A summary of many of the new techniques developed in the last two decades for spectrum analysis of discrete time series is presented in this tutorial. An examination of the underlying time series model assumed by each technique serves as the common basis for understanding the differences among the various spectrum analysis approaches. Techniques discussed include the classical periodogram, classical Blackman-Tukey, autoregressive (maximum entropy), moving average, autotegressive-moving average, maximum likelihood, Prony, and Pisarenko methods. A summary table in the text provides a concise overview for all methods, including key references and appropriate equations for computation of each spectral estimate.

Spectrum analysis&#8212;A modern perspective

This processor is capable of real time processing of blocks of video pixel or other two-dimensional data to yield the two-dimensional Discrete Cosine Transform (DCT) thereof. The processor can be used as part of a video bandwidth or image compression system. The circuitry comprises a first one-dimensional DCT processor (3) which simultaneously computes an entire row or column of vector inner products by using distributed arithmetic and using decimation-in-frequency to reduce the amount of memory capacity (ROM) required. Partial sums may also be used to further reduce ROM size. The one-dimensional transformed matrix from the first processor is stored in a transposition memory (5) and the transpose of the stored matrix is applied to a second one-dimensional DCT processor (7) of similar circuitry which computes the desired two-dimensional DCT of the input data matrix.

Two-dimensional discrete cosine transform processor.

Hybrid fast Fourier transform Adaptive LINear Element (FFT-ADALINE) algorithm for fast and accurate estimation of harmonics is proposed in this study. The FFT method can perform fast conversion from time domain to frequency domain, but it cannot respond immediately to any change of the measured harmonics due to the utilisation of buffer. Meanwhile, ADALINE has better capability to respond immediately due to its learning ability, but its settling time is about two cycles of the measurement signal. In the proposed method, both of the aforementioned algorithms are combined for harmonic estimation where it is able to respond immediately to any change of the measured harmonics and the settling time is reduced to half cycle of the measurement signal. The theory of the proposed algorithm is the application of FFT with weights updating rule to reduce the error of ADALINE instantaneously. The robustness of the proposed method is simulated via MATLAB Simulink. The validity of the simulation work is further proven by the experimental work, which has been done with Chroma programmable AC source model 6590 and non-linear load operations. The proposed algorithm operates in good and accurate performance with the settling time is within half cycle.

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Hybrid FFT-ADALINE algorithm with fast estimation of harmonics in power system

A method for transfer function calculation is described that derives its economy from the symmetry of the autocorrelation to double the number of lags. The imbalance in the number of lags between autocorrelations and cross-correlations is restored by calculating the negative lags of the cross-correlation without any extra computations. With both positive and negative lags available, the symmetry and periodicity constraints of the fast Fourier transform can be taken into account, and windowing the cross-correlation sequence is less ambiguous. This greatly increases the accuracy and convergence of the computed transfer function. Since the statistical significance of the transfer function estimate is higher, it is possible to obtain the transfer function using shorter data sequences. These last advantages more than outweigh the increase in resolution. >

Fast cross-correlation algorithm with application to spectral analysis

This paper reviews a VLSI architecture based on ‘Parallel Pipeline Projection Engine’ (PPPE) which is composed by Forward Radon Transform and Back-projection architecture. This PPPE architecture is modified by using the theory of two-dimensional Radon Transform. The novel architecture is primarily based on analytical relationship between the pixels on horizontal and vertical raster scan line and also between the projection angles. A new concept of Processing Blocks (PB) is developed with help of the theory of Radon Transform. In this novel PPPE architecture, the PB blocks can drive a large numbers of Processing Element (PE) blocks with some limitations. This limitation is also accounted by some error function from where the correct numbers of PE blocks are derived. The top level implementations have done for both of the existing and modified architecture and compared them by using Xilinx ISE simulator. Synthesized results for both of the novel and existing PPPE architecture has been done on ‘Field Programmable Gate Array’ (FPGA). It has been observed that novel PPPE architecture uses less numbers of hardware resources (multipliers, adders/subtractors) and as a result this modified architecture reduces the computational complexity, delay and latency as compared to the existing one.

Novel VLSI architecture for two-dimensional radon transform computations

The fast Fourier transform (FFT) provides an effective tool for the calculation of Fourier transforms involving a large number of data points. The paper presents new and simple derivations for the two basic FFT algorithms that provide an intuitive basis for the manipulations involved. The derivation for the "decimation in time" algorithm begins with a crude analysis for the zero frequency and fundamental components using only two data samples, one at the beginning and the second at the midpoint of the period of interest. Successive interpolations of data points midway between those previously used result in a refinement of the amplitudes already determined and a first value for the next higher order coefficients. The derivation of the "decimation in frequency" algorithm begins by resolving the original data set into two new data sets, one whose transform includes only even harmonic terms and a second whose transform includes only odd harmonic terms. Since the first of the two new data sets repeats after the midpoint, it can be transformed using only the first half of the data points. The second of the new data sets is multiplied by the negative fundamental function, thereby reducing its order by one and converting it into a data set that transforms into even harmonics only; in this form it can also be transformed using only the first half of the data set. Successive applications of this procedure result finally in reducing the operation to the calculation of a large number of simple two-data-point transforms.

S. Bertram

Papers

On the derivation of the fast Fourier transform