The short-time Fourier transform of a discrete-time signal, which is the Fourier transform of a “windowed” version of the signal, is interpreted as a sliding-window spectrum. This sliding-window spectrum is a function of two variables: a discrete time index, which represents the position of the window, and a continuous frequency variable. It is shown that the signal can be reconstructed from th...

Outlier detection is an important process for text document collections, but as the collection grows, the detection process becomes a computationally expensive task. Random projection has shown to provide a good fast approximation of sparse data, such as document vectors, for outlier detection. The random samples of Fourier and cosine spectrum have shown to provide good approximations of sparse...

OBJECTIVE The Fourier transform, a fundamental mathematic tool widely used in signal analysis, is ubiquitous in radiology and integral to modern MR image formation. Understanding MRI techniques requires a basic understanding of what the Fourier transform accomplishes. MR image encoding, filling of k-space, and a wide spectrum of artifacts are all rooted in the Fourier transform. CONCLUSION Th...

The Entropy/Influence conjecture, raised by Friedgut and Kalai (1996) [9], seeks to relate two different measures of concentration of the Fourier coefficients of a Boolean function. Roughly saying, it claims that if the Fourier spectrum is “smeared out”, then the Fourier coefficients are concentrated on “high” levels. In this note we generalize the conjecture to biased product measures on the d...

High-resolution Fourier transform nuclear magnetic resonance was used to observe the natural abundance (13)C spectrum of a 0.02 M solution of bovine pancreatic ribonuclease A. Peaks assignable to only three carbons were easily observed after 10 hr of signal averaging. A number of tentative assignments were made. As expected, the (13)C spectrum was appreciably richer in detail than the correspon...

A compressed sensing scheme for near-field imaging of corrugations of relative sparse Fourier components is proposed. The scheme employs random sparse measurement of near field to recover the angular spectrum of the scattered field. Surprisingly, it can be shown heuristically and numerically that under the Rayleigh hypothesis the angular spectrum is compressible and amenable to compressed sensi...

one of the most common signals used for achieving high range resolution in radar is stepped-frequency signals. when a target is stationary in these radars, dft (discrete fourier transform) based processing is used to attain high range resolution profile (hrrp). however, in the case of moving target, due to spreading of the echo signal spectrum, dft based processing is not optimal and decreases ...

In this paper, we report the synthesis of tin oxide (SnO2) nanoparticles by co-precipitation technique. The structural, surface morphology, thermal and optical properties of the SnO2 samples were analysed using X-ray diffraction (XRD), High-resolution transmission electron microscopy (HRTEM), Fourier transformed infrared (FTIR) spectrum, thermo gravimetric analysis (TGA/DT...

-Motor Current Signature Analysis (MCSA) has been successfully used for fault diagnosis in induction machines. The current spectrum of the induction machine for locating characteristic fault frequencies is used in MCSA. The spectrum is obtained using a Fast Fourier Transformation (FFT) that is performed on the signal under analysis. The fault frequencies occur in the motor current spectra are u...