Conjugate Duality and the Exponential Fourier Spectrum

1983 ◽  
Author(s):  
Wray Britton
Keyword(s):  
Fourier Spectrum ◽  
Conjugate Duality

Conjugate Duality and the Exponential Fourier Spectrum (Wray Britton)

SIAM Review ◽  
1985 ◽  
Vol 27 (4) ◽  
pp. 602-605
Author(s):  
Bert W. Rust
Keyword(s):  
Fourier Spectrum ◽  
Conjugate Duality

Electron holography in materials science

1991 ◽  
Vol 49 ◽  
pp. 670-671
Author(s):  
Hannes Lichte ◽  
Edgar Voelkl
Keyword(s):  
Electron Microscopy ◽  
Transmission Electron Microscopy ◽  
Materials Science ◽  
Fourier Spectrum ◽  
Object Wave ◽  
Electron Holography ◽  
Reconstruction Procedure ◽  
Numerical Reconstruction ◽  
Transmission Electron ◽  
Unique Interpretation

The object wave o(x,y) = a(x,y)exp(iφ(x,y)) at the exit face of the specimen is described by two real functions, i.e. amplitude a(x,y) and phase φ(x,y). In stead of o(x,y), however, in conventional transmission electron microscopy one records only the real intensity I(x,y) of the image wave b(x,y) loosing the image phase. In addition, referred to the object wave, b(x,y) is heavily distorted by the aberrations of the microscope giving rise to loss of resolution. Dealing with strong objects, a unique interpretation of the micrograph in terms of amplitude and phase of the object is not possible. According to Gabor, holography helps in that it records the image wave completely by both amplitude and phase. Subsequently, by means of a numerical reconstruction procedure, b(x,y) is deconvoluted from aberrations to retrieve o(x,y). Likewise, the Fourier spectrum of the object wave is at hand. Without the restrictions sketched above, the investigation of the object can be performed by different reconstruction procedures on one hologram. The holograms were taken by means of a Philips EM420-FEG with an electron biprism at 100 kV.

Image thresholding method based on Fourier spectrum and moment-preserving principle

2010 ◽  
Vol 30 (8) ◽  
pp. 2094-2097 ◽  
Author(s):  
Xin-ming ZHANG ◽  
Shuang LI ◽  
Yan-bin ZHENG ◽  
Hui-yun ZHANG
Keyword(s):  
Fourier Spectrum ◽  
Image Thresholding ◽  
Thresholding Method

Optimization of the Robots Fourier Spectrum by Using the Assisted Research, Neural Network, Smart Damper and LabVIEW Instrumentation

2012 ◽  
Vol 245 ◽  
pp. 24-32 ◽  
Author(s):  
Adrian Olaru ◽  
Serban Olaru ◽  
Aurel Oprean
Keyword(s):  
Neural Network ◽  
Transfer Function ◽  
Spectral Density ◽  
Vibration Analysis ◽  
Manufacturing Systems ◽  
Fourier Spectrum ◽  
Industrial Robots ◽  
Vibration Behavior ◽  
Power Spectral ◽  
The World

The most important things in the dynamic research of industrial robots are the vibration behavior, the transfer function and the vibration power spectral density between some of the robot joints and components. In the world this research is made without the assisted research. In each of the study cases in this paper was used the proper virtual Fourier analyzer and was presented one new method of the assisted vibration analysis. With this research it is possible the optimal choosing the base modulus type to avoid the frequencies from the robot spectrum. In the manufacturing systems, the most important facts are the vibration behavior of the robot, the compatibility with some other components of the system. All the VI where achieved in the LabVIEW soft 8.2 version, from National Instruments, USA. This method and the created virtual LabVIEW instrumentation are generally and they are possible to apply in many other dynamic behavior research.

Joint transform correlator subtracting a modified Fourier spectrum

1995 ◽  
Vol 34 (32) ◽  
pp. 7532 ◽  
Author(s):  
Martin Schönleber ◽  
Gregor Cedilnik ◽  
Hans-J. Tiziani
Keyword(s):  
Fourier Spectrum ◽  
Joint Transform Correlator

Characteristic Measures for the Representation of Manufactured Surface Quality

1996 ◽  
Author(s):  
Irem Y. Turner ◽  
R. S. Srinivasan ◽  
Kristin L. Wood
Keyword(s):  
Surface Characterization ◽  
Fourier Spectrum ◽  
Expansion Method ◽  
Design Parameters ◽  
Machining Processes ◽  
Wavelet Representation ◽  
Design And Manufacturing ◽  
Surface Precision ◽  
Signal Characterization ◽  
Generate Characteristic

Abstract In this paper, we investigate four methods that yield mathematical measures to analyze the precision of surfaces of manufactured parts. These four methods, namely the autocorrelation function, the Fourier spectrum, the Karhunen-Loève expansion, and a fractal-wavelet representation, are applied to surfaces produced from grinding processes. The first two methods are standard methods used in the surface analysis literature for qualitative signal characterization. The Karhunen-Loève expansion method, used in various signal processing applications, has never been applied to the field of surface characterization and representation. The fractal-wavelet representation has been previously proposed by the authors; its suitability to generate characteristic measures is investigated in this paper. The existence of characteristic measures of surface precision should aid designers in choosing process and design parameters and in comparing the precision between competing machining processes. The use of such measures is essential in taking a forward step towards integrating the fields of design and manufacturing.

Speech Synthesis Using Damped Sinusoids

2002 ◽  
Vol 45 (4) ◽  
pp. 639-650 ◽  
Author(s):  
James M. Hillenbrand ◽  
Robert A. Houde
Keyword(s):  
Spectrum Analysis ◽  
Speech Signal ◽  
Speech Synthesis ◽  
Fourier Spectrum ◽  
Fundamental Period ◽  
Speech Synthesizer ◽  
Perceptual Evaluation ◽  
Random Intervals ◽  
Sentence Intelligibility ◽  
Nonsense Syllables

A speech synthesizer was developed that operates by summing exponentially damped sinusoids at frequencies and amplitudes corresponding to peaks derived from the spectrum envelope of the speech signal. The spectrum analysis begins with the calculation of a smoothed Fourier spectrum. A masking threshold is then computed for each frame as the running average of spectral amplitudes over an 800-Hz window. In a rough simulation of lateral suppression, the running average is then subtracted from the smoothed spectrum (with negative spectral values set to zero), producing a masked spectrum. The signal is resynthesized by summing exponentially damped sinusoids at frequencies corresponding to peaks in the masked spectra. If a periodicity measure indicates that a given analysis frame is voiced, the damped sinusoids are pulsed at a rate corresponding to the measured fundamental period. For unvoiced speech, the damped sinusoids are pulsed on and off at random intervals. A perceptual evaluation of speech produced by the damped sinewave synthesizer showed excellent sentence intelligibility, excellent intelligibility for vowels in /hVd/ syllables, and fair intelligibility for consonants in CV nonsense syllables.

An analysis of the spectrum of a gravity anomaly over an inclined dike

Geophysics ◽  
1985 ◽  
Vol 50 (9) ◽  
pp. 1500-1501
Author(s):  
B. N. P. Agarwal ◽  
D. Sita Ramaiah
Keyword(s):  
Fourier Transform ◽  
Gravity Anomaly ◽  
Fourier Spectrum ◽  
Fourier Transforms ◽  
Weighted Average ◽  
Window Function ◽  
Average Spectrum ◽  
Amplitude Spectra ◽  
Distance Data ◽  
The Fourier Transform

Bhimasankaram et al. (1977) used Fourier spectrum analysis for a direct approach to the interpretation of gravity anomaly over a finite inclined dike. They derived several equations from the real and imaginary components and from the amplitude and phase spectra to relate various parameters of the dike. Because the width 2b of the dike (Figure 1) appears only in sin (ωb) term—ω being the angular frequency—they determined its value from the minima/zeroes of the amplitude spectra. The theoretical Fourier spectrum uses gravity field data over an infinite distance (length), whereas field observations are available only for a limited distance. Thus, a set of observational data is viewed as a product of infinite‐distance data with an appropriate window function. Usually, a rectangular window of appropriate distance (width) and of unit magnitude is chosen for this purpose. The Fourier transform of the finite‐distance and discrete data is thus represented by convolution operations between Fourier transforms of the infinite‐distance data, the window function, and the comb function. The combined effect gives a smooth, weighted average spectrum. Thus, the Fourier transform of actual observed data may differ substantially from theoretic data. The differences are apparent for low‐ and high‐frequency ranges. As a result, the minima of the amplitude spectra may change considerably, thereby rendering the estimate of the width of the dike unreliable from the roots of the equation sin (ωb) = 0.

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