Reconstruction of Two-Periodic Nonuniformly Sampled Band-Limited Signals Using a Discrete-Time Differentiator and a Time-Varying Multiplier

Tertinek, Stefan; Vogel, Christian

doi:10.1109/tcsii.2007.896801

Cited by 33 publications

(36 citation statements)

References 6 publications

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“…In our previous work [19], we derived one such special scheme consisting of an FIR filter designed as differentiator and a time-varying multiplier. The main advantage of that system is that designing the optimal reconstruction filters reduces to designing a simple FIR differentiator.…”

Section: A Contribution Of This Paper and Relation To Other Workmentioning

confidence: 99%

Reconstruction of Nonuniformly Sampled Bandlimited Signals Using a Differentiator–Multiplier Cascade

Tertinek

Vogel

2008

IEEE Trans. Circuits Syst. I

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This paper considers the problem of reconstructing a bandlimited signal from its nonuniform samples. Based on a discrete-time equivalent model for nonuniform sampling, we propose the differentiator-multiplier cascade, a multistage reconstruction system that recovers the uniform samples from the nonuniform samples. Rather than using optimally designed reconstruction filters, the system improves the reconstruction performance by cascading stages of linear-phase finite impulse response (FIR) filters and time-varying multipliers. Because the FIR filters are designed as differentiators, the system works for the general nonuniform sampling case and is not limited to periodic nonuniform sampling. To evaluate the reconstruction performance for a sinusoidal input signal, we derive the signal-to-noise-ratio at the output of each stage for the two-periodic and the general nonuniform sampling case. The main advantage of the system is that once the differentiators have been designed, they are implemented with fixed multipliers, and only some general multipliers have to be adapted when the sampling pattern changes; this reduces implementation costs substantially, especially in an application like time-interleaved analog-to-digital converters (TI-ADCs) where the timing mismatches among the ADCs may change during operation.

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Section: A Contribution Of This Paper and Relation To Other Workmentioning

confidence: 99%

Reconstruction of Nonuniformly Sampled Bandlimited Signals Using a Differentiator–Multiplier Cascade

Tertinek

Vogel

2008

IEEE Trans. Circuits Syst. I

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“…In Paper A of Part II, we propose a two-rate based reconstructor for twochannel TI-ADCs which is a popular TI-ADC configuration [76][77][78][79]. The basic two-rate based approach in Paper A is extended to a general M -channel TI-ADC reconstruction scheme in Paper B.…”

Section: 7(b)mentioning

confidence: 99%

Signal Reconstruction Algorithms for Time-Interleaved ADCs

Pillai¹

2015

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An analog-to-digital converter (ADC) is a key component in many electronic systems. It is used to convert analog signals to the equivalent digital form. The conversion involves sampling which is the process of converting a continuous-time signal to a sequence of discrete-time samples, and quantization in which each sampled value is represented using a finite number of bits. The sampling rate and the effective resolution (number of bits) are two key ADC performance metrics. Today, ADCs form a major bottleneck in many applications like communication systems since it is difficult to simultaneously achieve high sampling rate and high resolution. Among the various ADC architectures, the time-interleaved analog-to-digital converter (TI-ADC) has emerged as a popular choice for achieving very high sampling rates and resolutions. At the principle level, by interleaving the outputs of M identical channel ADCs, a TI-ADC could achieve the same resolution as that of a channel ADC but with M times higher bandwidth. However, in practice, mismatches between the channel ADCs result in a nonuniformly sampled signal at the output of a TI-ADC which reduces the achievable resolution. Often, in TI-ADC implementations, digital reconstructors are used to recover the uniform-grid samples from the nonuniformly sampled signal at the output of the TI-ADC. Since such reconstructors operate at the TI-ADC output rate, reducing the number of computations required per corrected output sample helps to reduce the power consumed by the TI-ADC. Also, as the mismatch parameters change occasionally, the reconstructor should support online reconfiguration with minimal or no redesign. Further, it is advantageous to have reconstruction schemes that require fewer coefficient updates during reconfiguration. In this thesis, we focus on reducing the design and implementation complexities of nonrecursive finite-length impulse response (FIR) reconstructors. We propose efficient reconstruction schemes for three classes of nonuniformly sampled signals that can occur at the output of TI-ADCs.iii Firstly, we consider a class of nonuniformly sampled signals that occur as a result of static timing mismatch errors or due to channel mismatches in TI-ADCs. For this type of nonuniformly sampled signals, we propose three reconstructors which utilize a two-rate approach to derive the corresponding single-rate structure. The two-rate based reconstructors move part of the complexity to a symmetric filter and also simplifies the reconstruction problem. The complexity reduction stems from the fact that half of the impulse response coefficients of the symmetric filter are equal to zero and that, compared to the original reconstruction problem, the simplified problem requires only a simpler reconstructor.Next, we consider the class of nonuniformly sampled signals that occur when a TI-ADC is used for sub-Nyquist cyclic nonuniform sampling (CNUS) of sparse multi-band signals. Sub-Nyquist sampling utilizes the sparsities in the analog signal to sample the signal at a lowe...

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“…This section describes how a filter design for the time instant n can be obtained without performing the computationally intensive calculation of the generalized inverse A K n † as given in (13) and (14). Instead, this generalized inverse is determined by resorting to results from the previous filter design without explicitly performing a matrix inversion.…”

Section: Order Recursive Least-squares Design Of a Time-varying Fmentioning

confidence: 99%

“…In comparison, the computationally most expensive operation of the well-known least-squares filter design algorithm, as presented in Section III, is the inversion of the matrix product A * K n A K n in (14). This matrix multiplication has a complexity of O K 2 R [19] with K< R, and the inversion of the resulting K-by-K matrix has a complexity of O K 3 , when applying the Gaussian elimination.…”

Section: Summary Of the Filter Design Algorithmmentioning

confidence: 99%

Low complexity least-squares filter design for the correction of linear time-varying systems

Soudan

Vogel

2011

2011 20th European Conference on Circuit Theory and Design (ECCTD)

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In this paper, a low complexity algorithm for the design of a time-varying correction filter of finite impulse response (FIR) type is presented. Using the obtained filter design to correct a preceding time-varying system, a correction performance in the least-squares sense can be ensured. The adaptation of the filter design requires a moderate computational complexity and is suitable for real-time applications. Thus, a correction of nonperiodically time-varying systems can be achieved where design methods, which rely on computationally intensive operations, e.g. numerical integration, can not be applied. At the same time, its application is not limited to weakly time-varying systems as iterative solutions are, which can correct for weakly time-varying behavior by gradually reducing the induced signal error over multiple stages.

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Reconstruction of Two-Periodic Nonuniformly Sampled Band-Limited Signals Using a Discrete-Time Differentiator and a Time-Varying Multiplier

Cited by 33 publications

References 6 publications

Reconstruction of Nonuniformly Sampled Bandlimited Signals Using a Differentiator–Multiplier Cascade

Reconstruction of Nonuniformly Sampled Bandlimited Signals Using a Differentiator–Multiplier Cascade

Signal Reconstruction Algorithms for Time-Interleaved ADCs

Low complexity least-squares filter design for the correction of linear time-varying systems

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