Quantization errors in the fast Fourier transform

James, D.

doi:10.1109/tassp.1975.1162687

Cited by 36 publications

(15 citation statements)

References 8 publications

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“…The first one is the typical one, for which the coefficients are not scaled (Non-scaled). The second one (Truncated one [15]) is an approximation of Non-scaled that substitutes the value Fig. 4 are normalized.…”

Section: B Example Of Application: Fftmentioning

confidence: 99%

Accurate Rotations Based on Coefficient Scaling

Garrido

Gustafsson

Grajal

2011

IEEE Trans. Circuits Syst. II

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Abstract-This brief presents a novel approach for improving the accuracy of rotations implemented by complex multipliers, based on scaling the complex coefficients that define these rotations. A method for obtaining the optimum coefficients that lead to the lowest error is proposed. This approach can be used to get more accurate rotations without increasing the coefficient wordlength as well as to reduce the wordlengh without increasing the rotation error.The paper analyzes two different situations where the optimization method can be applied: rotations that can be optimized independently and sets of rotations that require the same scaling. These cases appear in important signal processing algorithms such as the discrete cosine transform (DCT) and the fast Fourier transform (FFT). Experimental results show that the use of scaling for the coefficients clearly improves the accuracy of the algorithms. For instance, improvements of about 8 dB in the Frobenius norm of the FFT are achieved with respect to using non-scaled coefficients.

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Section: B Example Of Application: Fftmentioning

confidence: 99%

Accurate Rotations Based on Coefficient Scaling

Garrido

Gustafsson

Grajal

2011

IEEE Trans. Circuits Syst. II

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“…The truncation of SOPOT coefficients appears to be equivalent to coefficient quantization problems of various transforms in the literature, such as [4,9,16], which have attracted the attention of many researchers. However, these results cannot be applied to our scheme for the following reasons.…”

Section: Truncation Noise Shaping Of Sopot Coefficientsmentioning

confidence: 99%

“…In statistical model based approaches [9,16], these truncation errors are assumed as independent random variables with mean value of zero and their cross terms will vanish for the expectation of sum of truncation noises. In our work, however, these errors are subject to the orthogonal conditions, and they cannot be assumed as independent random variables with mean value of zero.…”

Section: Modeling the Noise From A Series Of Ifft Coefficient Blocksmentioning

confidence: 99%

A joint encoder–decoder framework for supporting energy efficient audio decoding

Huang

Wang

2009

Multimedia Systems

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In comparison with the relatively slow progress of battery technology, semiconductor memory has improved much more rapidly, making storage a less critical limiting factor in designing low power embedded systems such as PDAs.To exploit such technology trends, we present a novel framework, a joint encoder-decoder framework (JEDF), which allows the decoder to tradeoff energy and memory consumption without sacrificing playback quality. We employ sumof-powers-of-two (SOPOT) technique, an approximate signal processing (ASP) technique, in an MPEG AAC decoder to reduce the computational workload. The SOPOT introduces additional ASP noise (in the decoder) on top of the quantization noise introduced in the process of lossy compression (in the encoder). The sum of these two kinds of noise may become audible when it exceeds the masking threshold. We tackle this problem from a new perspective: the proposed JEDF allows the ASP and quantization noises to be shaped jointly to match the masking threshold. In the case that the perceptual room between the masking threshold and the quantization noise is insufficient for the ASP noise, the JEDF can reduce the quantization noise level which results in an increase in bitrate. To implement the proposed scheme, we have developed two new techniques: (1) SOPOT truncation noise shaping; (2) truncation noise allocation based on a perceptual model. Experimental results show the effectiveness of our approach.Communicated by Cormac Sreenan.

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“…De ne Y = Yr + jYi as the original output and Q(Y ) as the quantized output, the mean square error (MSE) of numerical decomposition is expressed as in Eq. (9). Similarly, the MSE of direct implementation can also be simply derived as 4σ 2 .…”

Section: Iii-a Quantization Loss Modelmentioning

confidence: 99%

“…James [9] derived the xed-point MSE analysis of quantization loss for mixed-radix FFT algorithms with conventional complex multipliers. Perlow and Denk [10] proposed an error propagation model to estimate the performance of nite wordlength FFT architecture.…”

Section: Iv-a Quantitive Simulationmentioning

confidence: 99%

Integer FFT with Optimized Coefficient Sets

Chang

Nguyen

2007

2007 IEEE International Conference on Acoustics, Speech and Signal Processing - ICASSP '07

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In this paper, the principle of nding the optimized coef cient set of integer fast Fourier transform (IntFFT) is introduced. IntFFT has been regarded as an approximation of original FFT since it utilizes lifting scheme (LS) and decomposes the complex multiplication of twiddle factor into three lifting steps. Based on the observation of the quantization loss model of lifting operations, we can select an optimized coef cient set and achieve better signal-to-quantizationnoise ratio (SQNR). A mixed-radix 128-point FFT is used to compare the SQNR performance between IntFFT and other FFT implementations. A xed-point simulation environment with the presence of additive white Gaussian noise (AWGN) channel is also constructed for comparison purposes.

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Quantization errors in the fast Fourier transform

Cited by 36 publications

References 8 publications

Accurate Rotations Based on Coefficient Scaling

Accurate Rotations Based on Coefficient Scaling

A joint encoder–decoder framework for supporting energy efficient audio decoding

Integer FFT with Optimized Coefficient Sets

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