This paper presents the application of the Linear Sequential Array (LSA) retiming approach, developed for conventional digit-recurrence algorithms, to on-line multiplication. The result is a modular and fast pipelined...
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This paper presents the application of the Linear Sequential Array (LSA) retiming approach, developed for conventional digit-recurrence algorithms, to on-line multiplication. The result is a modular and fast pipelined structure which due to a small constant fan-out and cycle time independent of precision is suitable for FPGA implementation. First we present the basics of on-line multiplication, and determine data dependencies according to the LSA design methodology. Based on these dependencies we redesign the traditional on-line multiplier to obtain the LSA structure. Since in DSP applications one of the multiplier operands is fixed for a long sequence of operations, we briefly present a parallel-serial multiplication unit that receives one of the operands in parallel and the other operand in Most-Significant-Digit-First format. Performance and area results are provided for the LSA on-line multiplier design and then compared with the conventional on-line design, using Xilinx FPGAs as the target technology.
We are presenting a new class of transforms which facilitates the processing of signals that are nonlinearly stretched or compressed in time. We refer to nonlinear stretching and compression as warping. While the magn...
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We are presenting a new class of transforms which facilitates the processing of signals that are nonlinearly stretched or compressed in time. We refer to nonlinear stretching and compression as warping. While the magnitude of the Fourier transform is invariant under time shift operations, and the magnitude of the scale transform is invariant under (linear) scaling operations, the new class of transforms is magnitude invariant under warping operations. The new class contains the Fourier transform and the scale transform as special cases. Important theorems, like the convolution theorem for Fourier transforms, are generalized into theorems that apply to arbitrary members of the transform class. Cohen's class of time-frequency distributions is generalized to joint representations in time and arbitrary warping variables. Special attention is payed to a modification of the new class of transforms that maps an arbitrary time-frequency contour into an impulse in the transform domain. A chirp transform is derived as an example.
The aim of this work is to contrast techniques used to estimate two instantaneous frequency parameters of the surface electromyographic (EMG) signal, the instantaneous median frequency and the instantaneous mean frequ...
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The aim of this work is to contrast techniques used to estimate two instantaneous frequency parameters of the surface electromyographic (EMG) signal, the instantaneous median frequency and the instantaneous mean frequency, based on their estimation error. Three methods are compared: Cohen class and Cohen-Posch class time-frequency representations are used to compute both the above-mentioned instantaneous frequency parameters, and a cross-time-frequency based technique is adopted to derive the instantaneous mean frequency. The results demonstrate that the algorithm based on Cohen-Posch class transformations leads to a standard deviation of the instantaneous frequency parameters that is smaller than that obtained using Cohen class representations. However, the cross-time-frequency estimation procedure for instantaneous mean frequency produced the smallest standard deviation compared to the other techniques. The algorithms based on Cohen class and Cohen-Posch class transformations often provided a lower bias than the cross-time-frequency based technique. This advantage was particularly evident when the instantaneous mean frequency varied non-linearly within the epochs used to derive the cross-time-frequency representation of the surface EMG signal.
This paper proposes a novel time-frequency maximum likelihood (t-f ML) method for direction-of-arrival (DOA) estimation for non-stationary signals, and compares this method with conventional maximum likelihood DOA est...
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This paper proposes a novel time-frequency maximum likelihood (t-f ML) method for direction-of-arrival (DOA) estimation for non-stationary signals, and compares this method with conventional maximum likelihood DOA estimation techniques. Time-frequency distributions localize the signal power in the time-frequency domain, and as such enhance the effective SNR, leading to improved DOA estimation. The localization of signals with different t-f signatures permits the division of the time-frequency domain into smaller regions, each contains fewer signals than those incident on the array. The reduction of the number of signals within different time-frequency regions not only reduces the required number of sensors, but also decreases the computational load in multi-dimensional optimizations. Compared to the recently proposed time-frequency MUSIC (t-f MUSIC), the proposed t-f ML method can be applied in coherent environments, without the need to perform any type of preprocessing that is subject to both array geometry and array aperture.
In this paper, we use the concept of evolutionary spectrum to solve key problems in array processing. We present Cross-power Evolutionary Periodogram for direction finding and blind separation of nonstationary signals...
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In this paper, we use the concept of evolutionary spectrum to solve key problems in array processing. We present Cross-power Evolutionary Periodogram for direction finding and blind separation of nonstationary signals. We model nonstationary signals received by each sensor in the array as a sum of complex sinusoids with time-varying amplitudes. These amplitudes carry information about the direction of arrival which may also be time-varying. We first estimate the time-varying amplitudes, then use the results for the estimation of evolutionary cross-power distributions of the sensor data. Next, using cross-power estimates at time-frequency samples of interest, we estimate the directions of arrival using one of the existing high resolution direction finding methods. If the directions are time-varying, we select time-frequency points around the time of interest. By carrying out the estimation at different times, we obtain the directions as a function of time. If the sources are stationary, then we can use all time-frequency points of interest for the estimation of fixed directions. We also use whitening and subspace methods to find the mixing matrix and separate the signals received by the array. Simulation examples illustrating the performances of the proposed algorithms are presented.
The analysis of vehicle signals with methods derived from the theory of nonlinear dynamics is a potential tool to classify different vehicles. The nonlinear dynamical methodologies provide alternate system information...
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The analysis of vehicle signals with methods derived from the theory of nonlinear dynamics is a potential tool to classify different vehicles. The nonlinear dynamical methodologies provide alternate system information that the linear analysis tools have ignored. In order to observe the nonlinear dynamic phenomena more clearly, and estimate system invariants more robustly, we exploit the maximum power blind beamforming algorithm as a signal enhancement and noise reduction method when locations of a source and sensors are unknown. The dynamical behavior of an acoustic vehicle signal is studied with the use of correlation dimension D2 and Lyapunov exponents. To characterize the nonlinear dynamic behavior of the acoustic vehicle signal, Taken's embedded theory is used to form an attractor in phase space based on a single observed time series. The time series is obtained from the coherently enhanced output of a blind beamforming array. Then the Grassberger-Procaccia algorithm and Sano-Sawada method are exploited to compute the correlation dimension and Lyapunov exponents. In this paper, we also propose some efficient computational methods for evaluating these system invariants. Experimental classification results show that the maximum power blind beamforming processing improves the estimation of the invariants of the nonlinear dynamic system. Preliminary results show that the nonlinear dynamics is useful for classification applications.
This paper outlines means of using special sets of orthonormally related windows to realize Cohen's class of time-frequency distributions (TFDs). This is accomplished by decomposing the kernel of the distribution ...
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This paper outlines means of using special sets of orthonormally related windows to realize Cohen's class of time-frequency distributions (TFDs). This is accomplished by decomposing the kernel of the distribution in terms of the set of analysis windows to obtain short time Fourier transforms (STFTs). The STFTs obtained using these analysis windows are used to form spectrograms which are then linearly combined with proper weights to form the desired TFD. A set of orthogonal analysis windows which also have the scaling property proves to be very effective, requiring only 1 + log2(N - 1) distinct windows for an overall analysis of N + 1 points, where N = 2n, with n a positive integer. Application of this theory offers very fast computation of TFDs, since very few analysis windows needed and fast, recursive STFT algorithms can be used. Additionally, it is shown that a minimal set of specially derived orthonormal windows can represent most TFDs, including Reduced Interference Distributions (RIDs) with only three distinct windows plus an impulse window. Finally, the Minimal Window RID (MW-RID) which achieves RID properties with only one distinct window and an impulse window is presented.
The multistage detection algorithm has been widely accepted as an effective interference cancellation scheme for next generation Wideband Code Division Multiple Access (W-CDMA) base stations. In this paper, we propose...
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The multistage detection algorithm has been widely accepted as an effective interference cancellation scheme for next generation Wideband Code Division Multiple Access (W-CDMA) base stations. In this paper, we propose a real-time implementation of this detection algorithm in the uplink system, where we have achieved both high performance in the interference cancellation and computational efficiency. When interference cancellation converges, the difference of the detection vectors between two consecutive stages is mostly zero. We recode the estimation bits, mapping from ±1 to 0 and ±2. Bypassing all the zero terms saves computations. Multiplication by ±2 can be easily implemented in hardware as arithmetic shifts. The system delay of a three-stage detector can be reduced by half with satisfactory bit error rate. We also propose a VLSI implementation of this algorithm that has the potential of real-time performance. The detector handling up to eight users with 12-bit fixed point precision was fabricated using a 1.2 μm CMOS technology.
We present a high performance implementation of the FFT algorithm on the BOPS ManArray parallel DSP processor. The ManArray we consider for this application consists of an array controller and 2 to 4 fully interconnec...
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We present a high performance implementation of the FFT algorithm on the BOPS ManArray parallel DSP processor. The ManArray we consider for this application consists of an array controller and 2 to 4 fully interconnected processing elements. To expose the parallelism inherent to an FFT algorithm we use a factorization of the DFT matrix in Kronecker products, permutation and diagonal matrices. Our implementation utilizes the multiple levels of parallelism that are available on the ManArray. We use the special multiply complex instruction, that calculates the product of two complex 32-bit fixed point numbers in 2 cycles (pipelinable). Instruction level parallelism is exploited via the indirect Very Long Instruction Word (iVLIW). With an iVLIW, in the same cycle a complex number is read from memory, another complex number is written to memory, a complex multiplication starts and another finishes, two complex additions or subtractions are done and a complex number is exchanged with another processing element. Multiple local FFTs are executed in Single Instruction Multiple Data (SIMD) mode, and to avoid a costly data transposition we execute distributed FFTs in Synchronous Multiple Instructions Multiple Data (SMIMD) mode.
In this paper, we use the concept of evolutionary spectrum to solve key problems in array processing. We present Cross-power Evolutionary Periodogram for direction finding and blind separation of nonstationary signals...
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In this paper, we use the concept of evolutionary spectrum to solve key problems in array processing. We present Cross-power Evolutionary Periodogram for direction finding and blind separation of nonstationary signals. We model nonstationary signals received by each sensor in the array as a sum of complex sinusoids with time-varying amplitudes. These amplitudes carry information about the direction of arrival which may also be time-varying. We first estimate the time-varying amplitudes, then use the results for the estimation of evolutionary cross-power distributions of the sensor data. Next, using cross-power estimates at time-frequency samples of interest, we estimate the directions of arrival using one of the existing high resolution direction finding methods. If the directions are time-varying, we select time-frequency points around the time of interest. By carrying out the estimation at different times, we obtain the directions as a function of time. If the sources are stationary, then we can use all time-frequency points of interest for the estimation of fixed directions. We also use whitening and subspace methods to find the mixing matrix and separate the signals received by the array. Simulation examples illustrating the performances of the proposed algorithms are presented.
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