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Least Squares Matrix Algorithm for State-Space Modelling of Dynamic Systems

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Journal of Signal and Information Processing 2011年第4期2卷 287-291页

作者： juuso T. Olkkonen Hannu Olkkonen 不详

This work presents a novel least squares matrix algorithm (LSM) for the analysis of rapidly changing systems using state-space modelling. The LSM algorithm is based on the Hankel structured data matrix representation. The state transition matrix is updated without the use of any forgetting function. This yields a robust estimation of model parameters in the presence of noise. The computational complexity of the LSM algorithm is comparable to the speed of the conventional recursive least squares (RLS) algorithm. The knowledge of the state transition matrix enables feasible numerical operators such as interpolation, fractional differentiation and integration. The usefulness of the LSM algorithm was proved in the analysis of the neuroelectric signal waveforms.

关键词： State-Space Modelling Dynamic System Analysis EEG

Shifted Linear Interpolation Filter

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Journal of Signal and Information Processing 2010年第1期1卷 44-49页

作者： Hannu Olkkonen juuso T. Olkkonen 不详

Linear interpolation has been adapted in many signal and image processing applications due to its simple implementation and low computational cost. In standard linear interpolation the kernel is the second order B-spline. In this work we show that the interpolation error can be remarkably diminished by using the time-shifted B-spline as an interpolation kernel. We verify by experimental tests that the optimal shift is. In VLSI and microprocessor circuits the shifted linear interpolation (SLI) algorithm can be effectively implemented by the z-transform filter. The interpolation error of the SLI filter is comparable to the more elaborate higher order cubic convolution interpolation.

关键词： Linear Interpolation Cubic Convolution B-splines VLSI

Log-Time Sampling of Signals: Zeta Transform

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Open Journal of Discrete Mathematics 2011年第2期1卷 62-65页

作者： Hannu Olkkonen juuso T. Olkkonen 不详

We introduce a general framework for the log-time sampling of continuous-time signals. We define the zeta transform based on the log-time sampling scheme, where the signal x(t)is sampled at time instants tn=Tlogn,n=1,2,....The zeta transform of the log-time sampled signals can be described by a linear combination of Riemann zeta function, which firmly joins the log-time sampling process to the number theory. The instantaneous sampling frequency of the log-sampled signal equals fn=n/T,n=1,2,..., i.e. it increases linearly with the sampling number. We describe the properties of the log-sampled signals and discuss several applications in nonuniform sampling schemes.

关键词： Sampling Z-Transform Zeta Function

Accelerated Series for Riemann Zeta Function at Odd Integer Arguments

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Open Journal of Discrete Mathematics 2013年第1期3卷 18-20页

作者： juuso T. Olkkonen Hannu Olkkonen Department of Applied Physics University of Eastern Finland Kuopio Finland VTT Technical Research Centre of Finland Espoo Finland

Riemann zeta function is an important tool in signal analysis and number theory. Applications of the zeta function include e.g. the generation of irrational and prime numbers. In this work we present a new accelerated series for Riemann zeta function. As an application we describe the recursive algorithm for computation of the zeta function at odd integer arguments.

关键词： Riemann Zeta Function Converging Series Number Theory Cryptography Signal Processing Compressive Sensing

Complex Hilbert Transform Filter

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Journal of Signal and Information Processing 2011年第2期2卷 112-116页

作者： juuso T. Olkkonen Hannu Olkkonen 不详

Hilbert transform is a basic tool in constructing analytical signals for a various applications such as amplitude modulation, envelope and instantaneous frequency analysis, quadrature decoding, shift-invariant multi-rate signal processing and Hilbert-Huang decomposition. This work introduces a complex Hilbert transform (CHT) filter, where the real and imaginary parts are a Hilbert transform pair. The CHT filtered signal is analytic, i.e. its Fourier transform is zero in negative frequency range. The CHT filter is constructed by half-sample delay operators based on the B-spline transform interpolation and decimation procedure. The CHT filter has an ideal phase response and the magnitude response is maximally flat in the frequency range 0 ≤ ω ≤ π. The CHT filter has integer coefficients and the implementation in VLSI requires only summations and register shifts. We demonstrate the feasibility of the CHT filter in reconstruction of the sign modulated CMOS logic pulses in a fibre optic link.

关键词： Hilbert Transform Analytic Signal Fractional Delay Filters

Reconstruction of Wireless UWB Pulses by Exponential Sampling Filter

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Wireless Sensor Network 2010年第6期2卷 462-466页

作者： juuso T. Olkkonen Hannu Olkkonen 不详

Measurement and reconstruction of wireless pulses is an important scheme in wireless ultra wide band (UWB) technology. In contrary to the band-limited analog signals, which can be recovered from evenly spaced samples, the reconstruction of the UWB pulses is a more demanding task. In this work we describe an exponential sampling filter (ESF) for measurement and reconstruction of UWB pulses. The ESF is constructed from parallel filters, which has exponentially descending impulse response. A pole cancellation filter was used to extract the amplitudes and time locations of the UWB pulses from sequentially measured samples of the ESF output. We show that the amplitudes and time locations of p sequential UWB pulses can be recovered from the measurement of at least 2p samples from the ESF output. For perfect reconstruction the number of parallel filters in ESP should be 2p. We study the robustness of the method against noise and discuss the applications of the method.

关键词： Wireless Sensor Networks UWB Network Security Finite Rate of Innovation

Design of Orthogonal UWB Pulse Waveform for Wireless Multi-Sensor Applications

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Wireless Sensor Network 2010年第11期2卷 850-853页

作者： Hannu Olkkonen juuso T. Olkkonen 不详

In this work we propose an orthogonal pulse waveform for wireless ultra wideband (UWB) transmission. The design is based on an ideal low-pass prototype filter having a windowed sinc impulse response. The frequency response of the prototype filter is transferred to the high frequency region using a specific sign modulator. The UWB pulse waveform comprises of the weighted summation of the left singular vectors of the impulse response matrix. The power spectral density of the pulse waveform fulfils the FCC constraint (allowed frequency band 3.1-10.6 GHz) for unlicensed UWB transmission. Applications of the UWB pulse waveform in multi-channel wireless sensor networks are considered.

关键词： UWB Wireless Sensor Networks

Fast Converging Series for Riemann Zeta Function

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Open Journal of Discrete Mathematics 2012年第4期2卷 131-133页

作者： Hannu Olkkonen juuso T. Olkkonen Department of Applied Physics University of Eastern Finland Kuopio Finland VTT Technical Research Centre of Finland Espoo Finland

Riemann zeta function has a key role in number theory and in its applications. In this paper we present a new fast converging series for . Applications of the series include the computation of the and recursive computation of , and generally . We discuss on the production of irrational number sequences e.g. for encryption coding and zeta function maps for analysis and synthesis of log-time sampled signals.

关键词： Riemann Zeta Function Converging Series Number Theory Cryptography Signal Processing

Computation of Hilbert Transform via Discrete Cosine Transform

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Journal of Signal and Information Processing 2010年第1期1卷 18-23页

作者： Hannu Olkkonen Peitsa Pesola juuso T. Olkkonen 不详

Hilbert transform (HT) is an important tool in constructing analytic signals for various purposes, such as envelope and instantaneous frequency analysis, amplitude modulation, shift invariant wavelet analysis and Hilbert-Huang decomposition. In this work we introduce a method for computation of HT based on the discrete cosine transform (DCT). We show that the Hilbert transformed signal can be obtained by replacing the cosine kernel in inverse DCT by the sine kernel. We describe a FFT-based method for the computation of HT and the analytic signal. We show the usefulness of the proposed method in mechanical vibration and ultrasonic echo and transmission measurements.

关键词： Hilbert Transform Analytic Signal Envelope Analysis FFT