Discrete sine transform

About: Discrete sine transform is a research topic. Over the lifetime, 3269 publications have been published within this topic receiving 73181 citations.

The DFT : an owner's manual for the discrete Fourier transform

Abstract: Preface 1. Introduction. A Bit of History An Application Problems 2. The Discrete Fourier Transform (DFT). Introduction DFT Approximation to the Fourier Transform The DFT-IDFT pair DFT Approximations to Fourier Series Coefficients The DFT from Trigonometric Approximation Transforming a Spike Train Limiting Forms of the DFT-IDFT Pair Problems 3. Properties of the DFT. Alternate Forms for the DFT Basic Properties of the DFT Other Properties of the DFT A Few Practical Considerations Analytical DFTs Problems 4. Symmetric DFTs. Introduction Real sequences and the Real DFT (RDFT) Even Sequences and the Discrete Cosine Transform (DST) Odd Sequences and the Discrete Sine Transform (DST) Computing Symmetric DFTs Notes Problems 5. Multi-dimensional DFTs. Introduction Two-dimensional DFTs Geometry of Two-Dimensional Modes Computing Multi-Dimensional DFTs Symmetric DFTs in Two Dimensions Problems 6. Errors in the DFT. Introduction Periodic, Band-limited Input Periodic, Non-band-limited Input Replication and the Poisson Summation Formula Input with Compact Support General Band-Limited Functions General Input Errors in the Inverse DFT DFT Interpolation - Mean Square Error Notes and References Problems 7. A Few Applications of the DFT. Difference Equations - Boundary Value Problems Digital Filtering of Signals FK Migration of Seismic Data Image Reconstruction from Projections Problems 8. Related Transforms. Introduction The Laplace Transform The z- Transform The Chebyshev Transform Orthogonal Polynomial Transforms The Discrete Hartley Transform (DHT) Problems 9. Quadrature and the DFT. Introduction The DFT and the Trapezoid Rule Higher Order Quadrature Rules Problems 10. The Fast Fourier Transform (FFT). Introduction Splitting Methods Index Expansions (One ---> Multi-dimensional) Matrix Factorizations Prime Factor and Convolution Methods FFT Performance Notes Problems Glossary of (Frequently and Consistently Used) Notations References.

Low bit rate transform coder, decoder and encoder/decoder for high-quality audio

Abstract: A low bit-rate (192 kBits per second) transform encoder/decoder system (44.1 kHz or 48 kHz sampling rate) for high-quality music applications employs short time-domain sample blocks (128 samples/block) so that the system signal propagation delay is short enough for real-time aural feedback to a human operator. Carefully designed pairs of analysis/synthesis windows are used to achieve sufficient transform frequency selectivity despite the use of short sample blocks. A synthesis window in the decoder has characteristics such that the product of its response and that of an analysis window in the encoder produces a composite response which sums to unity for two adjacent overlapped sample blocks. Adjacent time-domain signal samples blocks are overlapped and added to cancel the effects of the analysis and synthesis windows. A technique is provided for deriving suitable analysis/synthesis window pairs. In the encoder, a discrete transform having a function equivalent to the alternate application of a modified Discrete Cosine Transform and a modified Discrete Sine Transform according to the Time Domain Aliasing Cancellation technique or, alternatively, a Discrete Fourier Transform is used to generate frequency-domain transform coefficients. The transform coefficients are nonuniformly quantized by assigning a fixed number of bits and a variable number of bits determined adaptively based on psychoacoustic masking. A technique is described for assigning the fixed bit and adaptive bit allocations. The transmission of side information regarding adaptively allocated bits is not required. Error codes and protected data may be scattered throughout formatted frame outputs from the encoder in order to reduce sensitivity to noise bursts.

A fast cosine transform in one and two dimensions

Abstract: The discrete cosine transform (DCT) of an N-point real signal is derived by taking the discrete Fourier transform (DFT) of a 2N-point even extension of the signal. It is shown that the same result may be obtained using only an N-point DFT of a reordered version of the original signal, with a resulting saving of 1/2. If the fast Fourier transform (FFT) is used to compute the DFT, the result is a fast cosine transform (FCT) that can be computed using on the order of N \log_{2} N real multiplications. The method is then extended to two dimensions, with a saving of 1/4 over the traditional method that uses the DFT.

On the Computation of the Discrete Cosine Transform

Abstract: An N -point discrete Fourier transform (DFT) algorithm can be used to evaluate a discrete cosine transform by a simple rearrangement of the input data. This method is about two times faster compared to the conventional method which uses a 2N -point DFT.

Fast Fourier transforms for nonequispaced data: a tutorial

Abstract: In this chapter we consider approximativemethods for the fast computation of multivariate discrete Fourier transforms for nonequispaced data (NDFT) in the time domain and in the frequency domain. In particularwe are interested in the approximation error as function of the arithmetic complexity of the algorithm. We discuss the robustness of NDFTiaalgorithms with respect to roundoff errors and applyNDFTalgorithms for the fast computation of Besseltransforms.