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

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 ~2NlogN to ~(17/9)NlogN for a power-of-two transform size N, and the exact count is strictly lowered for all N > 4. 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.Comment: 11 page

A fast algorithm for the computation of 2-D forward and inverse MDCT

International audienceA fast algorithm for computing the two-dimensional (2-D) forward and inverse modified discrete cosine transform (MDCT and IMDCT) is proposed. The algorithm converts the 2-D MDCT and IMDCT with block size M N into four 2-D discrete cosine transforms (DCTs) with block size ðM=4Þ ðN=4Þ. It is based on an algorithm recently presented by Cho et al. [An optimized algorithm for computing the modified discrete cosine transform and its inverse transform, in: Proceedings of the IEEE TENCON, vol. A, 21–24 November 2004, pp. 626–628] for the efficient calculation of onedimensional MDCT and IMDCT. Comparison of the computational complexity with the traditional row–column method shows that the proposed algorithm reduces significantly the number of arithmetic operations

A class of scaled Bessel sampling theorems

Sampling theorems for a class of scaled Bessel unitary transforms are presented. The derivations are based on the properties of the generalized Laguerre functions. This class of scaled Bessel unitary transforms includes the classical sine and cosine transforms, but also novel chirp sine and modified Hankel transforms. The results for the sine and cosine transform can also be utilized to yield a sampling theorem, different from Shannon's, for the Fourier transform

A Low-Area, Energy-Efficient 64-Bit Reconfigurable Carry Select Modified Tree-Based Adder for Media Signal Processing

Multimedia systems play an essential part in our daily lives and have drastically improved the quality of life over time. Multimedia devices like cellphones, radios, televisions, and computers require low-area and low-power reconfigurable adders to process greedy computation algorithms for the real-time audio/video signal and image processing such as discrete cosine transform, inverse discrete cosine transform, and fast Fourier transform, etc. In this thesis, a novel 64-bit reconfigurable adder is proposed and implemented to reduce the area and power consumption. This adder can be run-time reconfigured to different reconfigurable word lengths, i.e., one 64- bit, two 32-bits, four 16-bits or eight 8-bits addition, depending on the partition signal command. A Carry Select Modified Tree (CSMT) based adder is used in the reconfigurable adder to reduce the area by 22 % and the power consumption by 47 % when compared to the conventional design. The proposed adder, implemented in 180 nm CMOS technology at 1.8-volt supply, has a worst-case Delay of 20.67 nanoseconds with an overall area of 36,417 μm² and power consumption of 447.93 μW

A comparative analysis of binary patterns with discrete cosine transform for gender classification

This paper presents a comparative analysis of binary patters for gender classification with a novel method of feature transformation for improved accuracy rates. The main requirements of our application are speed and accuracy. We investigate a combination of local binary patterns (LBP), Census Transform (CT) and Modified Census Transform (MCT) applied over the full, top and bottom halves of the face. Gender classification is performed using support vector machines (SVM). A main focus of the investigation is to determine whether or not a 1D discrete cosine transform (DCT) applied directly to the grey level histograms would improve accuracy. We used a public database of faces and run face and eye detection algorithms allowing automatic cropping and normalisation of the images. A set of 120 tests over the entire database demonstrate that the proposed 1D discrete cosine transform improves accuracy in all test cases with small standard deviations. It is shown that using basic versions of the algorithms, LBP is marginally superior to both CT and MCT and agrees with results in the literature for higher accuracy on male subjects. However, a significant result of our investigation is that, by applying a 1D-DCT this bias is removed and an equivalent error rate is achieved for both genders. Furthermore, it is demonstrated that DCT improves overall accuracy and renders CT a superior performance compared to LBP in all cases considered

Score extraction usign MPEG-4 T/F partial encoding

This paper describes the preliminary work in the development of an MPEG-4 audio transcoder between the time/frequency (T/F) and the structured audio (SA) formats. Our approach consists in not going from T/F format through to waveform data and back again to SA, but extracting the score information from an intermediate stage. For this intermediate form we have chosen the input of the filterbank and block switching tool, which consists of frequency data. This data is the result of windowing and applying the modified discrete cosine transform (MDCT) to the signal. The size of the window to be used is determined in a frame-by-frame basis by a psychoacoustics analysis of the data. In this paper we show that this approach is feasible by developing a system which extracts the score information from the filterbank and block switching tool output in a MPEG-4 T/F encoder by adapting and fine-tuning some existing processing techniques.Peer ReviewedPostprint (published version