Theoretical Upperbound of the Spurious-Free Dynamic Range in Direct Digital Frequency Synthesizers Realized by Polynomial Interpolation Methods

Ashrafi, Ashkan; Adhami, Reza R.

doi:10.1109/tcsi.2007.904660

Cited by 25 publications

(21 citation statements)

References 30 publications

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“…The SFDR upperbound can provide a meaningful criterion to stop the optimization algorithm targeted at achieving the highest SFDR for the desired hardware complexity. A comprehensive study of the SFDR upperbound for the polynomial interpolation methods is given in [9] where the SFDR upperbound was found as the Chebyshev minimax solution to an overdetermined system of equations.…”

Section: Introductionmentioning

confidence: 99%

“…Although the method given in [9] is a universal method of finding the SFDR upperbound for any polynomial interpolation based DDFS, it highly depends on the optimization algorithm employed to find the Chebyshev minimax solution of the overdetermined system of equations. Unfortunately, some of the available optimization packages do not provide a correct answer and may lead to an incorrect SFDR upperbound.…”

Section: Introductionmentioning

confidence: 99%

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On the SFDR Upperbound in DDFS Utilizing Polynomial Interpolation Methods

Ashrafi

2012

IEEE Trans. Circuits Syst. II

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In this brief, the theoretical analysis that obtains the upperbound of the spurious free dynamic range (SFDR) of the direct digital frequency synthesizers (DDFSs) with phaseto-sine mapper (PSM) structured by polynomial interpolation is revisited. A complete analysis of the SFDR upperbound of these DDFS architectures was provided by Ashrafi and Adhami in 2007, where the authors formulated the SFDR upperbound as the Chebyshev minimax solution to an overdetermined system of linear equations. However, some issues in finding the Chebyshev minimax solution were not made clear in that paper regarding the minimax error at the fundamental harmonic of the output sinusoid. These issues, along with the erroneous behavior of numerical computation packages used for solving the Chebyshev minimax problem, misled Chau and Chen to claim that the results of the aforementioned paper were wrong. This brief clarifies the issues with the original paper, exhibits the problems with some of the available numerical computation packages, and refutes the claims that Chau and Chen made.Index Terms-Chebyshev minimax approximation, direct digital frequency synthesizers (DDFSs), spurious free dynamic range (SFDR).

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On the SFDR Upperbound in DDFS Utilizing Polynomial Interpolation Methods

Ashrafi

2012

IEEE Trans. Circuits Syst. II

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“…The most critical stage in a DDFS is the PSAC. Many prior works for improving the performance of PSAC include angular decomposition techniques [1,[3][4][5][6], angle rotation methods [7][8][9], polynomial approximations [10][11][12], and sine amplitude compression methods [13][14][15][16]. In the sine amplitude compression methods, they only use linear approximations to decrease a ROM size.…”

Section: Introductionmentioning

confidence: 99%

Design of direct digital frequency synthesizers based on unilateral second-order approximations

Lin

Chang

2011

2011 IEEE 15th International Symposium on Consumer Electronics (ISCE)

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A new sine amplitude compression technique employing unilateral second-order approximation methods is proposed for a direct digital frequency synthesizer. The technique uses a second-order polynomial approximation above or below the ideal sine function to reduce the errors. Both the approximation methods can save 10 bits per word in a ROM. By using Horner's rule and some design skills, we can reduce more arithmetic operations. A Xilinx FPGA design demonstrates the spurious free dynamic range of the proposed architecture.

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“…s 2 The phase after truncation of the L − W (LSBs). s 3 The truncated phase when the two most significant bits (MSBs) have been removed.…”

Section: Introductionmentioning

confidence: 99%

“…The phase truncation will give alias problems, well described by, e.g., Ashrafi et al [2]. Those are related only to the input wordlength, W , and weakly affected by the accumulator size L, according to the relation [3, eq.…”

Section: Introductionmentioning

confidence: 99%

Magnitude scaling for increased SFDR in DDFS

Källström

Gustafsson

2011

2011 Norchip

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Abstract-When generating a sine table to be used in, e.g., frequency synthesis circuits, a widely used way to assign the table content is to simply take a sine wave with the desired amplitude and quantize it using rounding. This results in uncontrolled rounding of up to 0.5 LSB, causing some noise. In this paper we present a method for increasing the signal quality, simply by adjust the amplitude within a ±0.5 range from the intended. This will not affect the maximum value of the sinusoid, but can increase the spurious free dynamic range with some dB.

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Theoretical Upperbound of the Spurious-Free Dynamic Range in Direct Digital Frequency Synthesizers Realized by Polynomial Interpolation Methods

Cited by 25 publications

References 30 publications

On the SFDR Upperbound in DDFS Utilizing Polynomial Interpolation Methods

On the SFDR Upperbound in DDFS Utilizing Polynomial Interpolation Methods

Design of direct digital frequency synthesizers based on unilateral second-order approximations

Magnitude scaling for increased SFDR in DDFS

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