Related papers: Confidence Intervals for the Savitzky-Golay Filter…
The Savitzky-Golay FIR digital filter is based on a least-squares polynomial fit to a hypothetical sample of equally spaced data. This gives the filter the ability to preserve moments of features like peaks in the input. Descriptions of the…
Savitzky-Golay (SG) filters are finite impulse response (FIR) realizations of least-squares polynomial regression and they are widely used for filtering (e.g. smoothing, interpolating, predicting, differentiating) and processing (e.g.…
Savitzky-Golay (SG) smoothers are noise suppressing filters operating on the principle of projecting noisy input onto the subspace of polynomials. A poorly selected polynomial order results in over- or under-smoothing which shows as either…
Local polynomial smoothing is a widespread technique in data analysis, and Savitzky-Golay (SG) filters are one of its most well-known realizations. In real settings, the effectiveness of SG filtering depends critically on proper tuning of…
The convolution of a Gaussian and a Cauchy distribution, known as the Voigt distribution, is widely used in spectroscopy and provides a natural framework for modeling heavy-tailed measurement noise. We derive analytical expressions for its…
In a previous report (Raju et al.,2023) we concluded that, if the goal was to preserve events such as saccades, microsaccades, and smooth pursuit in eye-tracking recordings, data with sine wave frequencies less than 100 Hz (-3db) were the…
This technical note is on digital filters for the high-fidelity estimation of a sinusoidal signal's frequency in the presence of additive noise. The complex noise is assumed to be white (i.e. uncorrelated) however it need not be Gaussian.…
A simple procedure for the design of recursive digital filters with an infinite impulse response (IIR) and non-recursive digital filters with a finite impulse response (FIR) is described. The fixed-lag smoothing filters are designed to…
Searches for binary inspiral signals in data collected by interferometric gravitational wave detectors utilize matched filtering techniques. Although matched filtering is optimal in the case of stationary Gaussian noise, data from real…
I investigate the sensitivity of gravitational-wave searches by analyzing the response of matched filters in stationary Gaussian noise. In particular, I focus on the ability to analytically model the distribution of observed filter…
For the purpose of maximum likelihood estimation of static parameters, we apply a kernel smoother to the particles in the standard SIR filter for non-linear state space models with additive Gaussian observation noise. This reduces the Monte…
In this paper we revisit a non-linear filter for {\em non-Gaussian} noises that was introduced in [1]. Goggin proved that transforming the observations by the score function and then applying the Kalman Filter (KF) to the transformed…
Clustering is a well-established technique in machine learning and data analysis, widely used across various domains. Cluster validity indices, such as the Average Silhouette Width, Calinski-Harabasz, and Davies-Bouldin indices, play a…
We propose a method which, given a sequence of stereo foggy images, estimates the parameters of a fog model and updates them dynamically. In contrast with previous approaches, which estimate the parameters sequentially and thus are prone to…
We investigate the effect of an important class of glitches occurring in the detector data on matched filter searches of gravitational waves from coalescing compact binaries in the advanced detector era. The glitches, which can be modeled…
Searching for gravitational-wave signals is a challenging and computationally intensive endeavor undertaken by multiple independent analysis pipelines. While detection depends only on observed noisy data, it is sometimes inconsistently…
Data assimilation methodologies are designed to incorporate noisy observations of a physical system into an underlying model in order to infer the properties of the state of the system. Filters refer to a class of data assimilation…
To achieve the sensitivity required to detect signals from neutral hydrogen from the Cosmic Dawn and Epoch of Reionisation it is critical to have a well-calibrated instrument which has a stable calibration over the course of the…
The problem of determining the intrinsic quality of a signal processing system with respect to the inference of an unknown deterministic parameter $\theta$ is considered. While the Fisher information measure $F(\theta)$ forms a classical…
The choice of delay-Doppler domain (DD) pulse shaping filter plays an important role in determining the performance of Zak-OTFS. Sinc filter has good main lobe characteristics (with nulls at information grid points) which is good for…