Comparative Study of AC Signal Analysis Methods for Impedance Spectroscopy Implementation in Embedded Systems

To calculate scattering of a vegetation field consisting of a large number of plants, an improved fast version of the hybrid method (FHM) combining fast multiple scattering theory (FMST) and a numerical electromagnetic approach has been developed. In the HM, we use a library of T-matrices and the Foldy–Lax (FL) equation to calculate the electromagnetic field interactions outside of the cylinders enclosing the individual plants. To improve CPU time and memory requirements, the FL equation is solved by a triplet of fast Fourier transforms (FFTs) consisting of two FFTs solving 2-D FFTs of spatial distribution of plants and one 1-D FFT for solving the transformation of the order of cylindrical waves in the translation addition theorem. The triple FFTs minimize the CPU time and the memory requirement for computing translation addition matrix, which has been the bottleneck of large-scale simulations in the HM. To account for nonperiodic distribution of scatterers in a corn field, the premultiplication and the postmultiplication processes were applied to the FHM. The proposed method is validated at L-band (1.4 GHz) for 100 corn plants of height 1.25 m occupying an area of 9.54 by 9.54 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text{m}^{2}$ </tex-math></inline-formula> . On a standard laptop, the CPU time is less than 6 min and the memory consumption is less than 710 Mbytes. The CPU time and the memory requirements are orders of magnitude more efficient than those required for solving the problem with a commercial software or using the previous version of the HM.

The Discrete Fourier Transform (DFT), which can be calculated efficiently by the Fast Fourier Transform (FFT), is one of the most commonly used tools for frequency estimation of a multi-frequency exponential signal. However, the performance of the FFT is inherently affected by spectral leakage when non-coherent sampling occurs. The Chirp-Z Transform (CZT), which can refine the spectrum to the narrowband range of the source signal accurately, can be generalized to a special form of DFT. This paper proposes a CZT based algorithm which can estimate frequencies of the multi-frequency exponential signal accurately. In our method, the CZT bin, as a nonlinear equation, is firstly used to describe the correspondence among the frequencies, amplitudes, phases and the observed spectrum. Then, the above nonlinear equation is rewritten as a linear equation with unknown frequencies. We further extend the proposed method to the Discrete-time Fourier Transform (DTFT), zero-padding FFT and DFT, which are the special cases of the CZT. We also give the derivation procedure of theoretical variance of our method. In our method, the spectrum leakage is fully considered as useful information to establish the linear equation set. Therefore, it can estimate the frequencies of multi-frequency exponential signal with high accuracy. Simulation results verify the performance of the proposed method.

Optical interferometry plays an important role in the topographical surface measurement and characterization in precision/ultra-precision manufacturing. An appropriate surface reconstruction algorithm is essential in obtaining accurate topography information from the digitized interferograms. However, the performance of a surface reconstruction algorithm in interferometric measurements is influenced by environmental disturbances and system noise. This paper presents a comparative analysis of three algorithms commonly used for coherence envelope detection in vertical scanning interferometry, including the centroid method, fast Fourier transform (FFT), and Hilbert transform (HT). Numerical analysis and experimental studies were carried out to evaluate the performance of different envelope detection algorithms in terms of measurement accuracy, speed, and noise resistance. Step height standards were measured using a developed interferometer and the step profiles were reconstructed by different algorithms. The results show that the centroid method has a higher measurement speed than the FFT and HT methods, but it can only provide acceptable measurement accuracy at a low noise level. The FFT and HT methods outperform the centroid method in terms of noise immunity and measurement accuracy. Even if the FFT and HT methods provide similar measurement accuracy, the HT method has a superior measurement speed compared to the FFT method.

Diffraction, Fourier Optics and Imaging

Historically, computationally-intensive data processing for space-borne instruments has heavily relied on ground-based computing resources. But with recent advances in functional densities of Field-Programmable Gate-Arrays (FPGAs), there has been an increasing desire to shift more processing on-board; therefore relaxing the downlink data bandwidth requirements. Fast Fourier Transforms (FFTs) are commonly-used building blocks for data processing applications, with a growing need to increase the FFT block size. Many existing FFT architectures have mainly emphasized on low power consumption or resource usage; but as the block size of the FFT grows, the throughput is often compromised first. In addition to power and resource constraints, space-borne digital systems are also limited to a small set of space-qualified memory elements, which typically lag behind the commercially available counterparts in capacity and bandwidth. The bandwidth limitation of the external memory creates a bottleneck for a large, high-throughput FFT design with large block size. In this paper, we present the Multi-Pass Wide Kernel FFT (MPWK-FFT) architecture for a moderately large block size (32K) with considerations to power consumption and resource usage, as well as throughput. We will also show that the architecture can be easily adapted for different FFT block sizes with different throughput and power requirements. The result is completely contained within an FPGA without relying on external memories. Implementation results are summarized.

Phase‐shift migration techniques that attempt to account for lateral velocity variations make substantial use of the fast Fourier transform (FFT). Generally, the Hermitian symmetry of the complex‐valued Fourier transform causes computational redundancies in terms of the number of operations and memory requirements. In practice a combination of the FFT with the well‐known real‐to‐complex Fourier transform is often used to avoid such complications. As an alternative means to the Fourier transform, we introduce the inherently real‐valued, non‐symmetric Hartley transform into phase‐shift migration techniques. By this we automatically avoid the Hermitian symmetry resulting in an optimized algorithm that is comparable in efficiency to algorithms based on the real‐to‐complex FFT. We derive the phase‐shift operator in the Hartley domain for migration in two and three dimensions and formulate phase shift plus interpolation, split‐step migration, and split‐step double‐square‐root prestack migration in terms of the Hartley transform as examples. We test the Hartley phase‐shift operator for poststack and prestack migration using the SEG/EAGE salt model and the Marmousi data set, respectively.

The Discrete Fourier Transform (DFT) is a mathematical procedure that stands at the center of the processing that takes place inside a Digital Signal Processor. It has been known and argued through the literatures that the Fast Fourier Transform (FFT) is useless in detecting a specific frequency in a monitored signal because most of the computed results are ignored. In this paper we will present an efficient FFT based method to detect specific frequencies in a monitored signal which is compared to the most frequently used method ¿the Goertzel's Algorithm¿. Parallel implementation structure show a fast computation method compared to the Goertzel's algorithm. Computational speedup gains of r using radix-r butterfly are shown.

The Discrete Fourier Transform (DFT) is a mathematical procedure that stands at the center of the processing inside a digital signal processor. It has been widely known and argued in relevant literature that the Fast Fourier Transform (FFT) is useless in detecting specific frequencies in a monitored signal of length N because most of the computed results are ignored. In this paper, we present an efficient FFT-based method to detect specific frequencies in a monitored signal, which will then be compared to the most frequently used method which is the recursive Goertzel algorithm that detects and analyses one selectable frequency component from a discrete signal. The proposed JM-Filter algorithm presents a reduction of iterations compared to the first and second order Goertzel algorithm by a factor of r, where r represents the radix of the JM-Filter. The obtained results are significant in terms of computational reduction and accuracy in fixed-point implementation. Gains of 15 dB and 19 dB in signal to quantization noise ratio (SQNR) were respectively observed for the proposed first and second order radix-8 JM-Filter in comparison to Goertzel algorithm.

Chapter 10 - DSP System Design: Dual-Tone Multi-Frequency (DTMF) Signaling

CHAPTER 10 - DSP System Design: Dual Tone Multi-Frequency (DTMF) Signaling

The reconfigurable computing (RC) aims to combine the flexibility of General-Purpose Processor (GPP) with performance of Application Specific Integrated Circuits (ASIC). There are several architectures proposed since RC’s inception in 1960s, but all have failed to become mainstream. The main factor preventing RC to become common practice is its requirement for implementers of algorithms (programmers) to be familiar with hardware design. In RC, a hardened processor cooperates with a dynamic reconfigurable Hardware Accelerator (HA) which is implemented on Field-Programmable Gate Array (FPGA). The HA implements crucial software kernel on hardware to increase performance and its design demands digital circuit expertise. In this paper a novel RC architecture is proposed that keeps the decades old programming practices intact while harnessing the power of HA. The architecture uses LLVM compiler infrastructure to receive an algorithm and then outputs the equivalent machine language, it then finds the most frequent instruction pairs and generates equivalent RC circuit called “Miniature Accelerator (MA)”. The instruction pairs are dynamically removed from pipeline and MA computed result replaces them in parallel. To demonstrate the concept the Fast Fourier Transform (FFT) algorithm which is core Digital signal processing (DSP) kernel is written in C and then executed on an ARM Cortex-M0. The execution of FFT function is improved by 14.12%. The proposed adaptive processor is fully backward compatible, compilation is automated, and no modification of exiting software or established programming paradigms is required.

In this study, the issue of phase discontinuity in multiple-input–multiple-output (MIMO) radar systems is analysed and described in detail, together with an efficient way for processing MIMO radar data by means of discrete-time Fourier transform (DFT) fast Fourier transform (FFT). In particular, here it is shown that the phase history of a point target illuminated by an MIMO radar shows a number of discontinuities because of the geometry of the antennas. It is also shown that these become negligible in the far range, whereas they represent an issue in the short range if not compensated properly because, in turn, they prevent DFT-based algorithms correctly focusing the received signals. It is shown that data from MIMO radars have to be pre-processed in order to allow an efficient DFT-based focalisation. For this purpose, together with a theoretical description of the problem, a sub-optimal algorithm is presented, discussed and tested against real data gathered by the Joint Research Centre (JRC) MIMO radar system.

We present a new method for numerical propagation through Lyot-style coronagraphs using finite occulting masks. Standard methods for coronagraphic simulations involve Fast Fourier Transforms (FFT) of very large arrays, and computing power is an issue for the design and tolerancing of coronagraphs on segmented Extremely Large Telescopes (ELT) in order to handle both the speed and memory requirements. Our method combines a semi-analytical approach with non-FFT based Fourier transform algorithms. It enables both fast and memory-efficient computations without introducing any additional approximations. Typical speed improvements based on computation costs are of about ten to fifty for propagations from pupil to Lyot plane, with thirty to sixty times less memory needed. Our method makes it possible to perform numerical coronagraphic studies even in the case of ELTs using a contemporary commercial laptop computer, or any standard commercial workstation computer.

BPA has a real-time phasor measurement system with more than 22 PMUs installed in substations feeding data to a control center. To assure the quality and accuracy of the measurement, BPA has developed an extensive test plan for PMUs. From simple beginnings of basic tests, these procedures have continually evolved with both the variety of PMU equipment and applications for which the data was used. Current test methods under development are aimed for more comprehensive characterization of PMU measurement and test process simplification. Basic test procedures assure steady state accuracy of magnitude, phase, and frequency measurement. Dynamic testing includes step changes to magnitude, phase and frequency as well as signals modulated on the power (60 Hz) waveform. These tests characterize speed of response, reproduction of measured values, and rejection of interference. All these effects have an analogy in the actual power system, so the results can be reasonably applied. Developing methods simplify the generation of test signals and analysis of results. A goal is to test for all measurement aspects that may create a problem and correct these before deployment. In addition, determining characteristics that can be used to adjust all measurements to the same basis will enable the performance of precision analysis regardless of the make or model of PMUs that are making the measurements.

The paper is devoted to theoretical and experimental investigation of specific influence of the randomness onto the accuracy of phase measurements made with the help of ground based noise waveform synthetic aperture radar. Noise waveform used in this system ensures high electromagnetic compatibility and interference immunity. Random nature of probing signals used in noise radars leads to randomness of the output signals and preserving residual fluctuation in the images generated. These random residuals along with the external noise introduce influence onto the overall accuracy of the phase measurements in Noise Radar. It has been shown a good agreement between theory and experiment.