reflection mechanism and do not require a reference measurement to be taken. The reference signal may be recovered using a successive approach wherein the reference is first estimated using cross-correlation with the received signal and the received signal is represented as a function of the reference signal. For each successive echo, the calculated echo may be subtracted from the received signal and then the estimate of the reference signal is refined. Using an analytical approach, the parameters of a transfer function modeling the reflection mechanism may be estimated by optimizing a cost function.
Claims(17) 1. A method for canceling echoes in a terahertz signal, the method comprising the steps of:
receiving a terahertz signal containing echoes; estimating a reference signal from the received signal; calculating the echoes as a function of the reference signal; for at least one of the successive echoes,
subtracting the calculated echo from the received signal to form a refined reference signal; and
re-calculating the echoes as a function of the refined reference signal.
2. The method of estimating the time-shift and amplitude of each echo as a function of the corresponding reference signal.
3. The method of 4. The method of 5. The method of 6. The method of 7. The method of 8. The method of 9. A method for canceling echoes in a terahertz signal, the method comprising the steps of:
receiving a terahertz signal containing echoes; calculating a reference signal as a function of the received signal; and estimating system parameters of a reflection mechanism by minimizing the energy of the calculated reference signal; and deconvolving the received signal with an inverse transfer function using the system parameters to remove at least one of the echoes. 10. The method of {circumflex over (x)} _{ref}(t)=X _{in} −βX _{in}(t−2d)where β is a system parameter representing the gain and d is a system parameter representing the time-shift.
11. The method of 12. The method of where n is the refractive index, L is the thickness of the slab and f
_{samp }is the sampling frequency.13. A system for canceling echoes in a terahertz signal, the system comprising:
a terahertz signal receiver for receiving a terahertz signal containing echoes; an estimator for estimating a reference signal from the received signal; an echo subtracter for subtracting an echo from the received signal to form a refined reference signal; and a signal calculator for calculating the echoes as a function of the reference signal, and for calculating the echoes as a function of the refined reference signal. 14. The system of 15. The system of 16. The system of 17. The system of Description The present invention relates to terahertz spectroscopy and imaging systems, and in particular, to systems and methods for processing terahertz signals to reduce the effect of echoes. Terahertz radiation is electromagnetic waves that have a frequency between 100 GHz and 30 THz, lying between the infrared and microwave parts of the spectrum. The radiation is non-ionizing and can penetrate most non-metallic objects but is absorbed by polar materials and liquids. Consequently, terahertz technology provides a number of spectroscopy and imaging applications, and is a fast-growing field. Terahertz pulses are distorted by passing though various materials including gases, liquids, and solids. It is well known that different materials alter the terahertz waves differently, depending on the material and the frequency content of the signal. It is the purpose of terahertz signal processing to detect and classify these changes. Depending on the application, some of the changes are undesired and must be compensated for. In terahertz signal processing a detected signal often contains several echoes of the same signal due to reflections of the signal. Depending on the setup, reflections can come from sample edges, wave-guide ends, the terahertz source structure, the terahertz detector structure or any of a number of other sources. In some cases, multiple reflection mechanisms may be combined. The simplest way to handle the reflection mechanisms in terahertz signal processing is to time-gate the signal before the occurrence of any echoes due to the reflections. However, by time-gating the signal, the frequency resolution of the signal is also decreased since it is inversely proportional to the time-length of the signal. Reduced frequency resolution results in a decreased image resolution in imaging applications, and in spectroscopy applications, may result in failing to detect spectroscopic indicators with a narrow frequency response. Other approaches to minimize the echo effect have attempted to solve the problem with the hardware setup. However, due to the inherent nature of terahertz systems this approach is practically impossible, or at the least, costly in terms of the system complexity and terahertz signal quality. Presently, the most practical solution involves taking an extra reference measurement without the sample to be measured present. The reference measurement is then differentiated or deconvolved from the main measurement to remove the reflection effects. However, in practice this may not be possible or easily accomplished. For example, if the reflection is coming from the sample to be measured, one could remove the sample and replace it with another object which generates exactly the same reflection effect. In spectroscopy, where the sample is unknown, or in cases where the sample is structurally complex, it is either impossible or very difficult to replace the sample without introducing other effects. Taking an extra reference measurement also does not account for the reflections within the structures of the terahertz emitter and detectors themselves. Also, temperature fluctuations, change in beam position, or other factors affecting laser stability between the reference measurement and sample measurement can introduce errors. Accordingly, there is a need for improved signal processing in terahertz spectroscopy and imaging applications that can remove the echo effects without using a measured reference signal. The present invention provides systems and methods of removing the adverse effect of reflections in a received terahertz signal without using a measured reference signal. The removal of the echo effect from the reflections without the use of a measured reference signal may be referred to as blind echo cancellation. The use of blind echo cancellations methods may be applied in applications where taking a measured reference signal is either impractical or may be inaccurate. Using blind echo cancellation methods also allows a larger time period of the signal to be analyzed, which in turn also allows a higher frequency resolution of the signal to be analyzed. This signal processing approach is beneficial in many applications, including imaging and spectroscopy applications. According to a first aspect of the invention, there is provided a method for canceling echoes in a terahertz signal comprising the steps of receiving a terahertz signal containing echoes; estimating a reference signal from the received signal; calculating the echoes as a function of the reference signal; and for at least one of the successive echoes, subtracting the calculated echo from the received signal to form a refined reference signal; and re-calculating the echoes as a function of the refined reference signal. The step of calculating the echoes and re-calculating the echoes comprises estimating the time-shift and amplitude of each of the echoes as a function of the corresponding reference signal. The step of subtracting the calculated echo may be repeated until a threshold is reached. The threshold may include defining the refined reference signal over a defined portion of the echo period; the number of recalculation iterations performed; the difference between the refined reference signal and the prior calculation of the refined reference signal. The received signal may be expressed as a sum of scaled, time-shifted reference signals. The reference signal may also be estimated using cross-correlation with the received terahertz signal. According to another aspect of the invention, there is provided a method for canceling echoes in a terahertz signal comprising the steps of receiving a terahertz signal containing echoes; calculating a reference signal as a function of the received signal; and estimating system parameters of a reflection mechanism by minimizing the energy of the reference signal. The system parameters may then be used in an inverse transfer function that may be used in a deconvolution with the received signal to remove at least one of the echoes. According to another aspect of the invention, there is provided a system for canceling echoes in a terahertz signal, the system comprising a terahertz signal receiver for receiving a terahertz signal containing echoes; an estimator for estimating a reference signal from the received signal; an echo subtracter for subtracting an echo from the received signal to form a refined reference signal; and a signal calculator for calculating the echoes as a function of the reference signal, and for calculating the echoes as a function of the refined reference signal. The reference signal may be modeled as a function of the received signal and the system parameters, wherein an attenuated and time-shifted received signal is subtracted from the received signal to remove the effects of the echo. The transfer function used to model the terahertz transmission may be based on a single slab medium in a vacuum. A preferred embodiment of the present invention will now be described in detail with reference to the drawings, in which: Referring to The laser source The signal processor The reflection mechanism may be modeled as an input-output system, where the input is the desired (reference) signal, and the output is the signal with echoes. Without considering the material dispersion of the sample, the system impulse response can be shown as: where δ(t) is the unit impulse function. This means that the output signal may be modeled as: wherein α Using the above model, the reference signal x Therefore, part of the reference signal related to this time interval may be recovered from the received signal. In the next interval between T Using an initial estimate of the reference signal based on the interval between T Due to dispersion and other effects, the time period of the echoes may be longer than the time period of the initial estimate of the time period of the reference signal (i.e. T For successive echoes, the echo removal process is similar to that shown for Echo Now referring to In the next step wherein α Next, in step In step If the determination in step If additional echoes are to be processed, the next echo period may be selected in step In some embodiments, the step Finally, in step Another way to recover the reference signal is to estimate the impulse response of the terahertz system and then deconvolving this with the received signal in the time or frequency domain to recover the reference signal. This approach may be referred to as an analytical blind echo cancellation approach. Modeling the sample as a single slab medium in a vacuum, we can represent the Z-transform of the transfer function as follows:
where n and L are the refractive index and thickness of the slab, respectively, and f Most of the reflection mechanisms found in terahertz systems may be modeled as above. The model may be considered a first-order reflection mechanism. Now referring to If the reflection system in the terahertz system may be modeled by the transfer function h Since the gain and the time-shift are known, they may be incorporated into the result if necessary. Then, an estimate of the reference signal may be recovered through the following convolution with the Z-transform of the received signal: where {tilde over (x)} Assuming that the analytical BEC algorithm applies, the reference signal may be calculated as follows:
In the ideal case, {circumflex over (d)}=d and {circumflex over (β)}=β, such that {circumflex over (x)} To find the optimal values of {circumflex over (d)} and {circumflex over (β)} in a blind fashion, a cost function may be used in the following form: For example, some embodiments of the invention may use the energy of {circumflex over (x)} This estimate takes into account only the first echo, but other embodiments may use more sophisticated functions to cancel the effect of the other echoes. In most cases, canceling the subsequent echoes may only provide marginal improvement in the signal quality. Next, in order to find the best calculation of the reference signal, the following optimization problem may be solved to find the optimal values of {circumflex over (d)} and {circumflex over (β)}:
Now referring to Next, in step Now referring to The signal receiver The function of the reference signal estimation block Next, the echo subtraction block The present invention has been described here by way of example only. Various modification and variations may be made to these exemplary embodiments without departing from the spirit and scope of the invention, which is limited only by the appended claims. Classifications
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