Spectral density estimation

About: Spectral density estimation is a research topic. Over the lifetime, 5391 publications have been published within this topic receiving 123105 citations.

Channel estimation for a communication system using spectral estimation

Abstract: Techniques for performing channel estimation in a multi-carrier system are described A frequency response estimate is initially obtained for a wireless channel based on a narrowband pilot sent on different sets of subbands in different symbol periods or a wideband pilot sent on all or most subbands in the system Spectral estimation is performed on the frequency response estimate to determine at least one frequency component of the frequency channel estimate, with each frequency component being indicative of a delay for a channel tap in an impulse response estimate for the wireless channel A channel estimate for the wireless channel is then obtained based on the frequency component(s) determined by the spectral estimation This channel estimate may be a channel profile, the impulse response estimate, an improved frequency response estimate, a signal arrival time, or some other pertinent information regarding the wireless channel

INL reconstruction of A/D converters via parametric spectral estimation

Abstract: The work presented in this paper builds on previous research done by the authors in detailing a novel procedure for obtaining a very fast measurement of the integral nonlinearity of an analog-to-digital converter (ADC). The core of the method is the parametric spectral estimation of the ADC output; the static characteristic is subsequently reconstructed as a sum of Chebyshev polynomials, in accordance with a previously developed procedure. The method allows one to test an ADC with sinusoids of any reasonable amplitude (even a slight overdrive is allowed), frequency (no synchronization is needed), and phase (which is digitally compensated). This approach is less accurate than the histogram test but incomparably faster (about 8000 samples are sufficient regardless of the ADC resolution).

A Robust Sparse Fourier Transform in the Continuous Setting

Abstract: In recent years, a number of works have studied methods for computing the Fourier transform in sub linear time if the output is sparse. Most of these have focused on the discrete setting, even though in many applications the input signal is continuous and naive discretization significantly worsens the sparsity level. We present an algorithm for robustly computing sparse Fourier transforms in the continuous setting. Let x(t) = x*(t) + g(t), where x* has a k-sparse Fourier transform and g is an arbitrary noise term. Given sample access to x(t) for some duration T, we show how to find a k-Fourier-sparse reconstruction x'(t) with [frac{1}{T}int0T abs{x(t) - x(t)}2 mathrm{d} t lesssim frac{1}{T}int0T abs{g(t)}2 mathrm{d}t. The sample complexity is linear in k and logarithmic in the signal-to-noise ratio and the frequency resolution. Previous results with similar sample complexities could not tolerate an infinitesimal amount of i.i.d. Gaussian noise, and even algorithms with higher sample complexities increased the noise by a polynomial factor. We also give new results for how precisely the individual frequencies of x* can be recovered.

Body Wave Separation in the Time-Frequency Domain

Abstract: Separation of a seismogram into its individual constitutive phases (Pand S-wave arrivals, surface waves, etc.) is a long-standing problem. In this letter, we use a high-resolution time-frequency transform to achieve this and reconstruct their individual waveforms in the time domain. The procedure is illustrated using microseismic events recorded during a hydraulic fracturing treatment. The synchrosqueezing transform is an extension of the continuous wavelet transform combined with frequency reassignment. Its high-resolution time-frequency decompositions allow for separation and identification of Pand S-waves with subtly different frequency contents that would not be recoverable using short-term Fourier transforms due to its smearing in the frequency domain. It is an invertible transform, thus allowing for signal reconstruction in the time domain after signal separation. The same approach is applicable to other seismic signals such as resonance frequencies and long-period events and offers promising new possibilities for enhanced signal interpretation in terms of underlying physical processes.

Spectral estimation and inverse initial boundary value problems

Abstract: We extend the classical spectral estimation problem to the infinite-dimensional case and propose a new approach to this problem using the Boundary Control (BC) method. Several applications to inverse problems for partial differential equations are provided.