In this paper, a new algorithm for the fast computation of a 2-D discrete cosine transform (DCT) is presented. It is shown that the N×N DCT, where N = 2m, can be computed using only N 1-D DCT’s and additions, in...In this paper, a new algorithm for the fast computation of a 2-D discrete cosine transform (DCT) is presented. It is shown that the N×N DCT, where N = 2m, can be computed using only N 1-D DCT’s and additions, instead of using 2N 1-D DCT’s as in the conventional row-column approach. Hence the total number of multiplications for the proposed algorithm is only half of that required for the row-column approach, and is also less than that of most of other fast algorithms, while the number of additions is almost comparable to that of others.展开更多
Aim To present an ASIC design of DA based 2 D IDCT. Methods\ In the design of 1 D IDCT is utilized a Chen based fast IDCT algorithm, and multiplier accumulators based on distributed algorithm contributes in reduc...Aim To present an ASIC design of DA based 2 D IDCT. Methods\ In the design of 1 D IDCT is utilized a Chen based fast IDCT algorithm, and multiplier accumulators based on distributed algorithm contributes in reducing the hardware amount and in enhancing the speed performance. Results and Conclusion\ VHDL simulation, synthesis and layout design of system are implemented. This 2 D IDCT ASIC design owns best timing performance when compared with other better designs internationally. Results of design prove to be excellent.展开更多
DHT of length p<sup>l</sup>q（p is odd and q is arbitrary） is turned into p<sup>l</sup> DHTs of length qand some additional operations, while the additional operations only involves the comput...DHT of length p<sup>l</sup>q（p is odd and q is arbitrary） is turned into p<sup>l</sup> DHTs of length qand some additional operations, while the additional operations only involves the computation ofcos-DFT and sin-DFT with length p. If the length of a DHT is p<sub>1</sub><sup>l<sub>1</sub></sup>…P<sub>N</sub><sup>l<sub>N</sub></sup>2<sup>l</sup>（P<sub>1</sub>…,P<sub>N</sub> are oddprimes）, a fast algorithm is obtained by the similar recursive technique. Therefore, the algorithmcan compute DHT of arbitrary length. The paper also Proves that operations for computingDHT of length N by the algorithm are no more than O（Nlog<sub>2</sub>N）, when the length is N=p<sup>l</sup>,operations of the algorithm are fewer than that of other known algorithms.展开更多
The Fourier transform is very important to numerous applications in science and engineering. However, its usefulness is hampered by its computational expense. In this paper, in an attempt to develop a faster method fo...The Fourier transform is very important to numerous applications in science and engineering. However, its usefulness is hampered by its computational expense. In this paper, in an attempt to develop a faster method for computing Fourier transforms, the authors present parallel implementations of two new algorithms developed for the type IV Discrete Cosine Transform （DCT-IV） which support the new interleaved fast Fourier transform method. The authors discuss the realizations of their implementations using two paradigms. The first involved commodity equipment and the Message-Passing Interface （MPI） library. The second utilized the RapidMind development platform and the Cell Broadband Engine （BE） processor. These experiments indicate that the authors＇ rotation-based algorithm is preferable to their lifting-based algorithm on the platforms tested, with increased efficiency demonstrated by their MPI implementation for large data sets. Finally, the authors outline future work by discussing an architecture-oriented method for computing DCT-IVs which promises further optimization. The results indicate a promising fresh direction in the search for efficient ways to compute Fourier transforms.展开更多
A generalized fast computational algorithm for the n -dimensional discrete cosine transform ( n- D DCT) of length N=2 m(m≥2) is presented. The developed algorithm is theoretically proved and its efficiency is evaluat...A generalized fast computational algorithm for the n -dimensional discrete cosine transform ( n- D DCT) of length N=2 m(m≥2) is presented. The developed algorithm is theoretically proved and its efficiency is evaluated. The theoretical results show that compared with the conventional method to compute the 1-D DCTs in n directions, the number of multiplications needed by this algorithm is only 1/n of that required by the conventional method; for the total number of additions, it is a bit more when N≤8 and much less when N≥16 than the coventional one. To validate the proposed algorithm, the case when n=3 is taken as an example and applied to the motion picture compression. The results show that the proposed method is superior to MPEG-2.展开更多
In this paper, we have proved that the lower bound of the number of real multiplications for computing a length 2(t) real GFT(a,b) (a = +/-1/2, b = 0 or b = +/-1/2, a = 0) is 2(t+1) - 2t - 2 and that for computing a l...In this paper, we have proved that the lower bound of the number of real multiplications for computing a length 2(t) real GFT(a,b) (a = +/-1/2, b = 0 or b = +/-1/2, a = 0) is 2(t+1) - 2t - 2 and that for computing a length 2t real GFT(a,b)(a = +/-1/2, b = +/-1/2) is 2(t+1) - 2. Practical algorithms which meet the lower bounds of multiplications are given.展开更多
This paper presents an analysis on and experimental comparison of several typical fast algorithms for discrete wavelet transform (DWT) and their implementation in image compression, particularly the Mallat algorithm, ...This paper presents an analysis on and experimental comparison of several typical fast algorithms for discrete wavelet transform (DWT) and their implementation in image compression, particularly the Mallat algorithm, FFT-based algorithm, Short- length based algorithm and Lifting algorithm. The principles, structures and computational complexity of these algorithms are explored in details respectively. The results of the experiments for comparison are consistent to those simulated by MATLAB. It is found that there are limitations in the implementation of DWT. Some algorithms are workable only for special wavelet transform, lacking in generality. Above all, the speed of wavelet transform, as the governing element to the speed of image processing, is in fact the retarding factor for real-time image processing.展开更多
In doubly selective fading channels, the orthogonal frequency division multiplexing (OFDM) multicarrier system may fail. Chirp like basis (fractional Fourier transform-fractional cosine transform) may be used instead ...In doubly selective fading channels, the orthogonal frequency division multiplexing (OFDM) multicarrier system may fail. Chirp like basis (fractional Fourier transform-fractional cosine transform) may be used instead of complex exponential basis in this case to improve the system performance. However, in multicarrier transmission, the high peak to average power ratio (PAPR) of the transmitted signal is one of the difficult problems that face both the chirp and the exponential basis. In this paper, an evaluation for the PAPR performance of a multicarrier system based on the fractional cosine transform (FrCT) is introduced and then compared with DFrFT and FFT. Moreover, applying the SLAM technique over these systems is provided to understand the behaviour of these systems when applying SLAM. Simulations verify that this system obtains a better PAPR performance. Moreover, further PAPR reduction can be gained using the well-known PAPR reduction methods. Moreover, applying SLAM technique improves the performance of (dB) by 4 dB to 5 dB and all systems become as competitive to each other when SLAM is applied. Finally, BER performance comparison among OFDM, Discrete Cosine Transform MCM (DCT- MCM), Discrete Hartley Transform MCM (DHT-MCM), DFrFT-OCDM and DFrCT- OCDM MCM systems was done by means of simulation over 100,000 multicarrier blocks for each one and showed that our proposed scenario gave the best performance.展开更多
This article proposes a new transceiver design for Single carrier frequency division multiple access(SCFDMA)system based on discrete wavelet transform(DWT). SCFDMA offers almost same structure as Orthogonal frequency ...This article proposes a new transceiver design for Single carrier frequency division multiple access(SCFDMA)system based on discrete wavelet transform(DWT). SCFDMA offers almost same structure as Orthogonal frequency division multiple access(OFDMA)with extra advantage of low Peak to Average Power Ratio(PAPR). Moreover,this article also suggests the application of Walsh Hadamard transform(WHT)for linear precoding(LP)to improve the PAPR performance of the system. Supremacy of the proposed transceiver over conventional Fast Fourier transform(FFT)based SCFDMA is shown through simulated results in terms of PAPR,spectral efficiency(SE)and bit error rate(BER).展开更多
For traditional JPEG image encryption,block position shuffling can achieve a better encryption effect and is resistant to non-zero counting attack.However,the numbers of non-zero coefficients in the 8×8 sub-block...For traditional JPEG image encryption,block position shuffling can achieve a better encryption effect and is resistant to non-zero counting attack.However,the numbers of non-zero coefficients in the 8×8 sub-blocks are unchanged using block position shuffle.For this defect,this paper proposes a fast attack algorithm for JPEG image encryption based on inter-block shuffle and non-zero quantization discrete cosine transformation coefficient attack.The algorithm analyzes the position mapping relationship before and after encryption of image blocks by detecting the pixel values of an image by the designed plaintext image.Then the preliminary attack result of the image blocks can be obtained from the inverse mapping relationship.Finally,the final attack result of the algorithm is generated according to the numbers of non-zero coefficients in each 8×8 block of the preliminary attack result.Every 8×8 block position is related with its number of non-zero discrete cosine transform coefficients in the designed plaintext.It is verified that the main content of the original image could be obtained without knowledge of the encryption algorithm and keys in a relatively short time.展开更多
Linear canonical transformation(LCT)is a generalization of the Fourier transform and fractional Fourier transform.The recent research has shown that the LCT is widely used in signal processing and applied mathematics,...Linear canonical transformation(LCT)is a generalization of the Fourier transform and fractional Fourier transform.The recent research has shown that the LCT is widely used in signal processing and applied mathematics,and the discretization of the LCT becomes vital for the applic-ations of LCT.Based on the development of discretization LCT,a review of important research progress and current situation is presented,which can help researchers to further understand the discretization of LCT and can promote its engineering application.Meanwhile,the connection among different discretization algorithms and the future research are given.展开更多
By introducing a form of reorder for multidimensional data, we propose a unified fast algo-rithm that jointly employs one-dimensional W transform and multidimensional discrete polynomial trans-form to compute eleven t...By introducing a form of reorder for multidimensional data, we propose a unified fast algo-rithm that jointly employs one-dimensional W transform and multidimensional discrete polynomial trans-form to compute eleven types of multidimensional discrete orthogonal transforms, which contain three types of m-dimensional discrete cosine transforms ( m-D DCTs) ,four types of m-dimensional discrete W transforms ( m-D DWTs) ( m-dimensional Hartley transform as a special case), and four types of generalized discrete Fourier transforms ( m-D GDFTs). For real input, the number of multiplications for all eleven types of the m-D discrete orthogonal transforms needed by the proposed algorithm are only 1/m times that of the commonly used corresponding row-column methods, and for complex input, it is further reduced to 1/(2m) times. The number of additions required is also reduced considerably. Furthermore, the proposed algorithm has a simple computational structure and is also easy to be im-plemented on computer, and the numerical experiments show that the computational efficiency is con-sistent with the theoretic analysis.展开更多
Steganography is a technique for hiding secret messages while sending and receiving communications through a cover item.From ancient times to the present,the security of secret or vital information has always been a s...Steganography is a technique for hiding secret messages while sending and receiving communications through a cover item.From ancient times to the present,the security of secret or vital information has always been a significant problem.The development of secure communication methods that keep recipient-only data transmissions secret has always been an area of interest.Therefore,several approaches,including steganography,have been developed by researchers over time to enable safe data transit.In this review,we have discussed image steganography based on Discrete Cosine Transform(DCT)algorithm,etc.We have also discussed image steganography based on multiple hashing algorithms like the Rivest–Shamir–Adleman(RSA)method,the Blowfish technique,and the hash-least significant bit(LSB)approach.In this review,a novel method of hiding information in images has been developed with minimal variance in image bits,making our method secure and effective.A cryptography mechanism was also used in this strategy.Before encoding the data and embedding it into a carry image,this review verifies that it has been encrypted.Usually,embedded text in photos conveys crucial signals about the content.This review employs hash table encryption on the message before hiding it within the picture to provide a more secure method of data transport.If the message is ever intercepted by a third party,there are several ways to stop this operation.A second level of security process implementation involves encrypting and decrypting steganography images using different hashing algorithms.展开更多
文摘In this paper, a new algorithm for the fast computation of a 2-D discrete cosine transform (DCT) is presented. It is shown that the N×N DCT, where N = 2m, can be computed using only N 1-D DCT’s and additions, instead of using 2N 1-D DCT’s as in the conventional row-column approach. Hence the total number of multiplications for the proposed algorithm is only half of that required for the row-column approach, and is also less than that of most of other fast algorithms, while the number of additions is almost comparable to that of others.
文摘Aim To present an ASIC design of DA based 2 D IDCT. Methods\ In the design of 1 D IDCT is utilized a Chen based fast IDCT algorithm, and multiplier accumulators based on distributed algorithm contributes in reducing the hardware amount and in enhancing the speed performance. Results and Conclusion\ VHDL simulation, synthesis and layout design of system are implemented. This 2 D IDCT ASIC design owns best timing performance when compared with other better designs internationally. Results of design prove to be excellent.
文摘DHT of length p<sup>l</sup>q（p is odd and q is arbitrary） is turned into p<sup>l</sup> DHTs of length qand some additional operations, while the additional operations only involves the computation ofcos-DFT and sin-DFT with length p. If the length of a DHT is p<sub>1</sub><sup>l<sub>1</sub></sup>…P<sub>N</sub><sup>l<sub>N</sub></sup>2<sup>l</sup>（P<sub>1</sub>…,P<sub>N</sub> are oddprimes）, a fast algorithm is obtained by the similar recursive technique. Therefore, the algorithmcan compute DHT of arbitrary length. The paper also Proves that operations for computingDHT of length N by the algorithm are no more than O（Nlog<sub>2</sub>N）, when the length is N=p<sup>l</sup>,operations of the algorithm are fewer than that of other known algorithms.
文摘The Fourier transform is very important to numerous applications in science and engineering. However, its usefulness is hampered by its computational expense. In this paper, in an attempt to develop a faster method for computing Fourier transforms, the authors present parallel implementations of two new algorithms developed for the type IV Discrete Cosine Transform （DCT-IV） which support the new interleaved fast Fourier transform method. The authors discuss the realizations of their implementations using two paradigms. The first involved commodity equipment and the Message-Passing Interface （MPI） library. The second utilized the RapidMind development platform and the Cell Broadband Engine （BE） processor. These experiments indicate that the authors＇ rotation-based algorithm is preferable to their lifting-based algorithm on the platforms tested, with increased efficiency demonstrated by their MPI implementation for large data sets. Finally, the authors outline future work by discussing an architecture-oriented method for computing DCT-IVs which promises further optimization. The results indicate a promising fresh direction in the search for efficient ways to compute Fourier transforms.
文摘A generalized fast computational algorithm for the n -dimensional discrete cosine transform ( n- D DCT) of length N=2 m(m≥2) is presented. The developed algorithm is theoretically proved and its efficiency is evaluated. The theoretical results show that compared with the conventional method to compute the 1-D DCTs in n directions, the number of multiplications needed by this algorithm is only 1/n of that required by the conventional method; for the total number of additions, it is a bit more when N≤8 and much less when N≥16 than the coventional one. To validate the proposed algorithm, the case when n=3 is taken as an example and applied to the motion picture compression. The results show that the proposed method is superior to MPEG-2.
文摘In this paper, we have proved that the lower bound of the number of real multiplications for computing a length 2(t) real GFT(a,b) (a = +/-1/2, b = 0 or b = +/-1/2, a = 0) is 2(t+1) - 2t - 2 and that for computing a length 2t real GFT(a,b)(a = +/-1/2, b = +/-1/2) is 2(t+1) - 2. Practical algorithms which meet the lower bounds of multiplications are given.
基金the Natural Science Foundation of China (No.60472037).
文摘This paper presents an analysis on and experimental comparison of several typical fast algorithms for discrete wavelet transform (DWT) and their implementation in image compression, particularly the Mallat algorithm, FFT-based algorithm, Short- length based algorithm and Lifting algorithm. The principles, structures and computational complexity of these algorithms are explored in details respectively. The results of the experiments for comparison are consistent to those simulated by MATLAB. It is found that there are limitations in the implementation of DWT. Some algorithms are workable only for special wavelet transform, lacking in generality. Above all, the speed of wavelet transform, as the governing element to the speed of image processing, is in fact the retarding factor for real-time image processing.
文摘In doubly selective fading channels, the orthogonal frequency division multiplexing (OFDM) multicarrier system may fail. Chirp like basis (fractional Fourier transform-fractional cosine transform) may be used instead of complex exponential basis in this case to improve the system performance. However, in multicarrier transmission, the high peak to average power ratio (PAPR) of the transmitted signal is one of the difficult problems that face both the chirp and the exponential basis. In this paper, an evaluation for the PAPR performance of a multicarrier system based on the fractional cosine transform (FrCT) is introduced and then compared with DFrFT and FFT. Moreover, applying the SLAM technique over these systems is provided to understand the behaviour of these systems when applying SLAM. Simulations verify that this system obtains a better PAPR performance. Moreover, further PAPR reduction can be gained using the well-known PAPR reduction methods. Moreover, applying SLAM technique improves the performance of (dB) by 4 dB to 5 dB and all systems become as competitive to each other when SLAM is applied. Finally, BER performance comparison among OFDM, Discrete Cosine Transform MCM (DCT- MCM), Discrete Hartley Transform MCM (DHT-MCM), DFrFT-OCDM and DFrCT- OCDM MCM systems was done by means of simulation over 100,000 multicarrier blocks for each one and showed that our proposed scenario gave the best performance.
文摘This article proposes a new transceiver design for Single carrier frequency division multiple access(SCFDMA)system based on discrete wavelet transform(DWT). SCFDMA offers almost same structure as Orthogonal frequency division multiple access(OFDMA)with extra advantage of low Peak to Average Power Ratio(PAPR). Moreover,this article also suggests the application of Walsh Hadamard transform(WHT)for linear precoding(LP)to improve the PAPR performance of the system. Supremacy of the proposed transceiver over conventional Fast Fourier transform(FFT)based SCFDMA is shown through simulated results in terms of PAPR,spectral efficiency(SE)and bit error rate(BER).
文摘For traditional JPEG image encryption,block position shuffling can achieve a better encryption effect and is resistant to non-zero counting attack.However,the numbers of non-zero coefficients in the 8×8 sub-blocks are unchanged using block position shuffle.For this defect,this paper proposes a fast attack algorithm for JPEG image encryption based on inter-block shuffle and non-zero quantization discrete cosine transformation coefficient attack.The algorithm analyzes the position mapping relationship before and after encryption of image blocks by detecting the pixel values of an image by the designed plaintext image.Then the preliminary attack result of the image blocks can be obtained from the inverse mapping relationship.Finally,the final attack result of the algorithm is generated according to the numbers of non-zero coefficients in each 8×8 block of the preliminary attack result.Every 8×8 block position is related with its number of non-zero discrete cosine transform coefficients in the designed plaintext.It is verified that the main content of the original image could be obtained without knowledge of the encryption algorithm and keys in a relatively short time.
基金supported by the National Natural Science Found-ation of China(No.62001193).
文摘Linear canonical transformation(LCT)is a generalization of the Fourier transform and fractional Fourier transform.The recent research has shown that the LCT is widely used in signal processing and applied mathematics,and the discretization of the LCT becomes vital for the applic-ations of LCT.Based on the development of discretization LCT,a review of important research progress and current situation is presented,which can help researchers to further understand the discretization of LCT and can promote its engineering application.Meanwhile,the connection among different discretization algorithms and the future research are given.
基金This work was supported by the National Natural Science Foundation of China (Grant No. 69974041).
文摘By introducing a form of reorder for multidimensional data, we propose a unified fast algo-rithm that jointly employs one-dimensional W transform and multidimensional discrete polynomial trans-form to compute eleven types of multidimensional discrete orthogonal transforms, which contain three types of m-dimensional discrete cosine transforms ( m-D DCTs) ,four types of m-dimensional discrete W transforms ( m-D DWTs) ( m-dimensional Hartley transform as a special case), and four types of generalized discrete Fourier transforms ( m-D GDFTs). For real input, the number of multiplications for all eleven types of the m-D discrete orthogonal transforms needed by the proposed algorithm are only 1/m times that of the commonly used corresponding row-column methods, and for complex input, it is further reduced to 1/(2m) times. The number of additions required is also reduced considerably. Furthermore, the proposed algorithm has a simple computational structure and is also easy to be im-plemented on computer, and the numerical experiments show that the computational efficiency is con-sistent with the theoretic analysis.
文摘Steganography is a technique for hiding secret messages while sending and receiving communications through a cover item.From ancient times to the present,the security of secret or vital information has always been a significant problem.The development of secure communication methods that keep recipient-only data transmissions secret has always been an area of interest.Therefore,several approaches,including steganography,have been developed by researchers over time to enable safe data transit.In this review,we have discussed image steganography based on Discrete Cosine Transform(DCT)algorithm,etc.We have also discussed image steganography based on multiple hashing algorithms like the Rivest–Shamir–Adleman(RSA)method,the Blowfish technique,and the hash-least significant bit(LSB)approach.In this review,a novel method of hiding information in images has been developed with minimal variance in image bits,making our method secure and effective.A cryptography mechanism was also used in this strategy.Before encoding the data and embedding it into a carry image,this review verifies that it has been encrypted.Usually,embedded text in photos conveys crucial signals about the content.This review employs hash table encryption on the message before hiding it within the picture to provide a more secure method of data transport.If the message is ever intercepted by a third party,there are several ways to stop this operation.A second level of security process implementation involves encrypting and decrypting steganography images using different hashing algorithms.
