Multirate Signal Processing Research Articles

Multirate synthesis of reverberators using subband filtering

As an important element in three-dimensional audio reproduction, reverberators serve to enhance the sense of spaciousness by synthesizing the sound reflections and reverberations pertaining to a particular listening environment. However, direct implementation of room responses generally proves impractical due to the extreme complexity of system dynamics. To overcome the difficulties encountered in long convolutions, an efficient multirate signal processing technique is proposed in this paper on the basis of subband filtering scheme. In this method, the frequency dependent property of reverberation time is incorporated into the design procedure. Further simplification follows from the synthesized infinite impulse response (IIR) implementation for each subband. Specifically, the regular IIR filter, the cascaded comb filters and nested allpass filters, and the cascaded comb filter and an FIR filter are developed to implement the subband filters. Genetic algorithms (GA) are employed to optimize the parameters of reverberators. Subjective listening tests are carried out to assess the performance of the proposed techniques. The results demonstrate that the implemented multirate reverberators are capable of delivering natural sensation of room reverberations, as compared to direct measurement.

Configurable Multirate Filter Banks

Multimedia communications require efficient and real-time implementations of multirate digital signal processing systems. The backbone structures of multirate systems are digital multirate filter banks. Therefore, efficient multimedia communications rely, in the first place, on real-time implementations of multirate filter banks. In this paper, we describe a Field Programmable Gate Array (FPGA) implementation of the analysis and synthesis filter banks which are the fundamental components of multirate systems. The implementation utilizes the parallel form of the distributed arithmetic technique which enables maximum exploitation of the parallelism inherent in the multirate filtering operation. Performance results demonstrate the effectiveness of the implementation and suggest that the FPGA platform is indeed attractive for implementing multirate filter banks.

Fractional Fourier domain analysis of cyclic multirate signal processing

The cyclic filter banks, which are used widely in the image subband coding, refer to signal processing on the finite field. This study investigates the fractional Fourier domain (FRFD) analysis of cyclic multirate systems based on the fractional circular convolution and chirp period. The proposed theorems include the fractional Fourier domain analysis of cyclic decimation and cyclic interpolation, the noble identities of cyclic decimation and cyclic interpolation in the FRFD, the polyphase representation of cyclic signal in the FRFD, and the perfect reconstruction condition for the cyclic filter banks in the FRFD. Furthermore, this paper proposes the design methods for perfect reconstruction cyclic filter bank and cyclic filter bank with chirp modulation in the FRFD. The proposed theorems extend the multirate signal processing in the FRFD, which also advance the applications of the theorems of filter bank in the FRFD on the finite signal field, such as digital image processing. At last, the proposed design methods for the cyclic filter banks in the FRFD are validated by simulations.

Efficient implementation of 3D filter for moving object extraction

In this paper the design and implementation of Multi-Dimensional (MD) filter, particularly 3-Dimensional (3D) filter, are presented. Digital (discrete domain) filters applied to image and video signal processing using the novel 3D multirate algorithms for efficient implementation of moving object extraction are engineered with an example. The multirate (decimation and/or interpolation) signal processing algorithms can achieve significant savings in computation and memory usage. The proposed algorithm uses the mapping relations of z-transfer functions between non-multirate and multirate mathematical expressions in terms of time-varying coefficient instead of traditional polyphase decomposition counterparts. The mapping properties can be readily used to efficiently analyze and synthesize MD multirate filters.

Fractional Fourier domain analysis of decimation and interpolation

The sampling rate conversion is always used in order to decrease computational amount and storage load in a system. The fractional Fourier transform (FRFT) is a powerful tool for the analysis of nonstationary signals, especially, chirp-like signal. Thus, it has become an active area in the signal processing community, with many applications of radar, communication, electronic warfare, and information security. Therefore, it is necessary for us to generalize the theorem for Fourier domain analysis of decimation and interpolation. Firstly, this paper defines the digital fre- quency in the fractional Fourier domain (FRFD) through the sampling theorems with FRFT. Secondly, FRFD analysis of decimation and interpolation is proposed in this paper with digital frequency in FRFD followed by the studies of interpolation filter and decimation filter in FRFD. Using these results, FRFD analysis of the sam- pling rate conversion by a rational factor is illustrated. The noble identities of decimation and interpolation in FRFD are then deduced using previous results and the fractional convolution theorem. The proposed theorems in this study are the bases for the generalizations of the multirate signal processing in FRFD, which can advance the filter banks theorems in FRFD. Finally, the theorems introduced in this paper are validated by simulations.

A Frequency-Translating Hybrid Architecture for Wide-Band Analog-to-Digital Converters

A parallel architecture for high-bandwidth analog-to-digital conversion is presented. The proposed architecture uses frequency translation along with multi-rate signal processing to digitize a wide-band continuous-time analog signal through an array of identical narrowband analog-to-digital converters (ADCs). The basic idea behind this structure is to decompose the input signal into smaller frequency (channels). Each channel is composed of a two-path system that includes mixers, identical low-pass filters and identical baseband ADCs. The signal in each two-path channel is sampled and digitized into narrowband quadrature signals. After digitizing the signal in each channel, the low-rate subband samples are upconverted back to their respective center frequencies, then filtered and combined to reconstruct the digital representation of the original wide-band input signal. The digital filters are designed to minimize the reconstruction error. The effects of some major nonidealities are discussed. Several simulation results are also presented to demonstrate the performance of the system.

Closed-Form Design of Generalized Maxflat$R$-Regular FIR$M$th-Band Filters Using Waveform Moments

Mth-band filters have found numerous applications in multirate signal processing systems, filter banks, and wavelets. In this paper, the design problem of generalized maxflat R-regular finite impulse response (FIR) Mth-band filters with a specified integer group delay at omega=0 is considered, and the closed-form expression for its impulse response is presented. The filter coefficients are directly derived by solving a linear system of Vandermonde equations that are obtained from the regularity condition of the maxflat R-regular FIR Mth-band filters via the blockwise waveform moments. Differing from the conventional FIR Mth-band filters with exactly linear phase responses, the generalized FIR Mth-band filters proposed in this paper have an arbitrarily specified integer group delay at omega=0. Moreover, a new efficient implementation of the generalized maxflat R-regular FIR Mth-band filters is proposed by making use of the relationship between the filter coefficients in the closed-form solution. Finally, several design examples are presented to demonstrate the effectiveness of the proposed FIR Mth-band filters

Anti-image FIR filters for large interpolation factors

In this paper, the design of FIR filters using novel window families is introduced. These window functions are having high side-lobe-fall-off-rate (SLFOR). The designed filters can be used as anti-imaging filters for large interpolation factors used in multirate signal processing. The performance of the proposed filters is compared with similar filters designed with Kaiser window, Dolph-Chebyshev window and optimum filters designed using Parks-McClellan method. It is observed that, filters designed with high SLFOR combinational window families are providing better image suppression with large interpolation factor. These filters provide smaller aliasing and imaging errors at the cost of smaller initial stopband attenuation.

Anti-image FIR filters for large interpolation factors

In this paper, the design of FIR filters using novel window families is introduced. These window functions are having high side-lobe-fall-off-rate (SLFOR). The designed filters can be used as anti-imaging filters for large interpolation factors used in multirate signal processing. The performance of the proposed filters is compared with similar filters designed with Kaiser window, Dolph–Chebyshev window and optimum filters designed using Parks–McClellan method. It is observed that, filters designed with high SLFOR combinational window families are providing better image suppression with large interpolation factor. These filters provide smaller aliasing and imaging errors at the cost of smaller initial stopband attenuation.

Comparative Study of Interpolation Techniques for Ultra-Tight Integration of GPS/INS/PL Sensors

Ultra-tight architecture plays a key role in improving the robustness of the integrated GPS/INS/PL (Pseudolite) system by aiding GPS receiver's carrier tracking loops with the Doppler information derived from INS (Inertial Navigation System) velocity measurements. This results in a lower carrier tracking loop bandwidth and subsequent improvement in measurement accuracy. Some other benefits using this architecture include: robust cycle-slip detection and correction, improved anti- jam performance, and weak signal detection. Typically the integration/navigation filter run at a rate of 1 to 100 Hz, which is insufficient to aid the carrier tracking loop as such loops normally run at about 1000 Hz. Two approaches were envisioned to solve this problem. One approach is to run the navigation Kalman filter at a higher rate, and the other is to run the filter at a lower rate and interpolate the measurements to the required rate. Although the first approach seems to be straightforward, it is computationally very intensive and requires a huge amount of processing power, adding to the cost and complexity of the system. The second method interpolates the low rate Doppler measurements from the navigation filter using multirate signal processing algorithms. Due to its efficiency and simpler architectures the interpolation method is adopted here. Filtering is the key issue when designing interpolators as they remove the images caused in the upsampling process. Although direct form of filtering can be adopted, they increase the computations. To reduce the computational burden, two efficient ways of implementing the interpolators are proposed in this paper: Polyphase and CIC (Cascaded Integrator Comb). The paper summarizes the design and analysis of these two techniques, and our initial results suggest that CIC is relatively better in terms of performance and computational requirements.

Interactive Online Undergraduate Laboratories Using J-DSP

An interactive Web-based simulation tool called Java-DSP (J-DSP) for use in digital signal processing (DSP)-related electrical engineering courses is described. J-DSP is an object-oriented simulation environment that enables students and distance learners to perform online signal processing simulations, visualize Web-based interactive demos, and perform computer laboratories from remote locations. J-DSP is accompanied by a series of hands-on laboratory exercises that complement classroom and textbook content. The laboratories cover several fundamental concepts, including z transforms, digital filter design, spectral analysis, multirate signal processing, and statistical signal processing. Online assessment instruments for the evaluation of the J-DSP software and the associated laboratory exercises have been developed. Pre/postassessment data have been collected and analyzed for each laboratory in an effort to assess the impact of the tool on student learning.

2-D multirate algorithms for efficient implementation of edge detection

Edge detection is a fundamental issue in image analysis. This paper proposes multirate algorithms for efficient implementation of edge detector, and a design example is illustrated. The multirate (decimation and/or interpolation) signal processing algorithms can achieve considerable savings in computation and storage. The proposed algorithms result in mapping relations of their z-transfer functions between non-multirate and multirate mathematical expressions in terms of time-varying coefficient instead of traditional polyphase decomposition counterparts. The mapping properties can be readily utilized to efficiently analyze and synthesize multirate edge detection filters. The Very high-speed Hardware Description Language (VHDL) simulation results verify efficiency of the algorithms for real-time Field Programmable Gate-Array (FPGA) implementation.

On the synthesis of very sharp decimators and interpolators using the frequency-response masking technique

Decimation and interpolation are very common multirate signal processing operations. Conventional decimation or interpolation technique using polyphase filters has the advantage that for a given transition-band sharpness, the filter's computational complexity decreases with increasing interpolation or decimation factor. Nevertheless, if the transition band of the decimation or interpolation filter is very sharp, the complexity of the filter may still be very high. The complexity of a very sharp filter may be reduced using the frequency-response masking (FRM) technique. However, as shown in this paper, for a given transition-band sharpness, the computational complexity of the classical FRM method does not reduce as rapidly as the increase in decimation or interpolation factor. In this paper, we present a novel variant of the FRM technique for interpolation or decimation application. In this new variant, the computational complexity reduces as rapidly as the interpolation or decimation factor increases. The reduction in computational complexity increases with decreasing transition width. Over an order of magnitude reduction in computational complexity is achieved when compared with conventional polyphase approach in a particular example presented in this paper.

Performance limits of OWSS: A spectrally efficient WLAN system

Orthogonal wavelet spread spectrum (OWSS) is a new wireless LAN signaling scheme aimed at bit rates of 100 Mbps or higher. Starting with power complementary full-tree wavelet pulses, it spreads them using a suitable set of PN codes. The resulting system pulses preserve the power complementary property and satisfy the generalized Nyquist criterion, while possessing both a wide time and a wide frequency support. Benefits from these properties include successful equalization in spite of deep local fades caused by multipath channels, and high spectral efficiency-30-40% higher than OFDM for comparable net bit rates. This paper presents an overview of OWSS and explores the fundamental limits to its performance. In the overview, it discusses the properties of the OWSS pulses, the transmit signal spectrum, and the structure of the transmitter/receiver. Then, the investigation of fundamental limits to the performance is carried out by formulating the system as a multi-rate signal processing system, using hierarchical matrices, and thereupon minimizing the total mean-square error (TMSE). The TMSE governs the BER performance of the system, and is defined as the sum of the MSE of the unequalized residual error and the MSE due to the channel noise amplified by the forward equalizer. We formulate the problem at the chip level so as to truly discern the fundamental limits to the performance of the equalizer. This approach enables estimation of the optimum equalizer for mitigating the effect of the multipath channel, prior to correlation and detection blocks embedded in the FE-DFE loop, and thereby the system performance. Simulation results demonstrate its effectiveness. For a 108 Mbps system with a 50 ns delayspread channel, a low BER of 10^-^5 and spectral efficiency up to 5.2 bits/s/Hz can be achieved at an Eb/No of 19 dB.

Another FIR lattice structure

A new two multiplier FIR lattice structure is derived by using the digital two-pair concept, which produces two transfer functions Hi(z) and Hi′(z) having the complementary relationship Hi′(z)=z−iHi(–z−1), in contrast to the mirror image relationship, i.e. Hi′(z)=z−iHi(z−1) satisfied in the conventional FIR lattice structure. The new structure should be useful in crossover networks as well as in multirate signal processing. Copyright © 2005 John Wiley & Sons, Ltd.

On exploring inter-iteration parallelism within rate-balanced multirate multidimensional DSP algorithms

Although the notion of the parallelism in multidimensional applications has existed for a long time, it is so far unknown what the bound (if any) of inter-iteration parallelism in multirate multidimensional digital signal processing (DSP) algorithms is, and whether the maximum inter-iteration parallelism can be achieved for arbitrary multirate data flow algorithms. This paper explores the bound of inter-iteration parallelism within rate-balanced multirate multidimensional DSP algorithms and proves that this parallelism can always be achieved in hardware system given the availability of a large number of processors and the interconnections between them.

A multirate DSP model for estimation of discrete probability density functions

The problem of estimating a probability density function (PDF) from measurements has been widely studied by many researchers. Even though much work has been done in the area of PDF estimation, most of it was focused on the continuous case. We propose a new model-based approach for modeling and estimating discrete probability density functions or probability mass functions. This approach is based on multirate signal processing theory, and it has several advantages over the conventional histogram method. We illustrate the PDF estimation procedure and analyze the statistical properties of the PDF estimates. Based on this model, a novel scheme is introduced that can be used for estimating the PDF in the presence of noise. Furthermore, the proposed ideas are extended to the more general case of estimating multivariate PDFs. Finally, we also consider practical issues such as optimizing the coefficients of a digital filter, which is an integral part of the model. This allows us to apply the proposed model to solve real-world problems. Simulation results are given where appropriate in order to demonstrate the ideas.

The CBP Parameter: A Module Characterization Approach for DSP Software Optimization

Memory consumption is an important metric for DSP software implementation. In this paper, we develop a module characterization technique that promotes more economical use of memory resources at the system level. Our work is developed in the context of software synthesis from signal/video/image processing applications expressed as synchronous dataflow (SDF) graphs. SDF is a restricted form of dataflow where each computational module (actor) consumes and produces a fixed number of data values (tokens) on each execution. Usually, no assumption is made about when during the execution of an actor, the tokens are actually consumed and produceds the firing of an actor is treated as an atomic event for most purposes. However, we show in this paper that it is possible to concisely and precisely capture key properties pertaining to the relative times at which tokens are produced and consumed by an actor. We show this by introducing the consumed-before-produced (CBP) parameter, which provides a general method for characterizing the token transfer of an SDF actor. Good bounds on the CBP parameter can aid an SDF compiler in performing more aggressive optimizations for reducing buffer sizes on the edges between actors. We formally define the CBP parameters derive some useful properties of this parameters illustrate how the value of the parameter is derived by examining in detail the multirate FIR filter, which is a fundamental actor in multirate signal processing applicationss and examine CBP parameterizations for several other practical SDF actors.

Adaptive Volterra filters using multirate signal processing and their application to identification of loudspeaker systems

AbstractThe subband adaptive Volterra filter (SBAVF), which can assign the filter length of each subband arbitrarily, is proposed. If the frequency characteristics of a system to be identified are shifted to a certain bandwidth, it is usually not possible to carry out efficient identification by taking account of the shift of the bandwidth in a (full band) adaptive Volterra filter. On the other hand, in the proposed SBAVF, efficient system identification is possible by assigning a longer filter length to the dominant frequency range of the system of interest. When the proposed method is applied to a speaker system, it is shown through simulation results that the error attenuation can be improved from 1.5 dB to 7.5 dB in comparison with the conventional method. © 2004 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 87(7): 45–54, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.10135

Design of IIR half‐band filters with arbitrary flatness and its application to filter banks

AbstractHalf‐band filters are important for applications to multirate signal processing and wavelets. Previously, FIR half‐band filters have mainly been treated. However, it should be recognized that the IIR filter can produce frequency characteristics similar to those of the FIR filter with a low order. Also, in the applications of filter banks and wavelets, design of a half‐band filter is needed in which the degree of flatness can be specified arbitrarily. In the present paper, a new design method is proposed for an IIR half‐band filter with an arbitrary degree of flatness. In the present design method, the analytical solution of the filter coefficients is given in the case of a maximally flat filter. Also, in the case of a specified degree of flatness, the amplitude error in the stopband can be specified in the design. Further, the stability of the filter is studied and then the minimum group delay for causal stability is clarified. Finally, the IIR half‐band filter is applied to the design of a two‐channel filter bank and the effectiveness of the present design method is proven. © 2003 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 87(1): 10–18, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.10114