On Improved Accuracy Chirp Parameter Estimation using the DFRFT with Application to SAR-based Vibrometry

The Discrete Fractional Fourier Transform (DFRFT) has in recent years, become a useful tool for multicomponent chirp signal analysis. Chirp signals are transformed into spectral peaks in the chirp rate versus center frequency representation, whose coordinates are related to the underlying chirp parameters via a computed empirical peak to parameter mapping incorporated into the Santhanam-Peacock algorithm. In this thesis, we attempt to quantify the accuracy of the DFRFT approach by first studying the discretization error sources that arise from the transitioning of the continuous FRFT to DFRFT. Then, we refine prior work by Ishwor Bhatta to develop analytical expressions for the chirp rate and center frequency parameters instead of the empirical mapping approach. We further study the extensions of this refined DFRFT approach using zero padding, spectral peak interpolation, and chirp-z-transform based zooming. The performance of the refined estimators is compared versus the Cramer-Rao lower bound and shown to asymptotically approach the bound. This refined DFRFT approach is then applied to Synthetic Aperture Radar Vibrometry data from several vibrating targets and the estimated acceleration information and vibration frequencies are shown to be very close to the corresponding ground-truth accelerometer measurements

Interpolated-DFT-Based Fast and Accurate Amplitude and Phase Estimation for the Control of Power

The quality of energy produced in renewable energy systems has to be at the high level specified by respective standards and directives. The estimation accuracy of grid signal parameters is one of the most important factors affecting this quality. This paper presents a method for a very fast and accurate amplitude and phase grid signal estimation using the Fast Fourier Transform procedure and maximum decay sidelobes windows. The most important features of the method are the elimination of the impact associated with the conjugate's component on the results and the straightforward implementation. Moreover, the measurement time is very short - even far less than one period of the grid signal. The influence of harmonics on the results is reduced by using a bandpass prefilter. Even using a 40 dB FIR prefilter for the grid signal with THD = 38%, SNR = 53 dB and a 20-30% slow decay exponential drift the maximum error of the amplitude estimation is approximately 1% and approximately 0.085 rad of the phase estimation in a real-time DSP system for 512 samples. The errors are smaller by several orders of magnitude for more accurate prefilters.Comment: in Metrology and Measurement Systems, 201

Key parameters design for online battery electrochemical impedance tracker

International audienceNew applications in transport and energy storage require the use of Lithium-ion batteries. Advanced battery management systems including electrochemical impedance measurement are studied for the determination of the state of the battery, the prediction of the autonomy, the failure and security management. Taking into account constraints of cost and simplicity, we propose to use the existing electronics of current control and we evaluate the effect of the electronics design on the performance of a frequency evolutionary estimation of the electrochemical impedance. This recursive method relies on a wideband active approach and provides both an accurate estimate of the impedance in the frequency area and a tracking of its temporal variations. Benefits are the limitation of the data memory required and the amount of operations that can be completely carried out by a target such as a microcontroller. We propose a methodology to design the key parameters of electronics in function of the frequency band of interest and the desired accuracy. We highlighted that electronics of conventional BMS can host this tracking algorithm, with analog to digital converters of 10 bits or more, having an analog stage to adapt their dynamics, and that microcontrollers can be enough powerful to perform calculations, both in terms of number of operations and speed of execution. This design strategy has been applied to define a prototyping environment for a BMS based on an ARM microcontroller which is expected to provide the tracking impedance of a battery every 250 ms with less than 0,5 % of error

Single Bin Sliding Discrete Fourier Transform

The conventional method for spectrum analysis is the discrete Fourier transform (DFT), usually implemented using a fast Fourier transform (FFT) algorithm. However, certain applications require an online spectrum analysis only on a subset of M frequencies of an N-point DFT (M<N). In such cases, the use of single-bin sliding DFT (Sb-SDFT) is preferred over the direct application of FFT. The purpose of this chapter is to provide a concise overview of the Sb-SDFT algorithms, analyze their performance, and highlight advantages and limitations. Finally, a technique to mitigate the spectral leakage effect, which arises when using the Sb-SDFT in nonstationary conditions, is presented