Above the Nyquist Rate, Modulo Folding Does Not Hurt

Romanov, Elad; Ordentlich, Or

doi:10.1109/lsp.2019.2923835

Cited by 46 publications

(49 citation statements)

References 13 publications

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“…The sampling frequency should be at least twice the highest frequency contained in the signal. The Shannon-Nyquist sampling theorem [13] guarantees that any signal whose Fourier transform is supported on this bandwidth limit can be entirely reconstructed from the discrete-time signal as long as the frequency rate is at least twice this bandwidth limit, as illustrated by the following equation [32]:…”

Section: Resampling In Signature Verificationmentioning

confidence: 99%

Online signature verification using signature down-sampling and signer-dependent sampling frequency

Saleem

Kővári

2021

Neural Comput & Applic

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Online signature verification considers signatures as time sequences of different measurements of the signing instrument. These signals are captured on digital devices and therefore consist of a discrete number of samples. To enrich or simplify this information, several verifiers employ resampling and interpolation as a preprocessing step to improve their results; however, their design decisions may be difficult to generalize. This study investigates the direct effect of the sampling rate of the input signals on the accuracy of online signature verification systems without using interpolation techniques and proposes a novel online signature verification system based on a signer-dependent sampling frequency. Twenty verifier configurations were created for five different public signature databases and a variety of popular preprocessing approaches and evaluated for 20–40 different sampling rates. Our results show that there is an optimal range for the sampling frequency and the number of sample points that minimizes the error rate of a verifier. A sampling frequency range of 15–50 Hz and a signature point count of 60–240 provided the best accuracies in our experiments. As expected, lower ranges showed inaccurate results; interestingly, however, higher frequencies often decreased the verification accuracy. The results show that one can achieve better or at least the same verification accuracies faster by down-sampling the online signatures before further processing. The proposed system achieved competitive results to state-of-the-art systems for different databases by using the optimal sampling frequency. We also studied the effect of choosing individual sampling frequencies for each signer and proposed a signature verification system based on signer-dependent sampling frequency. The proposed system was tested using 500 different verification methods and improved the accuracy in 92% of the test cases compared to the usage of the original frequency.

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Section: Resampling In Signature Verificationmentioning

confidence: 99%

Online signature verification using signature down-sampling and signer-dependent sampling frequency

Saleem

Kővári

2021

Neural Comput & Applic

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“…Recently, the limited dynamic range problem in analog-todigital conversion has been partially addressed under the socalled unlimited sampling framework [19], showing that the Shannon-Nyquist sampling theorem also holds under a finite dynamic range constraint [20]. That is, a band-limited analog signal can be perfectly reconstructed from the discrete-time finite dynamic range signal resulting from folding the analog signal via a modulo operation, so that no clipping errors occur, before sampling under the Shannon-Nyquist condition.…”

Section: A Modulo-adc Benefitsmentioning

confidence: 99%

“…That is, a band-limited analog signal can be perfectly reconstructed from the discrete-time finite dynamic range signal resulting from folding the analog signal via a modulo operation, so that no clipping errors occur, before sampling under the Shannon-Nyquist condition. Unfortunately, although the proofs in [19], [20] are constructive in the sense of providing algorithms for perfectly recovering the original continuous-time signal from the folded discretetime signal, they break under quantization errors which are always present in ADCs. In other words, the results in [19], [20] cannot be directly used since, on top of sampling, a quantization operation is always performed by an ADC to convert the analog input signal to a discrete-time discretevalued digital signal.…”

Section: A Modulo-adc Benefitsmentioning

confidence: 99%

“…Unfortunately, although the proofs in [19], [20] are constructive in the sense of providing algorithms for perfectly recovering the original continuous-time signal from the folded discretetime signal, they break under quantization errors which are always present in ADCs. In other words, the results in [19], [20] cannot be directly used since, on top of sampling, a quantization operation is always performed by an ADC to convert the analog input signal to a discrete-time discretevalued digital signal. Still, the idea of applying a modulo operation to the analog signal before the ADC seems to be the key to address limited dynamic range in analog-to-digital conversion as explored in [21], where the so-called modulo-ADCs have been proposed.…”

Section: A Modulo-adc Benefitsmentioning

confidence: 99%

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On Full-Duplex Radios With Modulo-ADCs

Ordóñez

Ferrand

Duarte

et al. 2021

IEEE Open J. Commun. Soc.

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Wireless full-duplex (FD) transceivers have become more commonplace in the recent years, enabled by improvements in hardware as well as in signal processing algorithms dedicated to self-interference (SI) mitigation. A key design target for any FD radio is to limit the analog-to-digital converter (ADC) quantization noise affecting the signal of interest (SoI), which results from the difference in dynamic range between the SI and the SoI at the input of the ADC. Indeed, when using conventional ADCs, since the SI power is much larger than that of the SoI, the SI spans most of the ADC's dynamic range and the SoI becomes distorted by a large quantization noise. Reducing the power of the SI before the ADC, for example via analog domain SI cancellation, is so far the only means to mitigate this undesired effect. In this paper we consider the use of so-called modulo ADCs as a new tool to reduce the quantization noise that affects the SoI in the presence of SI. We demonstrate theoretically and numerically that by substituting the conventional ADCs with modulo-ADCs, which fold the analog input signal before analog-to-digital conversion, and by using appropriately designed analog gain control and digital-domain SI cancellation, one can reduce the quantization noise that affects the SoI. As such, the work in this paper provides a new technique for counteracting the detrimental effect of SI in analog-to-digital conversion and, thus, provides a new route to be explored in order to enhance the performance of FD radios.

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“…Recently, unlimited sampling framework with modulo sampling hardware was developed in [1]- [4]. Specifically, for a given x ∈ R and ∆ > 0, the modulo operation is defined as [1], [5] x…”

Section: Introductionmentioning

confidence: 99%

Multi-Channel Modulo Samplers Constructed From Gaussian Integers

Gong

Liu

2021

IEEE Signal Process. Lett.

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Recently, there is an increased interest in the study of modulo analog to digital converters (ADCs). These new systems can reconstruct a signal whose amplitude is much higher than the conventional ADC's dynamic range. Modulo ADCs are characterized by their modulo threshold and in the current literature, all existing works are limited to real-valued moduli. In this paper, we propose multi-channel modulo samplers with complex-valued moduli to sample a band-limited complex signal. Specifically, we discuss the construction of complex divisors from Gaussian integers and propose their efficient implementations. A memory-efficient, closed-form recovery algorithm is also proposed. Simulation results demonstrate that the proposed systems can provide stable reconstruction of a high dynamic range complex-valued signal at low sampling rates.

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Above the Nyquist Rate, Modulo Folding Does Not Hurt

Cited by 46 publications

References 13 publications

Online signature verification using signature down-sampling and signer-dependent sampling frequency

Online signature verification using signature down-sampling and signer-dependent sampling frequency

On Full-Duplex Radios With Modulo-ADCs

Multi-Channel Modulo Samplers Constructed From Gaussian Integers

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