In statistical signal processing, the sampling times are most often taken to be equally spaced. However, several applications need that non-uniform sampling is important. The major work on nonuniform sampling is for when the sampling times can be specified, and the signal processing community lacks tools to deal with standard issues like identification and decimation for signals sampled at non-uniform times. With a stochastic view, this thesis aims to fill this gap, and it provides tools to deal with errors induced by nonuniform sampling.
Much is gained by studying apriorie properties of frequency transforms and estimates, and the tools can be used for several signal processing problems. Nonuniform sampling is used in radar applications, medical applications, image processing and astronomical data processing. In uniform sampling , the sampling interval is fixed . Uniform sampling is also known as periodic sampling. In nonuniform sampling, the sampling time and amplitude are not predictable. Nonuniform sampling is also known as stochastic sampling.
Nonuniform sampling signal spectrum plays an important role in signal detection and tracking. In many applications, much interest lies in narrow band signal detection which may be recorded in very noisy environment. Therefore signal detection and frequency estimation becomes nontrial problems that require robust, high resolution spectrum estimation techniques[2]. We first consider Fast Fourier transform method of spectrum estimation which is most often used technique in spectral analysis.
By using FFT, frequency resolution of noise spectrum is decreased and variance is also reduced, but these may not be reduced to optimum level [3]. So we take nonparametric methods for spectrum estimation. The nonparametric methods emphasize on obtaining consistent estimate of the power spectrum through some average or smoothing operations performed directly on the periodogram or on the autocorrelation of the noisy data.
Although variance of the modified periodogram estimates is decreased, the effect of the operations are performed are expenses of reducing the frequency resolution, since frequency resolution of noisy signal is the main focus, The problem of PSDE becomes two fold. First , it is necessary to denoise the signal from its interfering background and then, to compute its power spectrum estimation such that frequency resolution is not decreased due to further windowing of data [4]. Illustrating frequency resolution in nonparametric methods averaging or modified periodogram for estimating power spectrum ensity. In comparison, the novel approach for power spectrum estimation is to maintain frequency resolution close to the original spectrum. Compare to FFT method which is also shown in the results[4]. The goals of this project are as follows: •To develop an apriorie estimation approach for nonuniform level sampling using MAT LAB tool. •To apply the periodgram approach for the predicted signals. •To evaluate the power spectrum density estimation methods for estimation accuracy.
