A new method for the design of energy transfer filters

This paper is concerned with the development of a new method for the design of Energy Transfer Filters (ETFs). ETFs are a new class of nonlinear filters recently proposed by the authors, which employ nonlinear effects to transfer signal energy from one frequency band to a different frequency location. The new method uses the powerful Orthogonal Least Squares (OLS) algorithm to solve the Least Squares problem associated with the design and compared with previous methods achieves much better filtering performance

A Frequency-selective Filter for Short-Length Time Series

An effective and easy-to-implement frequency filter is designed by convolving a Hamming window with the ideal rectangular filter response function. Three other filters, Hodrick-Prescott, Baxter-King, and Christiano-Fitzgerald, are critically reviewed. The behavior of the Hamming-windowed filter is compared to the others through their frequency responses and their application to both an artificial, known-structure series and to the Euro zone quarterly GDP series. The Hamming-windowed filter has almost no leakage and is thus much better than the others in eliminating high-frequency components and has a significantly flatter bandpass response. Its low-frequency behavior demonstrates better removal of undesired long-term components. These improvements are particularly evident when working with short-length time series, such as are common in macroeconomics. The proposed filter is stationary, symmetric, uses all the information contained in the raw data, and stationarizes series integrated up to order two. It thus proves to be a good candidate for extracting frequency-defined business-cycle componentsspectral analysis, bandpass filtering

Calibration of Low-Frequency, Wide-Field Radio Interferometers Using Delay/Delay-Rate Filtering

We present a filtering technique that can be applied to individual baselines of wide-bandwidth, wide-field interferometric data to geometrically select regions on the celestial sphere that contain primary calibration sources. The technique relies on the Fourier transformation of wide-band frequency spectra from a given baseline to obtain one-dimensional "delay images", and then the transformation of a time-series of delay images to obtain two-dimensional "delay/delay-rate images." Source selection is possible in these images given appropriate combinations of baseline, bandwidth, integration time and source location. Strong and persistent radio frequency interference (RFI) limits the effectiveness of this source selection owing to the removal of data by RFI excision algorithms. A one-dimensional, complex CLEAN algorithm has been developed to compensate for RFI-excision effects. This approach allows CLEANed, source-isolated data to be used to isolate bandpass and primary beam gain functions. These techniques are applied to data from the Precision Array for Probing the Epoch of Reionization (PAPER) as a demonstration of their value in calibrating a new generation of low-frequency radio interferometers with wide relative bandwidths and large fields-of-view.Comment: 17 pages, 6 figures, 2009AJ....138..219