The problem of query selectivity estimation for database queries is critical for efficientquery execution by database management systems. A query execution method strongly depends on earlyestimated size of a query result. This estimation determines a data access method used later during thequery execution. The selectivity parameter is a fraction of table rows that satisfy a single-table querycondition. For a selection condition of a range query where an attribute has a continuous domain, theselectivity is equivalent to a definite integral form probability density function (PDF) of attribute valuesdistribution. For a compound selection condition based on many attributes we need a multidimensionalspace-efficient non-parametric estimator of multivariate PDF of attribute values distribution. A knownapproach based on Discrete Cosine Transform (DCT) spectrum as an representation of multidimensionalPDF is considered. The energy compaction property of DCT lets omit a region of spectrum coefficientswith small absolute values without significant losing an accuracy of selectivity estimation. An area ofrelevant spectrum coefficients is called a sampling zone. Results of experiments from previous worksshows that applying the reciprocal shape of the sampling zone gives the least selectivity estimation errorsubject to a predetermined size of the zone. The main result of this work is a theoretical confirmation of onlyexperimental results from previous works. The paper presents the proof of the theorem that the reciprocalshape of the sampling zone is asymptotically error-optimal. The proof is based on calculus of variationsand the isoperimetric problem.

Digital speech copyright protection and forgery identification are the prevalent issues in our advancing digital world. In speech forgery, voiced part of the speech signal is copied and pasted to a specific location which alters the meaning of the speech signal. Watermarking can be used to safe guard the copyrights of the owner. To detect copy-move forgeries a transform domain watermarking method is proposed. In the proposed method, watermarking is achieved through Discrete Cosine Transform (DCT) and Quantization Index Modulation (QIM) rule. Hash bits are also inserted in watermarked voice segments to detect Copy-Move Forgery (CMF) in speech signals. Proposed method is evaluated on two databases and achieved good imperceptibility. It exhibits robustness in detecting the watermark and forgeries against signal processing attacks such as resample, low-pass filtering, jittering, compression and cropping. The proposed work contributes for forensics analysis in speech signals. This proposed work also compared with the some of the state-of-art methods.

The MDCT and IntMDCT Algorithm is widely utilized is Audio coding. By lifting scheme or rounding operation IntegerMDCT is evolved from Modified Discrete Cosine Transform. This method acquire the properties of MDCT and contribute excelling invertiblity and good spectral mean .In this paper we discuss about the audio codec like AAC and FLAC using MDCT and Integer MDCT algorithm and to find which algorithm shows better Compression Ratio(CR).The confines of this task is to hybriding lossy and lossless audio codec with diminished bit rate but with finer sound quality. Certainly the quality of the audio is figure out by Subjective and Objective testing which is in terms of MOS (Mean opinion square), ABx and some of the hearing aid testing methodology like PEAQ(Perceptual Evaluation Audio Quality) and ODG(Objective Difference Grade)is followed. Execution measure, that is Compression Ratio(CR) and Sound Pressure Level (SPL) is approximated.