Type-II/III DCT/DST algorithms with reduced number of arithmetic operations

Shao, Xuancheng; Johnson, Steven G.

doi:10.1016/j.sigpro.2008.01.004

Cited by 54 publications

(34 citation statements)

References 49 publications

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“…The DST-III and DCT-III are closely related. In particular, a DST-III can be obtained from a DCT-III, with the same number of flops, by reversing the inputs and multiplying every other output by −1 [9], [12], [50], [51]:…”

Section: Dst-iii From Dct-iiimentioning

confidence: 99%

“…Our fast algorithms are based on one of two recently published fast Fourier transform (FFT) algorithms [1], [3], which reduced the operation count for the discrete Fourier transform (DFT) of size N to 34 9 N log 2 N + O(N ) compared to the (previous best) splitradix algorithm's 4N log 2 N + O(N ) [4]- [8]. Given the new FFT, we treat a DCT as an FFT of real-symmetric inputs and eliminate redundant operations to derive the new algorithm; in other work, we applied the same approach to derive improved algorithms for the type-II and type-III DCT and DST [9].…”

Section: Introductionmentioning

confidence: 99%

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Type-IV DCT, DST, and MDCT algorithms with reduced numbers of arithmetic operations

Shao

Johnson

2008

Signal Processing

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We present algorithms for the type-IV discrete cosine transform (DCT-IV) and discrete sine transform (DST-IV), as well as for the modified discrete cosine transform (MDCT) and its inverse, that achieve a lower count of real multiplications and additions than previously published algorithms, without sacrificing numerical accuracy. Asymptotically, the operation count is reduced from 2N log 2 N + O(N ) to 17 9 N log 2 N + O(N ) for a power-of-two transform size N , and the exact count is strictly lowered for all N ≥ 8. These results are derived by considering the DCT to be a special case of a DFT of length 8N , with certain symmetries, and then pruning redundant operations from a recent improved fast Fourier transform algorithm (based on a recursive rescaling of the conjugate-pair split-radix algorithm). The improved algorithms for DST-IV and MDCT follow immediately from the improved count for the DCT-IV.

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Section: Dst-iii From Dct-iiimentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Type-IV DCT, DST, and MDCT algorithms with reduced numbers of arithmetic operations

Shao

Johnson

2008

Signal Processing

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“…We have tested the GT-I and GT-II methods on weather speech dataset of Carnegie Mellon University's speech group 1 and also 10 music in different genres. We compared results with DCT-I [6], DCT-II [9], DCT-III [10], DCT-IV [11] and Fast Walsh-Hadamard Transform (FWHT) [14] based on Peak Signal to Noise Ratio (PSNR) value, Energy Retained Percentage (ERP), Short-Time Objective Intelligibility (STOI) [12] and Perceptual Evaluation of Speech Quality (PESQ) [13]. We have considered several frame size and several compression ratio (CR).…”

Section: Expermental Results and Discussionmentioning

confidence: 99%

Audio Compression Using Graph-based Transform

Farzaneh

Toroghi

Asgari

2018

2018 9th International Symposium on Telecommunications (IST)

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Graph-based Transform is one of the recent transform coding methods which has been used in some stateof-arts for data decorrelation. In this paper, we propose a Graph-based Transform (GT) for audio compression. In this method we introduce a proper graph structure for audio. Then audio frames are projected onto an orthogonal matrix consisting of eigenvectors of the introduced graph matrix, leading to sparse coefficients. The results show that the proposed method can decorrelate audio signal better than other transform methods like Discrete Cosine Transform (DCT) and Walsh-Hadamard Transform (WHT).

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“…Given a sentence of N words w 1 , ..., w N , we stack the sequence of 1 There are several variants of DCT. We use DCT type II (Shao and Johnson, 2008) in our implementation AVG c 0 c 1 man bites dog dog bites man man bitten by dog…”

Section: Dct Sentence Embeddingsmentioning

confidence: 99%

Efficient Sentence Embedding using Discrete Cosine Transform

AlMarwani

Aldarmaki

Diab

2019

Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing and the 9th International Joint Conferen

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Vector averaging remains one of the most popular sentence embedding methods in spite of its obvious disregard for syntactic structure. While more complex sequential or convolutional networks potentially yield superior classification performance, the improvements in classification accuracy are typically mediocre compared to the simple vector averaging. As an efficient alternative, we propose the use of discrete cosine transform (DCT) to compress word sequences in an order-preserving manner. The lower order DCT coefficients represent the overall feature patterns in sentences, which results in suitable embeddings for tasks that could benefit from syntactic features. Our results in semantic probing tasks demonstrate that DCT embeddings indeed preserve more syntactic information compared with vector averaging. With practically equivalent complexity, the model yields better overall performance in downstream classification tasks that correlate with syntactic features, which illustrates the capacity of DCT to preserve word order information.

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Type-II/III DCT/DST algorithms with reduced number of arithmetic operations

Cited by 54 publications

References 49 publications

Type-IV DCT, DST, and MDCT algorithms with reduced numbers of arithmetic operations

Type-IV DCT, DST, and MDCT algorithms with reduced numbers of arithmetic operations

Audio Compression Using Graph-based Transform

Efficient Sentence Embedding using Discrete Cosine Transform

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