Improved technique for design of perfect reconstruction FIR QMF banks with lossless polyphase matrices

A technique is developed for the design of analysis filters in an M-channel maximally decimated, perfect reconstruction, finite-impulse-response quadrature mirror filter (FIR QMF) bank that has a lossless polyphase-component matrix E(z). The aim is to optimize the parameters characterizing E(z) until the sum of the stopband energies of the analysis filters is minimized. There are four novel elements in the procedure reported here. The first is a technique for efficient initialization of one of the M analysis filters, as a spectral factor of an Mth band filter. The factorization itself is done in an efficient manner using the eigenfilters approach, without the need for root-finding techniques. The second element is the initialization of the internal parameters which characterize E(z), based on the above spectral factor. The third element is a modified characterization, mostly free from rotation angles, of the FIR E(z). The fourth is the incorporation of symmetry among the analysis filters, so as to minimize the number of unknown parameters being optimized. The resulting design procedure always gives better filter responses than earlier ones (for a given filter length) and converges much faste

Breaking the seismic wall: how to improve gravitational wave detectors at low frequency

The era of gravitational-wave astronomy was enabled by the incredible sensitivity of the LIGO and VIRGO detectors. However, they are still plagued by technical noises at frequencies below 30 Hz, driven in part by the limitations of the seismic isolation of the detector. To detect gravitational waves at low frequency, the isolation performance must be improved to reduce these technical noises. To improve the performance of seismic isolation systems, I have developed HoQI a new interferometrically sensor, that can be applied to both the isolation tables and suspensions. HoQI has a resolution a factor 1000 higher than sensors currently used in LIGO and I have quantified the level of non-linearity present in the sensor and shown this to not be a limiting factor. HoQIs impact on the performance of the seismic isolation system has also been quantified, through the use of a accurate model of an Advanced LIGO isolation platform that I have developed. Using the model I have shown that using using HoQI, the expected isolation platform motion can be reduced by a factor of 70 at 0.1 Hz and a factor of 10 at 2 Hz. I have shown that the control filters used in this model can be improved by up to 70% by designing them using particle swarm optimisation