Showing papers on "Discrete sine transform published in 2015"
TL;DR: In this paper, a novel direction-finding method by the time-modulated array (TMA) is proposed through analyzing the harmonic characteristic of received signal, which requires only two antenna elements and a single RF channel.
Abstract: A novel direction-finding method by the time-modulated array (TMA) is proposed through analyzing the harmonic characteristic of received signal, which requires only two antenna elements and a single RF channel. The signal processing of the proposed method is concise, and its calculation amount concentrates on a two-point discrete Fourier transform (DFT). Numeric simulations are provided to examine the performance of the proposed method, and a simple S band two-element TMA is constructed and tested to verify its effectiveness.
84 citations
TL;DR: A novel double-image encryption–compression scheme proposed by combining compressive sensing with discrete fractional random transform based on two circular matrices, demonstrating the validity and security of the scheme.
79 citations
TL;DR: In this paper, a positive-sequence phase-angle estimation method based on discrete Fourier transform for the synchronization of three-phase power-electronic converters under distorted and variable-frequency conditions is proposed.
Abstract: This paper proposes a positive-sequence phase-angle estimation method based on discrete Fourier transform for the synchronization of three-phase power-electronic converters under distorted and variable-frequency conditions. The proposed method is designed based on a fixed sampling rate and, thus, it can simply be employed for control applications. First, analytical analysis is presented to determine the errors associated with the phasor estimation using standard discrete Fourier transform in a variable-frequency environment. Then, a robust phase-angle estimation technique is proposed, which is based on a combination of estimated positive and negative sequences, tracked frequency, and two proposed compensation coefficients. The proposed method has one cycle transient response and is immune to harmonics, noises, voltage imbalances, and grid frequency variations. An effective approximation technique is proposed to simplify the computation of the compensation coefficients. The effectiveness of the proposed method is verified through a comprehensive set of simulations in Matlab software. Simulation results show the robust and accurate performance of the proposed method in various abnormal operating conditions.
49 citations
TL;DR: A function for calculating Euclidean distance transform in large binary images of dimension three or higher in Matlab that significantly outperforms the Matlab’s standard distance transform function “bwdist” both in terms of the computation time and the possible data sizes.
Abstract: In this note, we introduce a function for calculating Euclidean distance transform in large binary images of dimension three or higher in Matlab. This function uses transparent and fast line-scan algorithm that can be efficiently implemented on vector processing architectures such as Matlab and significantly outperforms the Matlab’s standard distance transform function “bwdist” both in terms of the computation time and the possible data sizes. The described function also can be used to calculate the distance transform of the data with anisotropic voxel aspect ratios. These advantages make this function especially useful for high-performance scientific and engineering applications that require distance transform calculations for large multidimensional and/or anisotropic datasets in Matlab. The described function is publicly available from the Matlab Central website under the name “bwdistsc”, “Euclidean Distance Transform for Variable Data Aspect Ratio”.
45 citations
TL;DR: The theory of a DHT that is shown to arise from a discretization scheme based on the theory of Fourier-Bessel expansions is proposed and evaluated and can be used to approximate the continuous forward and inverse Hankel transform in the same manner that the discrete Fourier transform is known to be able to approximation the continuous Fouriertransform.
Abstract: Previous definitions of a discrete Hankel transform (DHT) have focused on methods to approximate the continuous Hankel integral transform. In this paper, we propose and evaluate the theory of a DHT that is shown to arise from a discretization scheme based on the theory of Fourier-Bessel expansions. The proposed transform also possesses requisite orthogonality properties which lead to invertibility of the transform. The standard set of shift, modulation, multiplication, and convolution rules are derived. In addition to the theory of the actual manipulated quantities which stand in their own right, this DHT can be used to approximate the continuous forward and inverse Hankel transform in the same manner that the discrete Fourier transform is known to be able to approximate the continuous Fourier transform.
43 citations
TL;DR: This paper proposes reality-preserving fractional versions of the discrete Fourier, Hartley, generalized Fouriers, and generalized Hartley transforms, which have random outputs and many parameters and thus are very flexible.
Abstract: Real transforms require less complexity for computations and less memory for storages than complex transforms. However, discrete fractional Fourier and Hartley transforms are complex transforms. In this paper, we propose reality-preserving fractional versions of the discrete Fourier, Hartley, generalized Fourier, and generalized Hartley transforms. All of the proposed real discrete fractional transforms have as many as $O(N^{2})$ parameters and thus are very flexible. The proposed real discrete fractional transforms have random eigenvectors and they have only two distinct eigenvalues 1 and $-$ 1. Properties and relationships of the proposed real discrete fractional transforms are investigated. Besides, for the real conventional discrete Hartley and generalized discrete Hartley transforms, we propose their alternative reality-preserving fractionalizations based on diagonal-like matrices to further increase their flexibility. The proposed real transforms have all of the required good properties to be discrete fractional transforms. Finally, since the proposed new transforms have random outputs and many parameters, they are all suitable for data security applications such as image encryption and watermarking.
43 citations
19 Apr 2015
TL;DR: Objective results indicate that this representation of f0 improves f0 prediction over traditional short-term approaches and is comparable to the recently proposed CWT-HMM, while using less parameters.
Abstract: We propose a representation of f0 using the Continuous Wavelet Transform (CWT) and the Discrete Cosine Transform (DCT). The CWT decomposes the signal into various scales of selected frequencies, while the DCT compactly represents complex contours as a weighted sum of cosine functions. The proposed approach has the advantage of combining signal decomposition and higher-level representations, thus modeling low-frequencies at higher levels and high-frequencies at lower-levels. Objective results indicate that this representation improves f0 prediction over traditional short-term approaches. Subjective results show that improvements are seen over the typical MSD-HMM and are comparable to the recently proposed CWT-HMM, while using less parameters. These results are discussed and future lines of research are proposed.
37 citations
TL;DR: The numerical simulations have demonstrated the validity and high security level of the image cryptosystem based on the novel transform which is similar to fractional Fourier transform and gyrator transform to some extent.
37 citations
TL;DR: The derived overall intraframe coding approaches can generalize the mentioned two approaches, provide improved coding gains and produce less blocking effects at low bitrates.
Abstract: Conventional intraframe coding is performed in two steps First, a block of pixels are predicted by copying previously reconstructed neighbor pixels of the block along an angular direction inside the block Then, the prediction residual block is transform coded with the well-known 2D discrete cosine transform (DCT) Recently, it has been shown that transforming the intraprediction residuals with the odd type-3 discrete sine transform along the prediction direction and the DCT along the perpendicular direction improves the compression performance More recently, a recursive prediction approach has been proposed to improve intra prediction performance Both of these recent approaches utilize Markov processes to develop improvements in either the transform or the prediction step but not in both In this paper, both the intraprediction and the transform steps are obtained based on 2D Markov processes The derived overall intraframe coding approaches can generalize the mentioned two approaches, provide improved coding gains and produce less blocking effects at low bitrates
31 citations
TL;DR: A new, fast and computationally efficient lateral subpixel shift registration algorithm is presented that reduces computation time and memory requirements without sacricing the accuracy associated with the usual FFT approach accuracy.
Abstract: A new, fast and computationally efficient lateral subpixel shift registration algorithm is presented. It is limited to register images that differ by small subpixel shifts otherwise its performance degrades. This algorithm significantly improves the performance of the single-step discrete Fourier transform approach proposed by Guizar-Sicairos and can be applied efficiently on large dimension images. It reduces the dimension of Fourier transform of the cross correlation matrix and reduces the discrete Fourier transform (DFT) matrix multiplications to speed up the registration process. Simulations show that our algorithm reduces computation time and memory requirements without sacricing the accuracy associated with the usual FFT approach accuracy.
28 citations
TL;DR: A new guaranteed stable SDFT (gSDFT) algorithm of which the computational requirement is the lowest among the existing stable S DFT algorithms and is mathematically equivalent to that of the DFT regardless of the window size and the time index.
Abstract: Discrete orthogonal transforms such as the discrete Fourier transform (DFT), discrete Hartley transform (DHT), and Walsh?Hadamard transform (WHT) play important roles in the fields of digital signal processing, filtering, and communications. In recent years, there has been a growing interest in the sliding transform process where the transform window is shifted one sample at a time and the transform process is repeated.
TL;DR: It is found that the attenuation histo-images can be uniquely determined from the TOF-PET histo -images by considering boundary conditions.
Abstract: In positron emission tomography (PET) imaging, attenuation correction with accurate attenuation estimation is crucial for quantitative patient studies. Recent research showed that the attenuation sinogram can be determined up to a scaling constant utilizing the time-of-flight information. The TOF-PET data can be naturally and efficiently stored in a histo-image without information loss, and the radioactive tracer distribution can be efficiently reconstructed using the DIRECT approaches. In this paper, we explore transmission-less attenuation estimation from TOF-PET histo-images. We first present the TOF-PET histo-image formation and the consistency equations in the histo-image parameterization, then we derive a least-squares solution for estimating the directional derivatives of the attenuation factors from the measured emission histo-images. Finally, we present a fast solver to estimate the attenuation factors from their directional derivatives using the discrete sine transform and fast Fourier transform while considering the boundary conditions. We find that the attenuation histo-images can be uniquely determined from the TOF-PET histo-images by considering boundary conditions. Since the estimate of the attenuation directional derivatives can be inaccurate for LORs tangent to the patient boundary, external sources, e.g. a ring or annulus source, might be needed to give an accurate estimate of the attenuation gradient for such LORs. The attenuation estimation from TOF-PET emission histo-images is demonstrated using simulated 2D TOF-PET data.
01 Dec 2015
TL;DR: Experimental results show that GFTs derived from graph templates lead to sparser signal representations and fewer encoding bits than DCT for a set of natural test images, and optimal edge weights are computed assuming each template is a graph describing the inter-pixel correlation in a Gaussian Markov Random Field.
Abstract: The graph Fourier transform (GFT) — adaptive to the signal structures of local pixel blocks — has recently been shown to be a good alternative to fixed transforms, e.g., the Discrete Cosine Transform (DCT), for image coding. However, the majority of proposed GFTs assume an underlying 4-connected graph structure with vertical and horizontal edges only. In this paper, we propose a design methodology to select more general sparse graph structures and edge weights, on which GFTs are defined for block-based coding. Specifically, we first cluster blocks via the Lloyd-Max algorithm based on their principal gradients, which are eigenvectors of the computed structure tensors. For each cluster a graph template with edges orthogonal to the principal gradient is designed. Finally, optimal edge weights are computed assuming each template is a graph describing the inter-pixel correlation in a Gaussian Markov Random Field (GMRF). Experimental results show that GFTs derived from our graph templates lead to sparser signal representations and fewer encoding bits than DCT for a set of natural test images.
TL;DR: Simulation indicates that the discrete cosine transform provides better initial values than discrete Fourier transform does, and it converges to a more accurate level by updating with spectrum-based slopes comparing to the slope updates from finite difference in classical method.
TL;DR: The M-RDGT offers a computationally efficient implementation as well as a real-valued formulation of the multiwindow complex-valued discrete Gabor transform (M-CDGT) and its corresponding biorthogonality constraint between analysis windows and synthesis windows is modified.
Abstract: Based on the biorthogonal analysis approach, a multiwindow real-valued discrete Gabor transform (M-RDGT) for periodic sequences is presented to efficiently analyze the dynamic time-frequency content of a signal containing components with multiple and/or time-varying frequencies. The M-RDGT offers a computationally efficient implementation as well as a real-valued formulation of the multiwindow complex-valued discrete Gabor transform (M-CDGT). The completeness condition of the M-RDGT is proved to be equivalent to its biorthogonality constraint between analysis windows and synthesis windows. The M-RDGT can utilize the fast discrete Hartley transform algorithms for fast computation and has a simple relationship with the M-CDGT such that its coefficients can be directly computed from the M-RDGT coefficients. Therefore, the M-RDGT offers an efficient method to compute the M-CDGT. Since the analyzed sequence, analysis and synthesis windows in the existing M-CDGT must have an equal period, if the period of a sequence is very long, solving its windows requires a huge amount of computation and memory and could lead to numerical instability. To overcome this problem, a modified M-RDGT for long-periodic (or even infinite) sequences is presented and its corresponding biorthogonality constraint between analysis windows and synthesis windows is modified, in which the period of the analysis and synthesis windows is independent of the period of a analyzed sequence so that one can apply short windows to process any long-periodic (or even in finite) sequence. Finally, the multirate-based parallel implementation of the M-RDGT is presented, which has shown to be effective and fast for time-frequency analysis.
TL;DR: Numerical simulation about one-dimensional signal demonstrates that the MRFrFT has an important feature that the magnitude and phase of its output are both random.
Abstract: We propose a multichannel random discrete fractional Fourier transform (MRFrFT) with random weighting coefficients and partial transform kernel functions First, the weighting coefficients of each channel are randomized Then, the kernel functions, selected based on a choice scheme, are randomized using a group of random phase-only masks (RPOMs) The proposed MRFrFT can be carried out both electronically and optically, and its main features and properties have been given Numerical simulation about one-dimensional signal demonstrates that the MRFrFT has an important feature that the magnitude and phase of its output are both random Moreover, the MRFrFT of two-dimensional image can be viewed as a security enhanced image encryption scheme due to the large key space and the sensitivity to the private keys
03 Dec 2015
TL;DR: This paper proposes a new approach to this problem, designing a new transform that can be steered in any chosen direction and that is defined in a rigorous mathematical way, enabling precise matching of directionality in each image block, and thereby achieving improved coding efficiency.
Abstract: Block-based separable transforms tend to be inefficient when blocks contain arbitrarily shaped discontinuities. For this reason, transforms incorporating directional information are an appealing alternative. In this paper, we propose a new approach to this problem, designing a new transform that can be steered in any chosen direction and that is defined in a rigorous mathematical way. This new steerable DCT allows to rotate in a flexible way pairs of basis vectors, enabling precise matching of directionality in each image block, and thereby achieving improved coding efficiency. We tested the proposed transform on several images and the results show that it provides a significant performance gain compared to the DCT. Moreover, the mathematical framework on which the steerable DCT is based allows to generalize the transform to more complex steering patterns than a single pure rotation.
TL;DR: A new modulated hopping Discrete Fourier Transform (mHDFT) algorithm which is characterized by its merits of high accuracy and constant stability is presented and the numerical simulation results verify the effectiveness and superiority of the proposed algorithm.
Abstract: A new modulated hopping Discrete Fourier Transform (mHDFT) algorithm which is characterized by its merits of high accuracy and constant stability is presented. The proposed algorithm, which is based on the circular frequency shift property of DFT, directly moves the k-th DFT bin to the position of k = 0, and computes the DFT by incorporating the successive DFT outputs with arbitrary time hop L. Compared to previous works, since the pole of mHDFT precisely settles on the unit circle in the Z-plane, the accumulated errors and potential instabilities, which are caused by the quantization of the twiddle factor, are always eliminated without increasing much computational effort. The numerical simulation results verify the effectiveness and superiority of the proposed algorithm.
TL;DR: Simulation results show that the proposed ADMR algorithm provides higher recognition rates than those obtained in previous studies, in addition to a superiority of SVM performance compared to ANN performance at low signal-to-noise ratios.
Abstract: Automatic digital modulation recognition (ADMR) has become an interesting problem in wireless communication systems with various civil and military applications. In this paper, an ADMR algorithm is proposed for both orthogonal frequency division multiplexing and multi-carrier code division multiple access systems using discrete transforms and mel-frequency cepstral coefficients (MFCCs). The proposed algorithm uses one of the discrete cosine transform, discrete sine transform, and discrete wavelet transform with MFCCs to extract the modulated signal coefficients, and uses also either a support vector machine (SVM) or an artificial neural network (ANN) for modulation classification. Simulation results show that the proposed algorithm provides higher recognition rates than those obtained in previous studies, in addition to a superiority of SVM performance compared to ANN performance at low signal-to-noise ratios.
Posted Content•
TL;DR: It is proved that the DFnT of a circular convolution of two sequences equals either one circularly convolving with the DFt of the other, which not only gives the coefficients of the Talbot image, but can also be useful for optical and digital signal processing and numerical evaluation of the Fresnel transform.
Abstract: Discrete trigonometric transformations, such as the discrete Fourier and cosine/sine transforms, are important in a variety of applications due to their useful properties. For example, one well-known property is the convolution theorem for Fourier transform. In this letter, we derive a discrete Fresnel transform (DFnT) from the infinitely periodic optical gratings, as a linear trigonometric transform. Compared to the previous formulations of DFnT, the DFnT in this letter has no degeneracy, which hinders its mathematic applications, due to destructive interferences. The circular convolution property of the DFnT is studied for the first time. It is proved that the DFnT of a circular convolution of two sequences equals either one circularly convolving with the DFnT of the other. As circular convolution is a fundamental process in discrete systems, the DFnT not only gives the coefficients of the Talbot image, but can also be useful for optical and digital signal processing and numerical evaluation of the Fresnel transform.
TL;DR: A modeling scheme to decompose the discrete Fourier transform (DFT) matrix recursively into a set of sparse matrices and is able to obtain different FFT representations with less computation operations than state of the arts.
15 Mar 2015
TL;DR: The generation of the orthogonal signal is achieved by the discrete Fourier transform (DFT) filter, which offers better harmonics immunity and DC component rejection capacity and makes the proposed DFT-PLL especially suitable for harmonically distorted and frequency-varying applications.
Abstract: A new single-phase synchronous reference frame phase-locked loop (SRF-PLL) is proposed in this paper. The key point to implement single-phase SRF-PLL is how to generate the orthogonal signal accurately, even under polluted grids with harmonics and DC components. In this paper, the generation of the orthogonal signal is achieved by the discrete Fourier transform (DFT) filter. Compared with conventional SRF-PLLs, the DFT-based PLL (DFT-PLL) proposed offers better harmonics immunity and DC component rejection capacity. Besides, the proposed method incorporates grid frequency variations by adjusting the sampling period of DFT according to the estimated frequency. Also, digital implementation of DFT-PLL is simple and straightforward with low computational burden. These advantages make the proposed DFT-PLL especially suitable for harmonically distorted and frequency-varying applications. Experimental results and comparisons with two another widely used SRF-PLLs are given to validate the effectiveness and advantages of the proposed method.
TL;DR: It is proved that the first eight eigenvectors converge to the corresponding Hermite functions, and it is conjecture that this convergence result remains true for all eigenvctors.
Abstract: The search for a canonical set of eigenvectors of the discrete Fourier transform has been ongoing for more than three decades. The goal is to find an orthogonal basis of eigenvectors which would approximate Hermite functions---the eigenfunctions of the continuous Fourier transform. This eigenbasis should also have some degree of analytical tractability and should allow for efficient numerical computations. In this paper we provide a solution to these problems. First, we construct an explicit basis of (nonorthogonal) eigenvectors of the discrete Fourier transform, thus extending the results of [F. N. Kong, IEEE Trans. Circuits Syst. II. Express Briefs, 55 (2008), pp. 56--60]. Applying the Gram--Schmidt orthogonalization procedure we obtain an orthogonal eigenbasis of the discrete Fourier transform. We prove that the first eight eigenvectors converge to the corresponding Hermite functions, and we conjecture that this convergence result remains true for all eigenvectors.
TL;DR: A proposed method of calculating the 2r × 2r -point 2-D QDFT uses 18N2 less multiplications than the well-known column-row method and method of calculation based on the symplectic decomposition.
Abstract: In this paper, a general, efficient, split algorithm to compute the two-dimensional quaternion discrete Fourier transform (2-D QDFT), by using the special partitioning in the frequency domain, is introduced. The partition determines an effective transformation, or color image representation in the form of 1-D quaternion signals which allow for splitting the N × M-point 2-D QDFT into a set of 1-D QDFTs. Comparative estimates revealing the efficiency of the proposed algorithms with respect to the known ones are given. In particular, a proposed method of calculating the 2r × 2r -point 2-D QDFT uses 18N2 less multiplications than the well-known column-row method and method of calculation based on the symplectic decomposition. The proposed algorithm is simple to apply and design, which makes it very practical in color image processing in the frequency domain.
TL;DR: A low complexity estimation algorithm using interpolated discrete Fourier transform approach is introduced to replace the gradient descent (GD) or the chirp z transform (CZT) methods.
Abstract: Frequency offset estimation algorithms for M-ary quadrature amplitude modulation based on the maximization of the periodogram of fourth-power samples have been investigated. In this letter, a low complexity estimation algorithm using interpolated discrete Fourier transform approach is introduced to replace the gradient descent (GD) or the chirp $z$ transform (CZT) methods. The numerical simulations and complexity analysis demonstrate that the proposed estimator has much lower computational complexity than that of GD and CZT without performance degradation.
01 Oct 2015
TL;DR: 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.
Abstract: 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.
TL;DR: In this paper, the authors studied discrete Hilbert boundary value problems in the case of the upper half lattice and proved that the solutions converge to those of the associated continuous Hilbert boundary values.
Abstract: We study discrete Hilbert boundary value problems in the case of the upper half lattice. The solutions are given in terms of the discrete Cauchy transforms for the upper and lower half space while the study of their solvability is based on the discrete Hardy decomposition for the half lattice. Furthermore, the solutions are proved to converge to those of the associated continuous Hilbert boundary value problems.
TL;DR: The GMRES method with the PSHNS preconditioner demonstrates meshsize-independent and wavenumber-insensitive convergence behavior, and a fast algorithm is applied to solve the subsystem during the preconditionsing process using discrete Sine transform.
05 Mar 2015
TL;DR: An architecture for real time hardware implementation of Hilbert Transform (HT) using Fast Fourier Transform (FFT) using Xilinx Kintex- 7 based FPGA is presented and the results acquired are presented in comparison to results obtained through MATLAB simulations.
Abstract: This paper presents an architecture for real time hardware implementation of Hilbert Transform (HT) using Fast Fourier Transform (FFT). HT is studied and its various application areas are discussed in the paper. Two different architectures are proposed using Fast Fourier Transform (FFT) for the implementation. Implementation of HT using the proposed FFT based architectures are compared with the implementations using Discrete Fourier Transform (DFT) and Discrete Hartley Transform (DHT). The proposed FFT based architectures are implemented on Xilinx Kintex- 7 based FPGA and the results acquired are presented in comparison to results obtained through MATLAB simulations. The architecture implemented supports transform length of 8192 points as a demonstrator to the idea using 24 bit fixed point arithmetic. Detailed comparison study in terms of resource utilization and timing analysis is also carried out and the results are reported.
Dissertation•
11 Dec 2015
TL;DR: This thesis focuses on extending HEVC through the use of multiple transforms, and uses two different types of transforms based separable orthogonal transforms and Discrete Trigonometric Transforms (DTTs) in particular.
Abstract: State of the art video codecs use transforms to ensure a compact signal representation. The transform stage is where compression takes place, however, little variety is observed in the type of transforms used for standardised video coding schemes: often, a single transform is considered, usually a Discrete Cosine Transform (DCT). Recently, other transforms have started being considered in addition to the DCT. For instance, in the latest video coding standard, High Efficiency Video Coding (HEVC), the 4x4 sized blocks can make use of the Discrete Sine Transform (DST) and, in addition, it also possible not to transform them. This fact reveals an increasing interest to consider a plurality of transforms to achieve higher compression rates. This thesis focuses on extending HEVC through the use of multiple transforms. After a general introduction to video compression and transform coding, two transform designs are studied in detail: the Karhunen Loeve Transform (KLT) and a Rate-Distortion Optimised Transform are considered. These two methods are compared against each other by replacing the transforms in HEVC. This experiment validates the appropriateness of the design. A coding scheme that incorporates and boosts the use of multiple transforms is introduced: several transforms are made available to the encoder, which chooses the one that provides the best rate-distortion trade-off. Consequently, a design method for building systems using multiple transforms is also described. With this coding scheme, significant amounts of bit-rate savings are achieved over HEVC, especially when using many complex transforms. However, these improvements come at the expense of increased complexity in terms of coding, decoding and storage requirements. As a result, simplifications are considered while limiting the impact on bit-rate savings. A first approach is introduced, in which incomplete transforms are used. This kind of transforms use one single base vector and are conceived to work as companions of the HEVC transforms. This technique is evaluated and provides significant complexity reductions over the previous system, although the bit-rate savings are modest. A systematic method, which specifically determines the best trade-offs between the number of transforms and bit-rate savings, is designed. This method uses two different types of transforms based separable orthogonal transforms and Discrete Trigonometric Transforms (DTTs) in particular. Several designs are presented, allowing for different complexity and bitrate savings trade-offs. These systems reveal the interest of using multiple transforms for video coding.