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This paper presents methods for rational sampling rate conversion performed in the domains of discrete Fourier transform and discrete cosine transform. Several important issues, such as the conversion error performance and the required computational complexity based on the proposed fast transform algorithms, are discussed in detail. Compared to the conventional lowpass filter based time-domain methods that have been commonly used for many applications, the proposed ones are shown to achieve substantial improvements on conversion accuracy at reduced computational costs.

Several specific features have been incorporated into Motion estimation (ME) in H.264 coding standard to improve its coding efficiency. However, they result in very high computational load. In this paper, a fast ME algorithm is proposed to reduce the computational complexity. First, a mode discriminant method is used to free the encoder from checking the small block size modes in homogeneous regions. Second, a condensed hierarchical block matching method and a spatial neighbor searching scheme are employed to find the best full-pixel motion vector. Finally, direction-based selection rule is utilized to reduce the searching range in sub-pixel ME process. Experimental results on commonly used QCIF and CIF format test sequences have shown that the proposed algorithm achieves a reduction of 88% ME process time on average, while incurring only 0.033dB loss in PSNR and 0.50% increment on the total bit rate compared with that of exhaustive ME process, which is a default approach adopted in the JM reference software.

Most speech enhancement algorithms are based on the assumption that speech and noise are both Gaussian in the discrete cosine transform (DCT) domain. For further enhancement of noisy speech in the DCT domain, we consider multiple statistical distributions (i.e., Gaussian, Laplacian and Gamma) as a set of candidates to model the noise and speech. We first use the goodness-of-fit (GOF) test in order to measure how far the assumed model deviate from the actual distribution for each DCT component of noisy speech. Our evaluations illustrate that the best candidate is assigned to each frequency bin depending on the Signal-to-Noise-Ratio (SNR) and the Power Spectral Flatness Measure (PSFM). In particular, since the PSFM exhibits a strong relation with the best statistical fit we employ a simple recursive estimation of the PSFM in the model selection. The proposed speech enhancement algorithm employs a soft estimate of the speech absence probability (SAP) separately for each frequency bin according to the selected distribution. Both objective and subjective tests are performed for the evaluation of the proposed algorithms on a large speech database, for various SNR values and types of background noise. Our evaluations show that the proposed soft decision scheme based on multiple statistical modeling or the PSFM provides further speech quality enhancement compared with recent methods through a number of subjective and objective tests.

A novel multiple description coding framework, called structure unanimity multiple description coding, is proposed in this paper. Each wavelet coefficient is first decomposed into an odd position coefficient made from the bits in the odd positions and an even position coefficient made from the bits in the even positions. These two types of coefficients form the odd image and the even image, respectively, which are next encoded, and then transmitted using two different channels. Since the two images share the same hierarchical tree structure, only coefficient values in the redundancy parts need to be coded, resulting in improved coding efficiency. To meet the requirements of the packet switching network, these two images are rearranged in tree blocks, and the tree blocks in the even image and odd image are grouped to form the row and column packets, respectively. These packets are next separately dispatched through diverse channels. Since the row and the column packets have limited intersections, even with simultaneous loss of row and column packets, the proposed system exhibits good error resilient ability. Experimental results have verified the improved performance of the proposed algorithm.

Single sensor color digital cameras use color filter arrays (CFAs) for capturing an image. Color interpolation is then applied to the captured data for reconstructing the full color image. In this paper we present techniques for interpolating the CFA data in the YUV color space to obtain the full color image. The resulting color images could be directly used in the DCT based JPEG compression scheme. We have also used the concept of sub-band DCT computation for interpolating the individual components of color images in the DCT domain. Based on a simple strategy for computing the Y, U, and V components, several modifications are also proposed for improving the quality of the reconstructed images. We have observed that median filtering of the chrominance components improves the visual quality of the interpolated color image. The results are also compared with some of the well known interpolation algorithms and are found to have competitive advantages considering the speed of computations, quality of the image reconstruction, storage requirements, and false color suppression.

A novel approach to pitch estimation of speech signals using an adaptive lattice notch filter (ALNF) is proposed. Based on a good convergence property and an unbiased frequency estimate with respect to the noise variance, the pitch period is estimated using the ALNF. Simulation results have verified that the ALNF is very effective in estimating the pitch period of the given speech signal under background noise environments.

In this paper, we describe the results of a series of psychophysical experiments that investigated the relationships among defect visibility, content importance, and perceived impairment in digital video. Various types of controlled defects were inserted into normal video and shown to our test subjects. The defects varied in their strength, location, appearance, size, and duration. We measured three specific subjective quantities: the defect detection probabilities, the perceived impairment, and the content importance. Impairment was found to be tightly related to defect visibility but only weakly related to content importance.

Recently, an image compression algorithm based on the warped discrete cosine transform has been proposed (Cho and Mitra, IEEE Trans Circuits Systems Video Technol 10 (8) (2000) 1364). The algorithm outperforms JPEG, especially for images with high frequency contents and compound images consisting of picture and text. In this paper, we improve the compression performance by optimizing the parameters of WDCT in the rate-distortion (R-D) sense, whereas the algorithm of Cho and Mitra considers distortion only. The optimization algorithm finds the WDCT matrices for each block which minimize the distortion for the given bit budget. The problem is formulated in a form that can be solved by the Lagrange multiplier technique. The major difference of the proposed algorithm from the conventional optimized JPEG is that the proposed algorithm controls the rate and distortion by warping the frequency contents of input signals before DCT, whereas the conventional optimized JPEG controls the R-D by manipulating the data after DCT, i.e. by adjusting the quantization matrix. The simulation results show that the proposed algorithm yields better performance than the conventional optimized JPEG at high bit rates and for images with high frequency components. Moreover, the proposed algorithm requires lower computational complexity, because only a single parameter is controlled to meet the R-D constraints.

As a complement to the periodogram, low-cost frequency estimators are of interest. In this paper we introduce a new approach for single frequency estimation using the warped discrete Fourier transform (WDFT). The WDFT corresponds to sampling the z-transform of a finite length sequence at warped points in the frequency domain by using an allpass function which allows to increase the frequency resolution locally. We focus on a first-order allpass function with a complex valued warping parameter. If the warping parameter is zero, the WDFT reduces to the discrete Fourier transform. Performance and complexity aspects of the proposed algorithm are discussed and finally, we provide an perspective on how the WDFT can be used to reduce the complexity of existing estimators in the case of multiple sinusoids.

This paper presents a novel scheme of wavelet image coding, called X-tree coding. An X-tree is defined as a spatial hierarchical tree whose all descendants are insignificant, and it is used to denote 2-D clustered insignificant wavelet coefficients of an image. Two new coding schemes, the progressive X-tree approach and the stack X-tree approach, which are the X-tree versions of the embedded zerotree wavelet (EZW) algorithm and the stack-run coding algorithm, respectively, are proposed. Experimental results have shown that the performances of the proposed algorithms are better than those of the stack-run and the EZW algorithms, and are highly comparable to that of the set partitioning in hierarchical trees algorithm.

The application of the local relaxation (LR) method to the optical flow estimation has been shown to provide much better performance than the Gauss-Seidel method. However, the direct application of the existing LR method results in a relatively slow convergence because of the coupling of the Poisson equations in which optical flow estimation problem is framed. This paper presents modification of the LR method based on the decoupling of the Poisson equations resulting in a fast convergence. This speed up in convergence is more noticeable when the proposed method is combined with registered gradients such as displaced frame difference and motion compensated spatial gradients. The paper includes simulation results on artificial and real image sequences verifying the superiority of the proposed modification.

Digital dual-tone multi-frequency (DTMF) decoding is often performed by applying a frequency transformation to the received DTMF signal to measure the energies present at the DTMF frequencies. A DTMF decoding algorithm is developed using the concepts of non-uniform frequency sampling and subband decomposition. Since DTMF signals occupy the low-frequency band of the telephone bandwidth, an efficient computation is achieved by retaining only the higher subband in a two-band decomposition of the received signal. Simulations based on the AT&T TouchTone standard are presented to compare the performances of DTMF decoding algorithms based on the subband non-uniform discrete Fourier transform (SB-NDFT), NDFT, SB-DFT and DFT. Results show that the SB-NDFT-based algorithm is more robust to the variation of DTMF frequencies within the specified tolerance bands. Besides, it also requires a significantly lower computational effort to attain a specified level of performance.

The goal of image fusion is to integrate complementary information from multisensor data such that the new images are more suitable for the purpose of human visual perception and computer-processing tasks such as segmentation, feature extraction, and object recognition. This paper presents an image fusion scheme which is based on the wavelet transform. The wavelet transforms of the input images are appropriately combined, and the new image is obtained by taking the inverse wavelet transform of the fused wavelet coefficients. An area-based maximum selection rule and a consistency verification step are used for feature selection. The proposed scheme performs better than the Laplacian pyramid-based methods due to the compactness, directional selectivity, and orthogonality of the wavelet transform. A performance measure using specially generated test images is suggested and is used in the evaluation of different fusion methods, and in comparing the merits of different wavelet transform kernels. Extensive experimental results including the fusion of multifocus images, Landsat and Spot images, Landsat and Seasat SAR images, IR and visible images, and MRI and PET images are presented in the paper.

A new DFT computation method based on a subband decomposition described in a companion paper (Shentov et al., 1995) is investigated. The two distinct parts of the algorithm, a preprocessing Hadamard transform stage and a ‘correction’ stage, were interpreted as a filter-bank-plus-recombination network. This interpretation provides a better understanding of the errors caused by dropping subbands in the approximate partial-band DFT computation. In this paper we analyze the approximation errors and computational complexity of the new algorithm in partial-band DFT computation, in addition to outlining a number of its possible applications. Specifically, formulae for the approximation errors due to linear distortions and to aliasing are derived. Two new general formulae are found for the aliasing terms under different conditions; one of them gives an interesting matrix formulation for the coefficients describing the aliasing effects of all frequency bands separately. The computational complexity of the algorithm is analyzed both theoretically and in terms of running-time measurements. This concerns both the full- and partial-band analysis cases in various realization structures as introduced in Shentov et al. (1995). With these insights, the novel algorithm is compared to existing methods, especially for the computation of a limited number of frequency points. A number of application examples are included to illustrate the efficiency of the proposed method in computing approximately the DFT of signals with energies concentrated in small parts of the spectrum.

A new DFT computation method based on a subband decomposition is outlined for one- and two-dimensional (2-D) real-valued finite-length sequences. The two distinct parts of the algorithm, a preprocessing Hadamard-transform stage and a ‘correction’ stage are interpreted as a filter bank plus a recombination network, and are compared to the corresponding filter bank interpretation of the direct DFT and the classical FFT algorithms. The preprocessing stage decomposes the original sequence into a set of smaller length subsequences approximately separated in the spectral domain. The overall DFT is then given by a weighted sum of smaller length DFTs with the weights determined by the recombination network. The frequency-separation property of the subsequences permits elimination of the subsequences with negligible energy contribution from the DFT calculation thus resulting in a fast approximate DFT computation method. Various implementation schemes for the subband DFT computation method are outlined. As a first extension, adaptive versions are described, finding the band(s) of interest automatically. Furthermore, a generalized preprocessing stage as well as the extension to the 2-D case are addressed.

A certain class of frequency selective digital IIR filters, including the classical Butterworth, Chebyshev and elliptic filters, can be realized as a parallel connection of two real or complex conjugate allpass filter. In this paper, a generalized structure where the allpass branches include arbitrary real or complex weighting constants is discussed. Applications of these generalized doubly complementary filters include gain equalizers, digital filters with multilevel magnitude response, and sharpening the amplitude response of digital filters realized as a cascade of identical filter stages.

This paper describes an implementation of a digital filter bank that is able to analyze a large bandwidth (6.5 MHz) with very good resolution (100 Hz) and high selectivity (out-of-band rejection of 70 dB). A three-stage filter-bank architecture is proposed. It is modular and, for the second and the third stage, very repetitive. An interesting aspect is that in all stages the uncertainty in the channel assignment, due to the transition band of the filters, is a percentage of the filter bandwidth. In this way a high selectivity of the first stage is not needed. Incidentally, if complementary filters are used to implement the filter bank, very selective are needed. With this regard, a new design approach is formulated.

A new frequency-domain based technique is proposed. In the proposed method, the magnitude of the Fourier transform of the image is modified using a noval amplitude change function with the phase kept invariant. The inverse transform of the new 2D transform results in an enhanced image. The amplitude change function used is the Tukey's twicing function ( Exploratory Data Analysis , Addison-Wesley, Reading, MA, 1977). In many applications, multiple use of the twicing function is shown to yield better results. The proposed method is somewhat similar to the alpha-rooting method but does not suffer from certain objectionable artifacts associated with the latter and also exhibits less degradation due to noise. A postprocessing of the enhanced image generated using the proposed transform amplitude method via histogram modification has been found to improve the picture quality. A number of image enhancement examples are included illustrating the effectiveness of the proposed method.

Several techniques are available for implementing a scalar digital filter using lattice and ladder structures which are known to yield low noise realizations. Of these, the lattice and ladder structures proposed by Gray and Markel have the advantage of being internally scaled. Block implementation of a scalar digital filter offers a number of advantages. In this paper, new algorithms to realize block digital filters in the form of cascaded lattice or ladder two-pairs are proposed. Block lattice and ladder structures similar to Gray and Markel's scalar structure are obtained by using Levinson recursion. Also, normalized block lattice and ladder structures are developed.

Explicit expressions of transfer functions for digital tan filters with low-pass, high-pass, band-pass, and band-stop characteristics approximating given design specifications are advanced. The higher order transfer function satisfying the design specification is expressed as the product of first-order and second-order filter sections of identical forms but with different coefficient values. All coefficients of these low-order filter sections are expressed in explicit forms related simply to the specification values. Thus, the result developed can be easily applied for the cascade or time-sharing realization. The low-order filter section developed here can be implemented with the fewest multipliers. The design formulae for Butterworth, Chebyshev, inverse Chebyshev and elliptic approximations are included. The transfer functions for all these filters are expressed in the same form of low-order filter section with different coefficient values.

This paper presents a formal precedure for determining the state-space representations of any digital network consisting of adders, multipliers, and delays. Such representations are called state structures whenever the state variables are exclusively identified to the appropriately chosen internal node variables of the network. In general, the state structures corresponding to a given network are not unique. In Part I of the paper we present techniques of obtaining the various state structures where the associated state vectors have dimensions equal to the number of dynamic elements (in our case delays) in the network. In Part II we shall treat the subject of lowering the dimension of such state-space representations.

A novel principle known as block transformation is developed for the block implementation of two-dimensional (2-D) digital filters. It employs the one-dimensional (1-D) block implementation concept forwarded by Burrus ( 7 ) as a basic tool. Using this block transformation principle three distinct forms of 2-D block equations are derived. The generalized nature of the approach presented here facilitates the straightforward extension of this technique to higher dimensional digital filters.

The implementation of a discrete feedback compensator using block processing is discussed. In this scheme, a block of L measurements are accumulated before the processing is initiated. A block of L compensation samples are then computed and released serially into the system being compensated. Compensator implementations are developed both for the ARMA and the state-variable representations.

The phase sensitivity with respect to coefficient errors is studied for a class of lattice digital allpass filters. It is shown that corresponding to each lattice parameter there is a set of frequencies for which the phase response remains invariant to an arbitrary perturbation of the parameter. In addition, a simple result of sensitivity “amplification” in lossless two-pair networks is derived, which is used to obtain means and bounds on the sensitivity functions for these lattice structures in term of the lattice parameters. From these results some useful coefficient sensitivity properties are inferred. A practical example is included to better understand the interaction of sensitivity mechanisms in lattice allpass filter realizations, in the context of transfer functions realized as the parallel connection of two allpass filters. Finally, it is shown that the order reduction process intrinsic to the lattice synthesis procedure minimizes the L ∞ norm of the phase sensitivity at each step.

Necessary and sufficient conditions for reducibility of certain classes of multivariable polynomials are considered. The special case when a polynomial in that class can be factored into a finite product of single variable polynomials is investigated. A set of necessary and sufficient conditions for decomposing a multivariable p.r.f. into a sum of single variable p.r.f.'s is given. Examples to illustrate applications of sum and product separabilities of functions are given.

A class of linear phase digital filters is discussed for which the filter coefficients are simple functions of the parameters determining the desired frequency response. In the case of lowpass or highpass filters, the 6 dB cutoff frequency is the parameter considered here. Bandpass and bandstop filters are characterized by the center frequency and the bandwidth measured from the 6 dB cutoff frequencies. Notch filters with a first-order zero at the notch frequency are also discussed. The filters are variable over nearly the whole frequency range from zero to half the sampling frequency. Due to direct control of filter coefficients, the length of the filter does not change when it is made variable.

The necessary and sufficient conditions for the physical realizability of one-port structures obtained by imbedding several nonidentical tunnel diodes (represented by a parallel combination of a positive capacitor and a negative resistor) in a network of positive resistances and positive capacitances are presented in this paper. Some new results concerning ±RC networks are also included, in addition to an alternate simpler derivation of Bello and Kinariwala's results regarding such networks.

This paper presents several lemmas which are of importance in the synthesis of one-port and n-port active RC networks. Syntheses of such networks are viewed from the equivalent active LC network point of view by making use of RC-LC transformation. The first part deals with one-ports. Replacement of the resistance in the Darlington realization of a positive real impedance by an appropriate negative LC impedance results in the odd part of the positive real function at the input. An inverse LC-RC transformation yields the decomposition, partitioning, and consequently the synthesis, of active RC impedances. Admittances are treated by a dual procedure. This approach is extended in the second part to the synthesis of active RC immittance matrices of order n. It is shown that in the latter case, the number of active elements needed is at most equal to n.

A unique decomposition of active RC driving-point impedance functions is presented, which has been obtained by considering the driving-point synthesis problem in terms of the reflection coefficient. Application of the decomposition has been shown to guarantee the realization of the driving-point impedance in Kinariwala's cascade configuration and Sandberg's special configurations, each containing one negative impedance converter. The method imposes no restriction on the impedance function, except that it has only to be a real rational function. The decomposition technique can be easily programmed for a digital computer.