Real-Time Fast Fourier Transform Implementation for Analyzing Railway Coaches' Vibrations

International audience

Discrete Fourier transform (DFT) plays an important role in digital signal processing. In this paper, we present a novel optical real-time discrete Fourier transformer with complex-valued outputs, which is enabled by the inverse temporal Talbot effect. In the system, an input pulse train is first quadratically phase-modulated as in an inverse temporal Talbot system and then split into two channels. In the first channel, the pulse train is further amplitude-modulated pulse-by-pulse by a discrete data sequence to be transformed. In the second channel, a reference signal modulates the pulse train, which is for removing the residual quadratic phase profile in the output pulse train. The pulse trains in the two channels propagate through a shared dispersion medium with a proper dispersion value determined by the inverse temporal Talbot effect. A 90-degree optical hybrid and two balanced photodetectors are employed to retrieve the real and imaginary parts of the DFT results. In this scheme, the pulse repetition rate of the output pulse train is equal to the input one. In addition, we present a full theoretical framework to explain exactly the DFT relationship. We also demonstrate that the input data sequence can be complex-valued with the help of an I/Q modulator.

High precision length measurement by means of multi-sensory laser-feedback interferometry

We present a novel velocity and length measuring instrument based on laser-feedback interferometry. Uncertainties down to 10<SUP>-4</SUP> in length measurement of moving materials can be achieved by combining the measurement signals of two separate sensors. Furthermore the dependence on parameters like the angle of incidence can be eliminated mathematically and no accurate alignment is required. The signal processing unit utilizes a real-time fast Fourier transformation. Thus good signal to noise ratios and very accurate measurements of most scattering surfaces used in industrial production are possible.

Narrowband jamming of a spread spectrum signal can be filtered out in the frequency domain using acoustic surface wave convolvers as real time Fourier transformers. This is accomplished by employing modulated chirp signals as inputs. The particular frequency range in which the jammer occurs can be removed from the Fourier transformed signal by using a d.c. pulse and a balanced mixer. These concepts are discussed and experimental results demonstrating the use of the device as a Fourier transformer (with 110 MHz center frequency, 25 MHz bandwidth, and 14 μsec interaction range and 220 MHz center frequency, 50 MHz bandwidth and 14 μsec interaction range) are presented. The performance of the spread spectrum receiver using either pseudonoise or Barker codes and different jammers is discussed.

We propose and experimentally demonstrate a photonic technique for Fourier transformation of broadband optical spectrum and compression of time-bandwidth product (TBP) simultaneously. Conventionally, an optical spectrum could be Fourier transformed based on the so-called time-spectrum convolution technique with a linearly dispersive delay line. In this paper, a nonlinearly dispersive delay line is implemented by the convolution of an input optical spectrum in the spectral domain with a nonlinearly chirped temporal sinusoidal waveform in the time domain. By specially designing the chirp rate variation of the temporal waveform, an anamorphic Fourier transformation functionality is realized to compress the TBP of output waveform. The key feature of this paper is that it is the first time to our knowledge to carry out the Fourier transformation of an optical spectrum with TBP compression. In addition, since the dispersive delay line could be programmable with high resolution, this technique is adaptable for different optical spectra and realizable for a reconfigurable TBP compression ratio. Experimental results show that the TBP compression ratio is programmable from 1.6 to 3 by engineering the nonlinear dispersive delay line. After reconstructing the Fourier transform of optical spectrum from the output waveforms, the error rate of the recovered waveform is calculated quantitatively. Also, we discussed and proved the possibility to recover the input spectrum only with intensity information. This proposed method is promising to break the big data limitation of the conventional real-time optical spectrum Fourier transformation technique based on the TBP engineering for data compression.

A system is described which uses a real-time fast Fourier transform (FFT) spectrum analyzer to monitor radio interference near 408 MHzs occurring at a radio observatory. Direction of arrival, frequency, intensity, and time of occurrence are recorded under the control of a microcomputer. A sensitive receiver can be connected to any one of eight directional antennas to establish direction of arrival. The receiver output is digitized to 8 b, and analyzed by the FFT spectrum analyzer which has a real-time bandwidth of 0.5 MHz. A total bandwidth of 20 MHz is analyzed in segments of 0.4 MHz. The analyzer uses the modified periodogram method developed by P.D. Welch (IEEE Trans. Audio Electroacoust., vol.AU-15, p.70-3, June 1967), and a Kaiser-Bessel windowing function is applied to ensure low sidelobes. Dynamic range is 40 dB, and the interference monitor obtains high sensitivity to very weak interfering signals by time averaging. Several general design principles which arise out of certain constraints are elucidated. Some new results are presented concerning the detectability of small signals by FFT processors.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A frequency-hopping signal measurement scheme based on real-time photonic Fourier transform is proposed and demonstrated. Through optical frequency-to-time mapping, real-time spectrum analysis of wideband high-speed frequency-hopping signal can be achieved without additional digital signal processing. In the experiment, the wideband and multiple frequency-hopping signals with 100-ns frequency-hopping period and 4–40 GHz frequency range are verified, respectively.

: This technical report summarizes the results of the research we have been engaged in regarding the use of surface acoustic wave devices in direct sequence spread spectrum receivers. The heart of this research has been the use of the device as a real-time Fourier transformer. A system of this type is sometimes referred to as a compressive receiver, and our use of the system has been primarily as a means to implement a narrowband interference rejection filter. In addition, we have studied many other topics such as rapid acquisition, Hilbert transform generation, etc. and these topics are all overviewed in this report. (Author)

We propose a photonics-assisted equivalent frequency sampling (EFS) method to analyze the instantaneous frequency of broadband linearly frequency modulated (LFM) microwave signals. The proposed EFS method is implemented by a photonic scanning receiver, which is operated with a frequency scanning rate slightly different from the repetition rate of the LFM signals. Compared with the broadband LFM signal analysis based on temporal sampling, the proposed method avoids the use of high-speed analog to digital converters, and the instantaneous frequency acquisition realized by frequency-to-time mapping is also simplified since real-time Fourier transformation is not required. Feasibility of the proposed method is verified through an experiment, in which frequency analysis of Kα-band LFM signals with a bandwidth up to 3 GHz is demonstrated with a moderate sampling rate of 100 MSa/s. The proposed method is highly demanded for analyzing the instantaneous frequency of broadband LFM signals used in radar and electronic warfare systems.

An ultrafast user localization scheme in beam steering optical wireless communication based on real-time Fourier Transform is demonstrated. All-optical dispersive operation enables ultrafast and real-time user-specific wavelength identification overcoming bottleneck in digital signal processing.

A microwave angle-of-arrival (AOA) measurement system based on the photonic real-time Fourier transformation (RTFT) is proposed and demonstrated. In the proposed system, photonic RTFT is implemented utilizing the temporal-spectrum convolution system, which is composed by an optical pulse source, an electro-optical modulator and a pair of dispersive elements with complementary dispersion values. The time delay of the linearly frequency-modulated (LFM) signals can be obtained, which are used to calculate the time-difference-of arrival (TDOA) and the corresponding AOA. A proof-ofconcept experiment is taken. The AOA measurement range from 25° to 155° is achieved with a measurement error of less than 3.4°. In this scheme, the problem of phase ambiguity in traditional AOA measurement systems is overcome.

The importance of having an efficient Fast Fourier Transform (FFT) implementation is universally recognized as one of the key enablers for the development of new and more powerful signal processing algorithms. In the field of telecommunications, one of its most recent applications is the Orthogonal Frequency Division Multiplexing (OFDM) modulation technique, whose superiority is recognized and endorsed by several standards. However, the horizon of standards is so wide and heterogeneous that a single FFT implementation hardly satisfies them all. In order to have a reusable, easily extensible and reconfigurable solution, most of the baseband processing is moving towards a software implementation: to this end several new Digital Signal Processor (DSP) architectures are emerging, each with its own set of differentiating properties. Within this context, we propose a software implementation of the FFT on the Block Processing Engine (BPE) platform. Several implementations have been investigated, ranging from a single instruction based approach, to others employing several instructions either in parallel or in pipeline. The outcome is a flexible set of solutions that leaves degrees of freedom in terms of computational load, achievable throughput and power consumption. The proposed implementations closely approach the theoretical clock cycles expected by dedicated hardware counterpart, thus making it a concrete alternative.

Recent developments and applications of system identification methods for the reversed-field pinch (RFP) machine EXTRAP T2R have yielded plasma response parameters for decoupled dynamics. These data sets are fundamental for a real-time implementable fast Fourier transform (FFT) decoupled discrete-time fixed-order strongly stabilizing synthesis as described in this work. Robustness is assessed over the data set by bootstrap calculation of the sensitivity transfer function worst-case -gain distribution. Output tracking and magnetohydrodynamic mode m = 1 tracking are considered in the same framework simply as two distinct weighted traces of a performance channel output-covariance matrix as derived from the closed-loop discrete-time Lyapunov equation. The behaviour of the resulting multivariable controller is investigated with dedicated T2R experiments.

The paper considers and analyzes the method of measuring the noise characteristics of electronic circuits and devices based on data collection by a digital oscilloscope with a built-in Fourier transform. The measurement process methodology and its analysis are demonstrated when determining the noise characteristics of industrial resistors. This includes, in particular, thermal (white) noise, which is the predominant type of resistor noise. The work includes an overview of the noise properties of resistors and existing measurement methods, as well as an understanding of the theory of such measurements. To determine the sources of noise in industrial resistors, a real-time fast Fourier transform (FFT) of the signal was run on an oscilloscope. Thermal (white) noise spectra were determined using the FFT tool using a total number of 212 points.. However, it is difficult to make any recommendations as to which setup should be used for a particular resistor type or technology, as for most setups the noise level is unknown and only a few measurement results are available. The ratio of the average value of the power spectral density (PSD) of thermal noise in the frequency range of measurements to its calculated theoretical value based on the ohmic rating of the measuring coal industrial resistors was estimated.