Polyphase Decomposition Research Articles

Agile Single- and Dual-Band All-Digital Transmitter Based on a Precompensated Tunable Delta–Sigma Modulator

In this paper, a new architecture for designing tunable single- and dual-band radio-frequency fully digital transmitters is proposed and validated. The proposed architecture excels the state of the art in terms of simplicity and flexibility. While its short critical path leverages the use of equivalent polyphase decomposition techniques to increase the global system’s sampling frequency, the capability of changing the system’s frequency response in real time enables its use in both single- and dual-band transmission scenarios. To mitigate a crosstalk in the dual-band scenario, a precompensation technique is also proposed. This novel concept has been successfully validated in a field-programmable gate array (FPGA) based transmitter. To validate both the proposed transmitter as well as the precompensation mechanism, spectrum and error-vector magnitude (EVM) measurements were obtained for two scenarios with a carrier frequency of 2.5 GHz: 1) single-band, using quadrature phase-shifting keying (QPSK), 16-quadrature amplitude modulation (QAM) and 64-QAM, with no intermediate frequency (IF), for different symbol rate (SR) values (from 3.125 up to 15.625 Msps) and 2) single- and dual-band, using QPSK and 16-QAM, with an SR of 3.125 Msps, for different IF values (from 2 up to 120 MHz). All the experimental results present EVM values below 2.6%, resulting in a well-defined constellation.

All-Digital Calibration of Timing Skews for TIADCs Using the Polyphase Decomposition

This brief proposes a new all-digital calibration technique suppressing the timing mismatch effect in time-interleaved analog-to-digital converters (TIADCs) for input at any Nyquist band (NB) using the equivalent polyphase structure of the TIADC. The correction technique is simple and does not require the adaptive digital synthesis filters. The timing mismatch is estimated based on an adaptive stochastic gradient descent technique, which is a promising solution for TIADCs operating at a very fast sampling rate. The digital circuit of the proposed calibration algorithm is designed and synthesized using a 28-nm fully depleted Silicon on insulator (FD-SOI) CMOS technology for the 11-b 60-dB SNR TIADC clocked at 2.7 GHz with the input in the first four NBs. The designed circuit occupies the area of 0.05 mm2 and dissipates the total power of 41 mW.

Design and Implementation of Less Complexity Fast Parallel FIR Filter

Filters play a vital role in information and communication technology. This project proposes a less complexity FFA based parallel FIR filter design and implementation. This paper proposes the design of fast parallel filter with the block sizes L=2,3 and 4 respectively. By employing parallelism two or more number of samples are processed at each clock cycle which can be effectively used for multirate applications. The number of complex multiplications are reduced by employing polyphase decomposition. Here for all the cases, the overall filter output responses is decomposed in to several sub parts which includes sub filters and adders used before and after filters. The computational complexity is reduced for the fast parallel FIR filter when compared to the conventional parallel FIR filter. The simulation is done in Verilog with cyclone II family and EP2C70F672C6 device and EP2C35F672C6 device. The hardware implementation is done with Altera DE2 board and the results are reported. The results shows that the fast parallel filtering is efficient in terms of computational complexity

Polyphase Decomposition for Tunable Band-Pass Sigma-Delta A/D Converters

The use of the polyphase decomposition technique applied to the noise transfer function (NTF) of band-pass sigma-delta $({\rm BP} \Sigma \Delta)$ modulators is introduced and theoretically analyzed. Schemes for a second-order and fourth-order band-pass noise shaping are discussed in detail. The method is usable for any order but the analog inaccuracy limits its application. It is shown that an extension to MASH configurations is possible. The method allows tunability of the centre frequency over a wide frequency range. Moreover, MASH schemes allow a rough-fine tuning with the rough tuning in the analog section followed by a fine digital adjustment. Simulation results verify the benefits and outline possible limits.

Theory and design of two-dimensional DFT modulated filter bank with arbitrary modulation and decimation matrices

It is well known that two-dimensional (2D) filter bank is far removed from a straightforward extension of one-dimensional (1D) filter bank. There are many challenging problems on the theory and design methods for the 2D filter bank. Among these problems, the perfect-reconstruction (PR) theory of the 2D DFT modulated filter bank with arbitrary modulation and decimation matrices remains an unsolved difficulty, which is the focus of this paper. The necessary and sufficient condition for perfect reconstruction (PR) is derived by using the polyphase decomposition of the analysis and synthesis filters, as well as the fast implementation structure of the filter bank. Then, the PR condition in frequency domain is transformed into a set of quadratic equations with respect to the prototype filter (PF), which is utilized to formulate the design problem into an unconstrained optimization problem. An efficient iterative algorithm is proposed to solve the problem. Numerical examples are included to verify the validity of the PR condition and the effectiveness of the design method.

Adaptive beamforming for acoustic echo cancellation using measured array models and subband filtering

Acoustic echo that can substantially undermine speech quality is one of the key issues must be addressed in practical telecommunication systems. In this paper, an evolutionary exposition is given in regard to the enhancing strategies for acoustic echo cancelers (AEC). On the basis basic adaptive filtering, a highly directional microphone array is designed as a fixed beamformer (FBF) to focus on the near-end speaker and suppress the echo from the far-end as well as noise and interference from the background. Design of the beamformer is based on array models interpolated from measured frequency responses. Subband (SB) filtering with polyphase decomposition is exploited to accelerate the cancellation process with multiple choice of step size in the subbands. To further enhance the canceler, adaptive generalized sidelobe canceler (GSC) can be utilized, which is comprised of a FBF for the near-end speech and an adaptive blocking module for the echo and noise. Objective tests in terms of echo return loss enhancement (ERLE) and perceptual evaluation of speech quality (PESQ) are conducted to compare four algorithms with various combinations of enhancement. The results show that the GSC-SB-AEC approach has attained the highest ERLE and best speech quality, even in a double-talk scenario.

A Low Complexity Subband Adaptive Filter with Two-Stage Decomposition

The conventional subband adaptive filter (SAF) based on poly-phase decomposition has fast convergence behavior compared by fullband adaptive filter. However, the complexity for one-stage signal decomposition increases significantly, as increasing the number of subband to improve the convergence further. To solve this problem, a new SAF is proposed in this letter, which is constructed with two-stage decomposition. Based on the proposed structure, an adaptive algorithm of updating coefficients is derived based on the principle of minimal disturbance. Compared to the conventional SAF with one-stage decomposition, the proposed one has similar convergence rate with a lower complexity. Theoretical analysis and simulation results validated the superiority of the proposed SAF.

Super resolution of aerial image by means of polyphase components reconstruction

Multi-frame super resolution reconstruction is a technology for obtaining a high resolution image from a set of blurred and aliased low resolution images. The most popular and widely used super resolution methods are motion based. However, the estimation of motion information (registration) is very difficult, computationally expensive and inaccurate, especially for aerial image. The sub-pixel registration error restricts the performance of the subsequent super resolution. Instead of trying to parameterize the motion estimation model, this paper proposes an image super resolution framework based on the polyphase components reconstruction algorithm and an improved steering kernel regression algorithm. Given an image observation model, a reversible 2D polyphase decomposition, which breaks down a high resolution image into polyphase components, is obtained. Though the assumption of diversity sampling, this paper adopts a fundamentally different approach, in which the low-resolution frames is used as the basis and the reference frame as the reference sub-polyphase component of the high resolution image for recovering the polyphase components of the high resolution image. The polyphase components, which fuse the low resolution frames with the complementary details, can be obtained by computing their expansion coefficients in terms of this basis using the available sub-polyphase components and then inversely transforming them into a high resolution image. This paper accomplishes this by formulating the problem as the maximum likelihood estimation, which guarantees a close-to-perfect solution. Furthermore, this paper proposes an improved steering kernel regression algorithm, to help restore the fusion image with mild blur and random noise. This paper adaptively refines the steering kernel regression function according to the local region context and structures. Thus, this new algorithm not only effectively combines denoising and deblurring together, but also preserves the edge information. Our framework develops an efficient and stable algorithm to tackle the huge size and ill-posedness of the super resolution problem, and improves the computational efficiency via avoiding registration and iterative computation. Several experimental results on synthetic data illustrate that our method outperforms the state-of-the-art methods in quantitative and qualitative comparisons. The proposed super resolution algorithm can indeed reconstruct high-frequency information which is otherwise unavailable in the single LR image. It can effectively suppress blur and noise, and produce visually pleasing resolution enhancement in aerial images.

Polyphase Decomposition of Digital Fractional-Delay Filters

This letter shows that, for arbitrary $M$ -fold polyphase decompositions, the polyphase components of digital fractional-delay (FD) filters correspond to FD filters as well, but with different delays and gains. For even values of $M$ , the components also have additional and different phase offsets. The letter also discusses the application of these results to the optimization of high-order filters with few unknowns.

A Novel Hybrid Method for Remote Sensing Image Approximation Using the Tetrolet Transform

Most existing image sparse approximation methods can reach their best performance only under the condition that the image has some certain properties. In addition, for the remote sensing image, it is difficult to obtain a good sparse result if it contains a lot of details. Focused on the two problems, in this paper, a novel hybrid method that is of some generality is proposed. The method exploits the advantages of the tensor product wavelet transform for representation of smooth images and the ability of the tetrolet transform to represent texture and edge effectively at the same time. Moreover, two specialized processes of decomposition are designed, which contribute to increasing the energy concentration further and preserving the information of the details as much as possible. The procedure of the proposed hybrid method is as follows: for a given remote sensing image, first, the usual tensor product wavelet transform is used, then the redundancy among adjacent wavelet coefficients is removed by making a polyphase decomposition to each subband with a p-fold filter, and after that, the approximation of the low frequency image can be obtained by reconstructing those preserved coefficients. Second, for the detailed image, the sparse decomposition is carried out by the tetrolet transform. For the high frequency subbands, an adaptive decomposition will be done for increasing the energy aggregation. After that, the approximation of the detailed image can be obtained by reconstructing those preserved coefficients. Numerical results indicate the high effectiveness of the procedure for remote sensing image sparse approximation.

Polyphase Structure Based Eigen Design of Two-Channel Quadrature Mirror Filter Bank

This paper presents a method for the design of two-channel quadrature mirror filter (QMF) banks with linear phase in frequency domain. Low-pass prototype filter of the QMF bank is implemented using polyphase decomposition. Prototype filter coefficients are optimized to minimize an objective function using eigenvalue- eigenvector approach without matrix inversion. The objective function is formulated as a weighted sum of four terms, pass-band error and stop-band residual energy of low-pass analysis filter, the square error of the overall transfer function at the quadrature frequency and amplitude distortion of the filter bank. The simulation results clearly show that the proposed method requires less computational efforts in comparison to the other state-of-art existing design methods.

Second Order Taylor Polyphase Reconstruction of Periodic-Nonuniform Samples in Time-Interleaved ADCs

This paper focuses on a filter bank approach for reconstructing periodic-nonuniform samples using second order Taylor polyphase decomposition for a four-channel time-interleaved ADC (TIADC). The proposed method is based on a parametric linear least squares approach to find the coefficients of synthesis filters used for signal reconstruction of periodic-nonuniform samples. The coefficients of synthesis filters found by linear least squares approach satisfy the general condition for an alias-free filter bank.

Gamma Splines and Wavelets

In this work we introduce a new family of splines termed as gamma splines for continuous signal approximation and multiresolution analysis. 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We study the properties of the discrete gamma splines in signal interpolation and approximation. We prove that the gamma splines obey the two-scale equation based on the polyphase decomposition. to introduce the shift invariant gamma spline wavelet transform for tree structured subscale analysis of asymmetric signal waveforms and for systems with asymmetric impulse response. Especially we consider the applications in biomedical signal analysis (EEG, ECG, and EMG). Finally, we discuss the suitability of the gamma spline signal processing in embedded VLSI environment.

Application of Generalized Sharpening Technique for Two-Stage Comb Decimator Filter Design

This paper introduces the generalized sharpening technique to improve the magnitude characteristics of comb decimation filter in passband as well in the folding bands. To this end we design two-stage comb filter. The first stage can be operated at low sampling rate by using polyphase decomposition. A simple compensator is applied in the second stage to improve the passband characteristic of the comb in the second stage. Then the generalized sharpening technique is applied to decrease the passband droop induced by the comb filter placed in the first stage. As a result, a computationally efficient comb-based decimation filter is obtained which presents better magnitude characteristics than previous proposed sharpening methods.

Multi-channel filter banks associated with linear canonical transform

The linear canonical transform (LCT) has been shown to be a powerful tool for optics and signal processing. This paper investigates multi-channel filter banks associated with the LCT. First, the perfect reconstruction (PR) conditions are analyzed and design method of PR filter banks for the LCT is proposed, which demonstrates that the LCT based filter banks can inherit conventional design methods of filter banks in the Fourier domain. Then polyphase decompositions in the LCT domain are defined and polyphase realization of the LCT based filter banks is derived in terms of polyphase matrices. Furthermore, multi-channel cyclic filter banks associated with the LCT are proposed by defining circular convolution in the LCT domain. The PR design method and polyphase representation of cyclic filter banks for the LCT are derived similarly. Finally, simulations validate the proposed design methods of the LCT based filter banks and also demonstrate potential application of the LCT based cyclic filter banks in image subband decomposition.

H∞-Optimal Fractional Delay Filters with Application to Pitch Shifting

Fractional delay filters are digital filters to delay discrete-time signals by a fraction of the sampling period. Since the delay is fractional, the intersample behavior of the original analog signal becomes crucial. In contrast to the conventional designs based on the Shannon sampling theorem with the band-limiting hypothesis, the present paper proposes a new approach based on the modern sampled-data H∞ optimization which aims at restoring the intersample behavior beyond the Nyquist frequency. By using the lifting transform or continuous-time polyphase decomposition, the design problem is equivalently reduced to a discrete-time H∞ optimization, which can be effectively solved by numerical computation softwares. Moreover, a closed-form solution is obtained under an assumption on the original analog signals. Using this closed-form solution, we introduce a sampling rate conversion with arbitrary conversion rate, and propose a new pitch shifting method for digital sound synthesis. Design examples are given to illustrate the advantage of the proposed method.

On Passband and Stopband CIC Improvements Using a Second Order IIR Filter

This paper proposes an efficient second order IIR filter which considerably improves the passband as well as the stopband of the Cascaded-Integrator-Comb (CIC) filter. Using the polyphase decomposition of the proposed filte, all filtering can be moved to a lower rate, which is D times less than the high input rate, where D is the decimation factor. The overall phase response of the compensated CIC is approximately linear in the passband. The design parameters are the number of cascaded CIC filter N, the decimator factor D, the passband frequency w p , and a weighted parameter a.

On Passband and Stopband Cascaded-Integrator-Comb Improvements Using a Second Order IIR Filter

This paper proposes an efficient second order IIR filter which considerably improves the passband as well as the stopband of the cascaded-integrator-comb (CIC) filter. Using the polyphase decomposition of the proposed filter, all filtering can be moved to a lower rate, which is D times less than the high input rate, where D is the decimation factor. The overall phase response of the compensated CIC is approximately linear in the passband. The design parameters are the number of cascaded CIC filter N, the decimator factor D, the passband frequency w p , and a weighted parameter a .

On Passband and Stopband CIC Improvements Using a Second Order IIR Filter

This paper proposes an efficient second order IIR filter which considerably improves the passband as well as the stopband of the Cascaded-Integrator-Comb (CIC) filter. Using the polyphase decomposition of the proposed filte, all filtering can be moved to a lower rate, which is D times less than the high input rate, where D is the decimation factor. The overall phase response of the compensated CIC is approximately linear in the passband. The design parameters are the number of cascaded CIC filter N, the decimator factor D, the passband frequency w p , and a weighted parameter a.

Power Consumption Models for Decimation FIR Filters in Multistandard Receivers

Decimation filters are widely used in communication‐embedded systems. In fact, decimation filters are useful for implementing channel filtering or selection with low‐computation complexity requirements. Many multistandard receiver designs that are required in ubiquitous embedded systems are based on a cascade of decimation filter processing. Filter number and implementation architectures have a significant impact on system performances, such as computation complexity, area, throughput, and power consumption. In this work, we present filter power consumption estimation models for FIR filters. Power consumption models were obtained from a large number of FIR filter syntheses using a direct form. Several curves that estimate power consumption were extracted from these synthesis results. Then, we have evaluated the impact of polyphase decomposition on power consumption of FIR filter and compared it with the direct form results. Some tips regarding power consumption were deduced for the polyphase implementation form. The aim of this work is to help a system designer to select an efficient implementation for FIR in terms of power consumption without having to implement and synthesize the different possible solutions. The proposed method is applied for STMicroelectronics libraries 90 nm and 65 nm low power then validated with a use case of multistandard receiver designing.