Signal processing of heart signals for the quantification of non-deterministic events

<p>Abstract</p> <p>Background</p> <p>Heart signals represent an important way to evaluate cardiovascular function and often what is desired is to quantify the level of some signal of interest against the louder backdrop of the beating of the heart itself. An example of this type of application is the quantification of cavitation in mechanical heart valve patients.</p> <p>Methods</p> <p>An algorithm is presented for the quantification of high-frequency, non-deterministic events such as cavitation from recorded signals. A closed-form mathematical analysis of the algorithm investigates its capabilities. The algorithm is implemented on real heart signals to investigate usability and implementation issues. Improvements are suggested to the base algorithm including aligning heart sounds, and the implementation of the Short-Time Fourier Transform to study the time evolution of the energy in the signal.</p> <p>Results</p> <p>The improvements result in better heart beat alignment and better detection and measurement of the random events in the heart signals, so that they may provide a method to quantify nondeterministic events in heart signals. The use of the Short-Time Fourier Transform allows the examination of the random events in both time and frequency allowing for further investigation and interpretation of the signal.</p> <p>Conclusions</p> <p>The presented algorithm does allow for the quantification of nondeterministic events but proper care in signal acquisition and processing must be taken to obtain meaningful results.</p

Efficient Spectral Power Estimation on an Arbitrary Frequency Scale

The Fast Fourier Transform is a very efficient algorithm for the Fourier spectrum estimation, but has the limitation of a linear frequency scale spectrum, which may not be suitable for every system. For example, audio and speech analysis needs a logarithmic frequency scale due to the characteristic of a human’s ear. The Fast Fourier Transform algorithms are not able to efficiently give the desired results and modified techniques have to be used in this case. In the following text a simple technique using the Goertzel algorithm allowing the evaluation of the power spectra on an arbitrary frequency scale will be introduced. Due to its simplicity the algorithm suffers from imperfections which will be discussed and partially solved in this paper. The implementation into real systems and the impact of quantization errors appeared to be critical and have to be dealt with in special cases. The simple method dealing with the quantization error will also be introduced. Finally, the proposed method will be compared to other methods based on its computational demands and its potential speed

Implementation of barycentric resampling for continuous wave searches in gravitational wave data

We describe an efficient implementation of a coherent statistic for continuous gravitational wave searches from neutron stars. The algorithm works by transforming the data taken by a gravitational wave detector from a moving Earth bound frame to one that sits at the Solar System barycenter. Many practical difficulties arise in the implementation of this algorithm, some of which have not been discussed previously. These difficulties include constraints of small computer memory, discreteness of the data, losses due to interpolation and gaps in real data. This implementation is considerably more efficient than previous implementations of these kinds of searches on Laser Interferometer Gravitational Wave (LIGO) detector data.Comment: 10 pages, 3 figure

Composite Cyclotomic Fourier Transforms with Reduced Complexities

Discrete Fourier transforms~(DFTs) over finite fields have widespread applications in digital communication and storage systems. Hence, reducing the computational complexities of DFTs is of great significance. Recently proposed cyclotomic fast Fourier transforms (CFFTs) are promising due to their low multiplicative complexities. Unfortunately, there are two issues with CFFTs: (1) they rely on efficient short cyclic convolution algorithms, which has not been investigated thoroughly yet, and (2) they have very high additive complexities when directly implemented. In this paper, we address both issues. One of the main contributions of this paper is efficient bilinear 11-point cyclic convolution algorithms, which allow us to construct CFFTs over GF$(2^{11})$. The other main contribution of this paper is that we propose composite cyclotomic Fourier transforms (CCFTs). In comparison to previously proposed fast Fourier transforms, our CCFTs achieve lower overall complexities for moderate to long lengths, and the improvement significantly increases as the length grows. Our 2047-point and 4095-point CCFTs are also first efficient DFTs of such lengths to the best of our knowledge. Finally, our CCFTs are also advantageous for hardware implementations due to their regular and modular structure.Comment: submitted to IEEE trans on Signal Processin