Showing papers on "Modified discrete cosine transform published in 1989"

Development of integer cosine transforms by the principle of dyadic symmetry

Abstract: The paper shows how to convert the order-8 cosine transforms into a family of integer cosine transforms (ICTs) using the theory of dyadic symmetry. The new transforms can be implemented using simple integer arithmetic. It was found that performance close to that of the DCT can be achieved with an ICT that requires only 4 bits for representation of its kernel com- ponent magnitude. Better performance can be achieved by some ICTs whose kernel components require longer bit lengths for representation. ICTs that require 3 bits or less for representation of their component magnitude are available but with degraded performance. The availability of many ICTs provides an engineer the freedom to tradeoff performance for simple implementation in design- ing a transform codec.

Input and output index mappings for a prime-factor-decomposed computation of discrete cosine transform

Abstract: A formal direct derivation of the prime-factor-decomposed computation algorithm is presented. The derivation is direct in the sense that it is based on the real cosine function without resort to the discrete Fourier transform expressions or the complex functions. Based on the equations obtained from the derivation, input and output index mappings are introduced in the form of tables. This tabulation enables any prime-factor-decomposable discrete cosine transform (DCT) to be implemented in a straight-forward manner. The use of the index mapping tables is demonstrated for the 12-point DCT. >

Trade-off's in the computation of mono- and multi-dimensional DCT's

Abstract: An overview of some alternative algorithms for one- and two-dimensional DCTs (discrete cosine transforms) is given. Operation counts are derived for typical examples useful in image processing. It is shown that it is possible to generalize the 2-D schemes to 3-D DCTs as well. The result is that a 3-D DCT can be obtained from a 3-D DFT (discrete Fourier transform) of the same size on reals at the cost of permutations and O(3/2N/sup 3/) multiplications. The scheme involves rotations on eight output points at a time. Improvements through scaling are discussed, and implementation issues (both in hardware and software) are addressed. >

A Fast Recursive Two Dimensional Cosine Transform

Abstract: This paper presents a recursive, radix two by two, fast algorithm for computing the two dimensional discrete cosine transform (2D-DCT). The algorithm allows the generation of the next higher order 2D-DCT from four identical lower order 2D-DCT's with the structure being similar to the two dimensional fast Fourier transform (2D-FFT). As a result, the method for implementing this recursive 2D-DCT requires fewer multipliers and adders than other 2D-DCT algorithms.

New fast algorithm to compute two-dimensional discrete Hartley transform

Abstract: A new fast algorithm for computing the two-dimensional discrete Hartley transform is presented. This algorithm requires the lowest number of multiplications compared with other related algorithms.

Efficient index mapping for computing discrete cosine transform

Abstract: In this letter, an efficient algorithm for computing the discrete cosine transform (DCT) is presented. It is based on an index mapping which converts an odd-length DCT to a realvalued DFT of the same length using permutations and sign changes only. The real-valued DFT can then be computed by efficient real-valued FFT algorithms such as the prime factor algorithm. The algorithm is more efficient than an earlier one because no postmultiplications are required.

Efficient FFT implementation on an IEEE floating-point digital signal processor

Abstract: The authors describe the implementation of real and complex FFT (fast Fourier transform) algorithms on the Motorola DSP96002. The DSP96002 is a general-purpose, dual-bus IEEE standard floating-point digital signal processor (DSP). At a 74-ns instruction cycle, the DSP96002 implements a 1024-point real FFT in 0.905 ms and a 1024-point complex FFT in 1.55 ms. This performance is achieved by calculating up to three floating-point results in a single instruction cycle, or 40.5 MFLOPS peak. A radix-2 FFT butterfly is executed every four cycles, an average of 33.75 IEEE MFLOPS. The instruction set and architecture of the DSP96002 provide the basis for efficient implementation of FFTs and other fast transforms, such as the discrete Walsh-Hadamard transform, discrete cosine transform, and discrete Hartley transform. >

Distributed arithmetic architecture for image coding

Abstract: A description is given of the development of a hardware circuit based on a distributed arithmetic architecture to obtain the fast DCT (discrete cosine transform) of a given image. This circuit not only provides DCT transform coefficients but also other transforms' coefficients. In addition, this circuit also provides inverse transforms with little or no change in components/interconnections. It has also demonstrated that this distributed arithmetic circuit can be used to obtain a fourth order FIR/IIR filter. >

ECG synthesis via discrete cosine transform

Abstract: Results on the modeling and synthesis of the electrocardiogram (ECG) from its component waves after a suitable transformation are presented. The transformed components add up to the transform of the complete beat and thus allow synthesis of the ECG. Pole-zero modeling of the transformed signals by the Shanks method proved very successful. >

Block diagonal structure in discrete transforms

Abstract: The author investigates and summarises some of the computational tasks of discrete transforms in which block diagonal structure plays a dominant role. Walsh-Hadamard transform (WHT) based algorithm designs for various well known discrete transforms are presented; it can be proved that, owing to their block diagonal structure, the WHT based discrete transforms are more efficient than those of the conventional radix-r algorithms for transforms of length N

Pseudolapped orthogonal transform

Abstract: The pseudo-LOT, a modified version of the lapped orthogonal transform (LOT), is introduced. It can be viewed as either a block transform with overlapping basis functions or a critically-sampled multirate filter bank with nearly perfect reconstruction. A fast algorithm for the pseudo-LOT, based on the discrete cosine transform, is presented.

Discrete Walsh-Hadamard transform vector quantization for motion-compensated frame difference signal coding

Abstract: Theoretical performance analysis and test simulations showed that the DWHT (discrete Walsh-Hadamard transform) is as good as the DCT (discrete cosine transform) for the encoding of low-correlation MCFD (motion-compensated frame difference) signals. However, the straightforward algorithm for the DWHT makes it a better choice than the DCT. The transform vector quantization (TRVQ) technique is employed for low bit rates. It is also observed that the robustness of the VQ (vector quantization) technique for the MCFD signals is much better than that of the VQ of the still frame images. >

Improved transform coding (imaging coding)

Abstract: A novel method for coding of images using the discrete cosine transform is presented. It is based on a modification of the idea of reducing subthreshold coefficients to zero during transform coding. A simple analysis shows that if the subthreshold coefficients are represented by reduced magnitudes other than zero, then the net error that results in a reconstructed pixel is less than if the coefficients have zero value. Based on this reasoning, the subthreshold coefficients are grouped according to their magnitudes, and only the average value of the coefficients in each group is selected in place of all the members of that group during coding. During image reconstruction, the average value of each group is used to generate all the members of that group. By selecting only one coefficient to represent many, the compression ratio is greatly improved. >

Comments on "Fast computation of the discrete cosine transform and the discrete Hartley transform" by H.S. Malvar

Abstract: The commenter shows that the algorithm presented in the above paper (ibid., vol.ASSP-35, no.10, p.1484-5, Oct. 1987) requires exactly the same number of multiplications as, but more additions than, prevalent methods for the computation of the DHT (discrete Hartley transform) by existing methods, contrary to the author's claim. >