Speaker Identification using Frequency Dsitribution in the Transform Domain

In this letter, we first propose new nearly tridiagonal commuting matrices of discrete Fourier transform (DFT) matrix and generalized DFT (GDFT) matrix. Then, using the block diagonalizations technique of circular-centrosymmetric and centrosymmetric matrices, we derive novel tridiagonal commuting matrices for each discrete cosine transform (DCT) and discrete sine transform (DST) matrices of the types I, IV, V, and VIII from the commuting matrices of the DFT and GDFT based on the relationships in matrix forms among DFT, GDFT, and various types of DCT and DST. Moreover, the novel tridiagonal commuting matrices of various types of DCT and DST do not have multiple eigenvalues. Last, with these novel commuting matrices, we can easily determine an orthonormal set of Hermite-like eigenvectors for each of their corresponding DCT or DST matrix.

This paper presents a new property called the Duality Theorem for the Discrete Sine Transform (DST). Discrete Sine Transform is a finite — length discrete transform which is related to the renowned Discrete Fourier Transform (DFT) and is quite popular in signal processing arena, but has remained in the oblivion from pure mathematicians. Many of the properties of the Discrete Sine Transform are akin to those of the Discrete Fourier Transform and Discrete Cosine Transform, subject to minor differences. A formal derivation of the Duality Theorem corresponding to the Discrete Sine Transform is given which was hitherto not mentioned or derived in the literature. The usage of Duality Theorem helps in finding the discrete time — domain function from the DST frequency domain and vice versa thereby reducing considerable labour involved in the evaluation of the summation and hence, saves computation time and cost of implementation to a considerable extent. DST finds applications in Image Processing, Signal Processing applications for Communication Systems, and in the numerical solutions of differential equations as well as partial differential equations of mathematics.

This paper proposes a high performance and low cost inverse discrete cosine transform (IDCT) processor for high definition Television (HDTV) applications by using cyclic convolution and hardwired multipliers. By properly arranging the input sequence, we formulate the one-dimensional (1-D) IDCT into cyclic convolution that is regular and suitable for VLSI implementation. The hardwired multiplier that implements multiplication with IDCT coefficients are first scaled and optimized by using the common sub-expression techniques. Based on these techniques, the data-path in the proposed two-dimensional (2-D) IDCT design costs 7504 gates plus 1024 bits of memory with 100 M pixels/sec throughput according to the cost estimation based on the cell library of COMPASS 0.6 μm SPDM CMOS technology. Also, we have verified that the precision analysis of the proposed 2-D 8 × 8 IDCT meets the demands of IEEE Std. 1180-1990. Due to the good performance in the computing speed as well as the hardware cost, the proposed design is compact and suitable for HDTV applications. This design methodology can be applied to forward DCT as well as other transforms like discrete sine transform (DST), discrete Fourier transform (DFT), and discrete Hartley transform (DHT).

According to Wang, there are four different types of DCT (discrete cosine transform) and DST (discrete sine transform) and the computation of these sinusoidal transforms can be reduced to the computation of the type-IV DCT. As the algorithms involve different sizes of transforms at different stages they are not so regular in structure. Lee has developed a fast cosine transform (FCT) algorithm for DCT-III similar to the decimation-in-time (DIT) Cooley–Tukey fast Fourier transform (FFT) with a regular structure. A disadvantage of this algorithm is that it involves the division of the trigonometric coefficients and may be numerically unstable. Recently, Hou has developed an algorithm for DCT-II which is similar to a decimation-in-frequency (DIF) algorithm and is numerically stable. However, an index mapping is needed to transform the DCT to a phase-modulated discrete Fourier transform (DFT), which may not be performed in-place. In the paper, a variant of Hou's algorithm is presented which is both in-place and numerically stable. The method is then generalised to compute the entire class of discrete sinusoidal transforms. By making use of the DIT and DIF concepts and the orthogonal properties of the DCTs, it is shown that simple algebraic formulations of these algorithms can readily be obtained. The resulting algorithms are regular in structure and are more stable than and have fewer arithmetic operations than similar algorithms proposed by Yip and Rao. By means of the Kronecker matrix product representation, the 1-D algorithms introduced in the paper can readily be generalised to compute transforms of higher dimensions. These algorithms, which can be viewed as the vector-radix generalisation of the present algorithms, share the in-place and regular structure of their 1-D counterparts.

Block frames called <i>directional analytic discrete cosine frames</i> (DADCFs) are proposed for sparse image representation. In contrast to conventional overlapped frames, the proposed DADCFs require a reduced amount of 1) computational complexity, 2) memory usage, and 3) global memory access. These characteristics are strongly required for current high-resolution image processing. Specifically, we propose two DADCFs based on discrete cosine transform (DCT) and discrete sine transform (DST). The first DADCF is constructed from parallel separable transforms of DCT and DST, where the DST is permuted by row. The second DADCF is also designed based on DCT and DST, while the DST is customized to have no DC leakage property which is a desirable property for image processing. Both DADCFs have rich directional selectivity with slightly different characteristics each other and they can be implemented as non-overlapping block-based transforms, especially they form Parseval block frames with low transform redundancy. We perform experiments to evaluate our DADCFs and compare them with conventional directional block transforms in image recovery.

Chapter 1 - Discrete Cosine and Sine Transforms

In this paper we present the Peak-to-Average Power Ratio decrease method targeted at energy efficiency improvement of the Radio-over-fiber telecommunication systems based on the Orthogonal Frequency Division Multiplexing. The scheme for the proposed method that consists in the signal precoding with discrete function is discussed in details. The simulation results obtained for five different precoding functions: Discrete Hartley Transform, Discrete Cosine Transform, Discrete Sine Transform, Fast Walsh-Hadamard Transform, and Discrete Fourier Transform, show the peak-to-average power ratio decrease of the transmitted signal up to 7 dB without degradation in noise immunity. Such a gain in transmitted power reduction corresponds to energy efficiency improvement by 5.15 dB in the case of 16-position quadrature amplitude modulation. The experimental study confirms the simulation results, providing the 6.5 dB peak-to-average power ratio decrease for Discrete Fourier Transform function.

A joint Hyperbolic Tangent Companding (HTC) technique and Discrete Cosine Transform (DCT) has been proposed to decrease of the PAPR ratio effects of the OFDMA System. The proposed schema utilizes DCT instead of the traditional discrete Fourier transform (DFT) as a requisite function to perform DCT OFDMA. HTC is an actual process to minimize the high PAPR of DCT OFDMA. However, the companded DCT OFDMA suffers from the bit-error-rate (BER) performance degradation by companding noise introduced. So, an effective scheme of estimation and noise cancellation for the compressed DCT OFDMA is introduced. By expressing the compressed signals as a combination of the main signals adding with the component of compressed noise, and the estimated compressed noise deduct from the received signals, leading to enhance the BER performance of the proposed system. The new proposed scheme minimizes PAPR by about 6.3 dB and 7.3 dB compare respectively, with the DFT OFDMA and DCT OFDMA without commanding. Also, it is noted that the proposed scheme of estimation and companding noise cancellation for the companded DCT OFDMA provides a great lowest BER degradation that can be neglected comparing with the premier DCT SC-FDMA system without PAPR reduction.

The processing efficiency of the widely used time-space (t-x) domain vertical seismic profiling (VSP) wavefield separation methods (such as median and singular value decomposition filtering) via one-dimensional discrete Fourier transform (DFT) depends on the wavefield separation method (or algorithm with processing parameter) and the total number of samples in the input VSP data. Once the wavefield separation method is determined, its processing efficiency is set and cannot be optimized. Although the popular frequency-wavenumber (f-k) domain VSP wavefield separation method via two-dimensional DFT has higher processing efficiency than the t-x domain VSP wavefield separation methods, its processing precision is susceptible to the spatial alias and Gibbs effects. For efficiency and precision improvements, we introduced the discrete cosine transform (DCT) operation into VSP wavefield separation for the first time, and proposed a high-efficiency and precision frequency-space (f-x) domain VSP wavefield separation method via DFT and DCT, in which the wavefield separation efficiency and precision can be optimized using the effective bandwidth cutoff frequency of the input VSP data. Based on the relationship between DFT and DCT, we combined their operations in the proposed method into one step (referred to as DCT–DFT) for further efficiency enhancement, thereby designing a high-efficiency and precision f-x domain VSP wavefield separation method via DCT–DFT. Theory analysis and synthetic and field VSP data examples show that the proposed method is highly efficient and precise, and can be widely used for three-dimensional (3D)-VSP data wavefield separation, especially for large distributed acoustic sensing (DAS)-VSP data.

Interpretation of eight-point discrete cosine and sine transforms as 3×3 orthogonal edge masks in terms of the Frei–Chen masks

Automatic Digital Modulation Recognition (ADMR) is becoming an interesting problem with various civil and military applications. In this paper, an ADMR algorithm in Multi-Carrier Code Division Multiple Access (MC-CDMA) systems using Discrete Transforms (DTs) and Mel-Frequency Cepstral Coefficients (MFCCs) is proposed. This algorithm uses various DT techniques such as the Discrete Wavelet Transform (DWT), Discrete Cosine Transform (DCT) and Discrete Sine Transform (DST) with MFCCs to extract features from the modulated signal and a Support Vector Machine (SVM) to classify the modulation orders. The proposed algorithm avoids over fitting and local optimal problems that appear in Artificial Neural Networks (ANNs). Simulation results shows the classifier is capable of recognizing the modulation scheme with high accuracy up to 90% - 100% using DWT, DCT and DST for some modulation schemes over a wide Signal-to-Noise Ratio (SNR) range in the presence of Additive White Gaussian Noise (AWGN) and Rayleigh fading channel, particularly at a low Signal-to-Noise ratios (SNRs).

In this letter, a novel method to realize all-optical discrete sine transform (DST) and discrete cosine transform (DCT) is proposed. The approach requires only one multimode interference (MMI) coupler and several phase shifters at the input and output ports. By properly arranging the length of the MMI coupler and adjusting the phase shifters, the DST can be directly realized all-optically. Meanwhile, the DCT is related to the DST with a simple formula. By changing the input phase and relabeling the output ports, it can also be realized on the MMI structure. The proposed methodology has no limit on the number of the inputs.

This paper deals with a novel steganographic technique which demonstrates the colour image authentication technique in frequency domain based on the Discrete Fourier Transform (DFT). The DFT is applied on sub-image block called mask of size 2 × 2 for frequency components of corresponding spatial component. This transforms process done from beginning to end mask in row major order of the carrier image. Image authentication is done by hiding secrete message/image into the transformed frequency components of carrier image. Four secrete message/image bits are fabricated within the transformed real frequency component of each carrier image byte except the LSB of first frequency component of each mask. After embedding, a delicate re-adjust phase is incorporated in all the frequency component of each mask, to keep the quantum value positive and non fractional in spatial domain. Robustness is achieved by hiding an authenticating or secretes message/image in the frequency component with positive and negatives both quantum values and invisibility is satisfied in spatial domain using delicate re-adjust phase. Inverse DFT (IDFT) is performed after embedding to transform embedded image in frequency domain to spatial domain. This novel technique is also applicable for secrete data transmission through carrier colour image by hiding secrete data. Experimental results conform that the proposed algorithm performs better than discrete cosine transformation (DCT), Quaternion Fourier Transformation (QFT) and Spatio Chromatic DFT (SCDFT) based schemes.

This paper deals with the problem of blind separation of audio signals from noisy mixtures. It proposes the application of a blind separation algorithm on the discrete cosine transform (DCT) or the discrete sine transform (DST) of the mixed signals, instead of performing the separation on the mixtures in the time domain. Wavelet denoising of the noisy mixtures is recommended in this paper as a preprocessing step for noise reduction. Both the DCT and the DST have an energy compaction property, which concentrates most of the signal energy in a few coefficients in the transform domain, leaving most of the transform domain coefficients close to zero. As a result, the separation is performed on a few coefficients in the transform domain. Another advantage of signal separation in transform domains is that the effect of noise on the signals in the transform domains is smaller than that in the time domain due to the averaging effect of the transform equations, especially when the separation algorithm is preceded by a wavelet denoising step. The simulation results confirm the superiority of transform domain separation to time domain separation and the importance of the wavelet denoising step.

A spectral 1st level FPGA trigger for detection of very inclined showers based on a 16-point discrete cosine transform for the Pierre Auger Observatory