An Observer-Based Adaptive Fourier Analysis [Tips &amp; Tricks]

Sujbert, László; Simon, Gyula; Peceli, G.

doi:10.1109/msp.2020.2982167

Cited by 11 publications

(9 citation statements)

References 13 publications

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“…• Architecture: radix-2, radix-4, or pipelined streaming • Transform length: 2 3 − 2 16 • Data representation: fixed or floating point • Data handling: scaling and rounding • Output ordering • Resource usage The goal of the applied FFT design is to aim for the highest achievable processing speed. This way the best comparison can be made with the processing speeds of the oSDFT structures.…”

Section: Fft Ipmentioning

confidence: 99%

“…This structure is highly stable and insensitive to numerical precision errors due to its control feedback loop [14]. Moreover, its added benefit is that it can be used efficiently for various applications, such as frequency estimation [15], [16], system identification [17] or digital filtering [13]. The disadvantage of this structure is that all the frequency bins -not just the ones of interest -must be calculated, as an observer first deconstructs the signal then reconstructs an estimation which is also used for the global control feedback loop.…”

Section: Introductionmentioning

confidence: 99%

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FPGA Realization of the Observer-Based Sliding Discrete Fourier Transform

2022

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Discrete Fourier transform (DFT) is a widely used method of signal analysis in digital signal processing. The DFT converts a signal from time domain to frequency domain for further processing. For fixed-size sliding window applications of the DFT, the observer-based sliding DFT (oSDFT) algorithm has been shown to be stable, accurate, and theoretically faster, than the well-known block-oriented fast Fourier transforms (FFT). However, no hardware implementation of the oSDFT has been proposed yet. In this paper, a hardware optimized implementation of two variants of the algorithm for FPGA is presented. Such implementation is compared with the Xilinx FFT Intellectual Property in terms of processing speed and hardware requirements. The structure is implemented in Verilog HDL using Vivado IDE, with the aim of maximizing the processing speed and minimizing the required hardware resources. The analysis of the FPGA-based oSDFT and FFT circuits in a sample-by-sample processing scenario, reveals, that the latency and energy usage of the oSDFT are smaller relative to the FFT. The latency and energy usage per sample processed of the implemented structures are up to 9 and 10 times lower than those of FFT respectively. The required resources for these methods are also presented and analyzed.

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Section: Fft Ipmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

FPGA Realization of the Observer-Based Sliding Discrete Fourier Transform

2022

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“…A previously published sliding spectrum analysis network cleverly implements a bank of N paths where each path is equivalent to the complex resonator in Figure 2 tuned to a frequency of 2k/N radians/sample [11,12]. The value for k in each path are one of the integers in the set k  {1,2,...,N-1}.…”

Section: Comparison With Previously Published Sdft Algorithmsmentioning

confidence: 99%

“…Other than increasing k and N, at the cost of additional computations alternate processing techniques can be effective in reducing the unwanted non-integer k SDFT output magnitude fluctuations. Those techniques are: 1) performing simple unity-gain lowpass filtering of the Figure 7(b) output magnitude samples; 2) implementing time-domain windowing of the input signal by means of frequency-domain convolution [1]; 3) if a real-valued input signal is a single tone we can convert that input signal to a positive-frequency only analytic signal, prior to SDFT processing, using a Hilbert transform network [14] (note that unlike the other listed options, this Hilbert option will not reduce the fluctuations caused by additional input frequency components); and 4) using the oSDFT networks in [11,12] will eliminate unwanted signal magnitude tracking fluctuations because their sinc frequency functions stretch rather than shift to provide complete attenuation of a real-valued input signal's negative-frequency spectral components and a periodic input signal's harmonics.…”

Section: Integer K and Non-integer K Sdft Signal Tracking Examplesmentioning

confidence: 99%

Improvements to the Sliding Discrete Fourier Transform Algorithm [Tips & Tricks]

Lyons¹,

Howard

2021

IEEE Signal Process. Mag.

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The IEEE Publication Services & Products Board (PSPB) last revised its Operations Manual Section 8.1.9 on Electronic Information Dissemination (known familiarly as "author posting policy") on 7 December 2012.PSPB accepted the recommendations of an ad hoc committee, which reviewed the policy that had previously been revised in November 2010. The highlights of the current policy are as follows: The policy reaffirms the principle that authors are free to post their own version of their IEEE periodical or conference articles on their personal Web sites, those of their employers, or their funding agencies for the purpose of meeting public availability requirements prescribed by their funding agencies. Authors may post their version of an article as accepted for publication in an IEEE periodical or conference proceedings. Posting of the final PDF, as published by IEEE Xplore®, continues to be prohibited, except for open-access journal articles supported by payment of an article processing charge (APC), whose authors may freely post the final version.  The policy provides that IEEE periodicals will make available to each author a preprint version of that person's article that includes the Digital Object Identifier, IEEE's copyright notice, and a notice showing the article has been accepted for publication.  The policy states that authors are allowed to post versions of their articles on approved third-party servers that are operated by not-for-profit organizations. Because IEEE policy provides that authors are free to follow public access mandates of government funding agencies, IEEE authors may follow requirements to deposit their accepted manuscripts in those government repositories.

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“…The leakage can be reduced by various omethods [25][26][27][28][29], which are mostly based on the estimation of fundamental frequency. However, the optimal measurement condition is to make the sampling process satisfy the requirement of coherent sampling for both the fundamental frequency and its harmonic frequencies simultaneously, which significantly increases the spectral resolution of the FFT and creates an ideal environment for critically ADDR performance evaluation of the DUT.…”

Section: Leakagementioning

confidence: 99%

An Audio Distortion Dynamic Range Index for Evaluating the Performance of Audio Systems

et al. 2020

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The dynamic range (DR) index lacking of an official definition leads to ambiguities in performance evaluation. The existing measurement methods of DR do not always match with the various actual application conditions, and some detailed distortion behavior of the device under test (DUT) is not extracted. In this paper, a new index for evaluating the DR performance of audio systems is proposed and validated, herein referred to as the audio distortion dynamic range (ADDR). It reduces the uncertainty of measurement conditions by an explicit definition and unifies the signal-to-noise ratio (SNR) and the signal-to-noise-and-distortion ratio (SINAD) indexes if under the same measurement condition. Moreover, to comprehensively reflect the impact of harmonic, spurious, and noise components on the DUT, the definitions of the traditional indexes based on classification of distorted components are replaced by the variable thresholds in the ADDR definition. Subsequently, the detailed steps of ADDR and the critical factors influencing its accuracy, are analyzed and then the optimized measurement conditions are given. Experiments based on simulated DUTs show the ADDR index can distinguish performance difference that the traditional indexes cannot distinguish, which proves it is an effective supplementary to the existing indexes in some real applications.

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An Observer-Based Adaptive Fourier Analysis [Tips & Tricks]

Cited by 11 publications

References 13 publications

FPGA Realization of the Observer-Based Sliding Discrete Fourier Transform

FPGA Realization of the Observer-Based Sliding Discrete Fourier Transform

Improvements to the Sliding Discrete Fourier Transform Algorithm [Tips & Tricks]

An Audio Distortion Dynamic Range Index for Evaluating the Performance of Audio Systems

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