This paper makes available a concise review of data windows and their affect on the detection of harmonic signals in the presence of broad-band noise, and in the presence of nearby strong harmonic interference. We also call attention to a number of common errors in the application of windows when used with the fast Fourier transform. This paper includes a comprehensive catalog of data windows along with their significant performance parameters from which the different windows can be compared. Finally, an example demonstrates the use and value of windows to resolve closely spaced harmonic signals characterized by large differences in amplitude.

On the use of windows for harmonic analysis with the discrete Fourier transform

A summary of many of the new techniques developed in the last two decades for spectrum analysis of discrete time series is presented in this tutorial. An examination of the underlying time series model assumed by each technique serves as the common basis for understanding the differences among the various spectrum analysis approaches. Techniques discussed include the classical periodogram, classical Blackman-Tukey, autoregressive (maximum entropy), moving average, autotegressive-moving average, maximum likelihood, Prony, and Pisarenko methods. A summary table in the text provides a concise overview for all methods, including key references and appropriate equations for computation of each spectral estimate.

Spectrum analysis&#8212;A modern perspective

The Nature of Remote Sensing: Introduction. Remote Sensing. Information Extraction from Remote-Sensing Images. Spectral Factors in Remote Sensing. Spectral Signatures. Remote-Sensing Systems. Optical Sensors. Temporal Characteristics. Image Display Systems. Data Systems. Summary. Exercises. References. Optical Radiation Models: Introduction. Visible to Short Wave Infrared Region. Solar Radiation. Radiation Components. Surface-Reflected. Unscattered Component. Surface-Reflected. Atmosphere-Scattered Component. Path-Scattered Component. Total At-Sensor. Solar Radiance. Image Examples in the Solar Region. Terrain Shading. Shadowing. Atmospheric Correction. Midwave to Thermal Infrared Region. Thermal Radiation. Radiation Components. Surface-Emitted Component. Surface-Reflected. Atmosphere-Emitted Component. Path-Emitted Component. Total At-Sensor. Emitted Radiance. Total Solar and Thermal Upwelling Radiance. Image Examples in the Thermal Region. Summary. Exercises. References. Sensor Models: Introduction. Overall Sensor Model. Resolution. The Instrument Response. Spatial Resolution. Spectral Resolution. Spectral Response. Spatial Response. Optical PSFopt. Image Motion PSFIM. Detector PSFdet. Electronics PSFel. Net PSFnet. Comparison of Sensor PSFs. PSF Summary for TM. Imaging System Simulation. Amplification. Sampling and Quantization. Simplified Sensor Model. Geometric Distortion. Orbit Models. Platform Attitude Models. Scanner Models. Earth Model. Line and Whiskbroom ScanGeometry. Pushbroom Scan Geometry. Topographic Distortion. Summary. Exercises. References. Data Models: Introduction. A Word on Notation. Univariate Image Statistics. Histogram. Normal Distribution. Cumulative Histogram. Statistical Parameters. Multivariate Image Statistics. Reduction to Univariate Statistics. Noise Models. Statistical Measures of Image Quality. Contrast. Modulation. Signal-to-Noise Ratio (SNR). Noise Equivalent Signal. Spatial Statistics. Visualization of Spatial Covariance. Covariance with Semivariogram. Separability and Anisotropy. Power Spectral Density. Co-occurrence Matrix. Fractal Geometry. Topographic and Sensor Effects. Topography and Spectral Statistics. Sensor Characteristics and Spectral Stastistics. Sensor Characteristics and Spectral Scattergrams. Summary. Exercises. References. Spectral Transforms: Introduction. Feature Space. Multispectral Ratios. Vegetation Indexes. Image Examples. Principal Components. Standardized Principal Components (SPC) Transform. Maximum Noise Fraction (MNF) Transform. Tasseled Cap Tranformation. Contrast Enhancement. Transformations Based on Global Statistics. Linear Transformations. Nonlinear Transformations. Normalization Stretch. Reference Stretch. Thresholding. Adaptive Transformation. Color Image Contrast Enhancement. Min-max Stretch. Normalization Stretch. Decorrelation Stretch. Color Spacer Transformations. Summary. Exercises. References. Spatial Transforms: Introduction. An Image Model for Spatial Filtering. Convolution Filters. Low Pass and High Pass Filters. High Boost Filters. Directional Filters. The Border Region. Characterization of Filtered Images. The Box Filter Algorithm. Cascaded Linear Filters. Statistical Filters. Gradient Filters. Fourier Synthesis. Discrete Fourier Transforms in 2-D. The Fourier Components. Filtering with the Fourier Transform. Transfer Functions. The Power Spectrum. Scale Space Transforms. Image Resolution Pyramids. Zero-Crossing Filters. Laplacian-of-Gaussian (LoG) Filters. Difference-of-Gaussians (DoG) Filters.Wavelet Transforms. Summary. Exercises. References. Correction and Calibration: Introduction. Noise Correction. Global Noise. Sigma Filter. Nagao-Matsuyama Filter. Local Noise. Periodic Noise. Distriping 359. Global,Linear Detector Matching. Nonlinear Detector Matching. Statistical Modification to Linear and Nonlinear Detector. Matching. Spatial Filtering Approaches. Radiometric Calibration. Sensor Calibration. Atmospheric Correction. Solar and Topographic Correction. Image Examples. Calibration and Normalization of Hyperspectral Imagery. AVIRIS Examples. Distortion Correction. Polynomial Distortion Models. Ground Control Points (GCPs). Coordinate Transformation. Map Projections. Resampling. Summary. Exercises References. Registration and Image Fusion: Introduction. What is Registration? Automated GCP Location. Area Correlation. Other Spatial Features. Orthrectification. Low-Resolution DEM. High-Resolution DEM. Hierarchical Warp Stereo. Multi-Image Fusion. Spatial Domain Fusion. High Frequency Modulation. Spectral Domain Fusion. Fusion Image Examples. Summary. Exercises. References. Thematic Classification: Introduction. The Importance of Image Scale. The Notion of Similarity. Hard Versus Soft Classification. Training the Classifier. Supervised Training. Unsupervised Training. K-Means Clustering Algorithm. Clustering Examples. Hybrid Supervised/Unsupervised Training. Non-Parametric Classification Algorithms. Level-Slice. Nearest-Mean. Artificial Neural Networks (ANNs). Back-Propagation Algorithm. Nonparametric Classification Examples. Parametric Classification Algorithms. Estimation of Model-Parameters. Discriminant Functions. The Normal Distribution Model. Relation to the Nearest-Mean Classifier. Supervised Classification Examples and Comparison to Nonparametric Classifiers. Segmentation. Region Growing. Region Labeling. Sub-Pixel Classification. The Linear Mixing Model. Unmixing Model. Hyperspectral Image Analysis. Visualization of the Image Cube. Feature Extraction. Image Residuals. Pre-Classification Processing and Feature Extraction. Classification Algorithms. Exercises. Error Analysis. Multitemporal Images. Summary. References. Index.

Remote sensing, models, and methods for image processing

SUMMARY In recent years methods of data analysis for point processes have received some attention, for example, by Cox & Lewis (1966) and Lewis (1964). In particular Bartlett (1963a,b) has introduced methods of analysis based on the point spectrum. Theoretical models are relatively sparse. In this paper the theoretical properties of a class of processes with particular reference to the point spectrum or corresponding covariance density functions are discussed. A particular result is a self-exciting process with the same second-order properties as a certain doubly stochastic process. These are not distinguishable by methods of data analysis based on these properties.

https://www.jstor.org/stable/info/2334319

Spectra of some self-exciting and mutually exciting point processes

Estimation of the parameters of a single-frequency complex tone from a finite number of noisy discrete-time observations is discussed. The appropriate Cramer-Rao bounds and maximum-likelihood (MI.) estimation algorithms are derived. Some properties of the ML estimators are proved. The relationship of ML estimation to the discrete Fourier transform is exploited to obtain practical algorithms. The threshold effect of one algorithm is analyzed and compared to simulation results. Other simulation results verify other aspects of the analysis.

Single tone parameter estimation from discrete-time observations

The finite Fourier transform of a finite sequence is defined and its elementary properties are developed. The convolution and term-by-term product operations are defined and their equivalent operations in transform space are given. A discussion of the transforms of stretched and sampled functions leads to a sampling theorem for finite sequences. Finally, these results are used to give a simple derivation of the fast Fourier transform algorithm.

The finite Fourier transform

A Branching Poisson Process Model for the Analysis of Computer Failure Patterns

The fast Fourier transform algorithm has a long and interesting history that has only recently been appreciated. In this paper, the contributions of many investigators are described and placed in historical perspective.

Historical notes on the fast Fourier transform

Remarks on the theory, computation and application of the spectral analysis of series of events

: A scheme for obtaining a stationary sequence of discrete random variables which has p-th order Markov dependence and a specified marginal distribution is presented. This DAR(p) process, which is a particular p-th order Markov chain, has the physical and correlation structure of an autoregressive process of order p. The process and its transition matrix are determined by the specified marginal distribution and by several other parameters which, independently of the marginal distribution, determine the correlation structure. Correlational properties and initial conditions for stationarity of the process are studied. Asymptotic properties for the process are also obtained. (Author)

https://calhoun.nps.edu/bitstream/10945/29821/1/discretetimeseri00jaco.pdf

Peter A. W. Lewis

Papers

The finite Fourier transform

A Branching Poisson Process Model for the Analysis of Computer Failure Patterns

Historical notes on the fast Fourier transform

Remarks on the theory, computation and application of the spectral analysis of series of events

Discrete time series generated by mixtures III: Autoregressive processes (DAR(p))