Showing papers on "Non-uniform discrete Fourier transform published in 1974"

Discrete Cosine Transform

Abstract: A discrete cosine transform (DCT) is defined and an algorithm to compute it using the fast Fourier transform is developed. It is shown that the discrete cosine transform can be used in the area of digital processing for the purposes of pattern recognition and Wiener filtering. Its performance is compared with that of a class of orthogonal transforms and is found to compare closely to that of the Karhunen-Loeve transform, which is known to be optimal. The performances of the Karhunen-Loeve and discrete cosine transforms are also found to compare closely with respect to the rate-distortion criterion.

Fourier Transform Computers Using CORDIC Iterations

Abstract: The CORDIC iteration is applied to several Fourier transform algorithms. The number of operations is found as a function of transform method and radix representation. Using these representations, several hardware configurations are examined for cost, speed, and complexity tradeoffs. A new, especially attractive FFT computer architecture is presented as an example of the utility of this technique. Compensated and modified CORDIC algorithms are also developed.

Coarse frequency estimation using the discrete Fourier transform (Corresp.)

Abstract: The discrete Fourier transform (DFT) is applied as a coarse estimator of the frequency of a sine wave in Gaussian noise. Probability of anomaly and the variance of the estimation error are determined by computer simulation for several DFT block sizes as a function of signal energy-to-noise density ratio \mathcal{E}/N_0 . Several data windows are considered, but uniform weighting gives the best performance.

Method and apparatus for computing the discrete Fourier transform recursively

Abstract: A wholly digital system for computing the discrete Fourier transform of sequentially received data in a recursive fashion. Two parallel shift registers store and shift the real and imaginary components of the complex number X k + iY k . The data in the parallel registers are successively shifted one bit per strobe in response to receipt of new data. Additional logic operates recursively on successive data inputs to compute the discrete Fourier transform.

Implementation of a fast Fourier transform (FFT) for image processing applications

Abstract: Different fast Fourier transform (FFT) algorithms for hardware implementation have been considered. We propose an implementation whereby two radix-N1/2passes are carried out in parallel and in which each N1/2-point transform is carried out via a serial input parallel output transform circuit. The processing rate is one clock cycle per input point for the N-point transform regardless of the value of N chosen. The circuit is being implemented with TTL logic and will be used to perform spatial frequency domain filtering on two dimensional infrared camera images in real time; real time meaning processing between frame display.

Frame-to-frame coding of television pictures using two-dimensional Fourier transforms (Corresp.)

Abstract: Two systems are described for reducing the data rate required to transmit TV signals. Basic to the operation of both systems is the fact that if there is an object in the scene moving more or less in linear translation, then the two-dimensional frame-difference signal computed during the present frame will be very similar to the frame-difference signal which was computed during the previous frame except for a linear translation. Thus the Fourier transform of the frame-difference signal will also be similar during successive frames except for a linear phase shift.

Comparative Study of a Discrete Linear Basis for Image Data Compression

Abstract: Transform image data compression consists of dividing the image into a number of nonoverlapping subimage regions and quantizing and coding the transform of the data from each subimage. Karhunen-Loeve, Hadamard, and Fourier transforms are most commonly used in transform image compression. This paper presents a new discrete linear transform for image compression which we use in conjunction with differential pulse-code modulation on spatially adjacent transformed subimage samples. For a set of thirty-three 64 × 64 images of eleven different categories, we compare the performancea of the discrete linear transform compression technique with the Karhunen-Loeve and Hadamard transform techniques. Our measure of performance is the mean-squared error between the original image and the reconstructed image. We multiply the mean-squared error with a factor indicating the degree to which the error is spatially correlated. We find that for low compression rates, the Karhunen-Loeve outperforms both the Hadamard and the discrete linear basis method. However, for high compression rates, the performance of the discrete transform method is very close to that of the Karhunen-Loeve transform. The discrete linear transform method performs much better than the Hadamard transform method for all compression rates.

Computer-generated Fourier transforms of helical particles

Abstract: An alternative method has been found to display the information contained in the Fourier transform of a helical particle. This allows a strong selection rule to be defined for the transform on the layer lines and consequently the discrimination between signal and noise contributions to the data can be improved.

Motion detection employing direct Fourier transforms of images

Abstract: Method and apparatus for directly converting between an image and the spatial or temporal Fourier transform thereof. To convert an image into its Fourier transform representation, the image interacts with strain waves in media that have electrical properties varying as a function of both the intensity pattern of the image and strain waves in the media. The electrical properties are measured to derive signals representing Fourier series terms defining the image. The derived signals are used to detect motion (including motion in the plane of the image), for image stabilization and scaling, and for pattern recognition. A new DEFT device (Direct Electronic Fourier Transform) obtains a Fourier transform representation of an image by utilizing photon assisted tunnelling current through an isolator film junction between two thin conductor films. Another new DEFT device provides spatial scanning similar to television raster scanning but utilizing completely different principles. Still another new DEFT device generates a two-dimensional spatial Fourier transform representation of an image without the need for two-dimensional scanning of the strain wave. An image is reconstructed from electrical signals obtained as described above by interacting uniform (but not necessarily coherent) light with strain waves that are a function of these electrical signals.

Direct application of the fast fourier transform to open resonator calculations.

Abstract: It is shown how fast Fourier transform techniques can be used to efficiently, numerically evaluate (convolution) integrals of the form often encountered in open resonator eigenmode calculations.

Two-dimensional digital processing of one-dimensional signal

Abstract: It is of importance to find the necessary and sufficient conditions under which the one-dimensional and two-dimensional processing of any general transform should be equivalent. These conditions are found. It is known that the Fourier transform does not possess the described property. It is shown in this paper that a one-dimensional Fourier transform cannot be equivalent to any two-dimensional transform. On the other hand it is shown that the two-dimensional Fourier transform is equivalent to a one-dimensional transform of another kind and that the processing can be performed by a fast algorithm.

Generation of Dolph-Chebyshev weights via a fast Fourier transform

Abstract: Dolph-Chebyshev weights, which realize a minimum side-lobe level for a specified main-lobe width, can be generated by a single fast Fourier transform (FFT). For an even number of elements 2H, the size of the FFT is H. This result has utility for spectral analysis as well as for array processing.

Walsh-Transform Analysis of Discrete Dyadic-Invariant Systems

Abstract: This short paper shows how the sampled output of a dyadic-invariant linear system with a given sequency-domain transfer function, in response to a sampled input, can be determined by 1) a term-wise multiplication of the sampled transfer function and the discrete Walsh transform of the sampled input function, followed by an inverse Walsh transform, or 2) a discrete dyadic convolution of the sampled impulse response and the sampled input directly in the time domain. Functions in both time and sequency domains are represented by column matrices, and discrete Walsh transformation is effected simply by the multiplication with a Walsh matrix. An example is included to illustrate both procedures. The validity of the solutions is further verified by showing that the governing dyadic differential equation of the system is satisfied.

An algorithm for performing an inverse chirp z-transform

Abstract: An efficient algorithm for the determination of the coefficients of a polynomial from evenly spaced sample values of that polynomial on a spiral contour in the complex plane is presented. It is useful for the determination of a sequence from evenly spaced values of its Fourier transform.

Parallel data streams and serial arithmetic for fast Fourier transform processors

Abstract: An algorithm is presented that introduces two degrees of parallelism into the implementation of fast Fourier transform (FFT) processors. That is, both the radix of factorization and the number of arithmetic units may be selected to achieve the required processing speed. A serial vector multiplier that is ideally suited to the implementation of a general radix arithmetic unit is described. It is subsequently shown that a fast Fourier processor having an attractive cost performance ratio can be built by employing serial arithmetic in the implementation of the algorithm developed.

Numerical calculations of the potential due to an arbitrary charge density using the fast Fourier transform

Abstract: The Green's function method of finding the voltage due to an arbitrary charge density is related to a convolution integral for simple geometries. The fast Fourier transform (FFT) algorithm is used to calculate the voltages on the grid points and it is argued that significant reduction of computer time is achieved for a large number of grid points.

One-dimensional Optical Fourier Transforms of Line Tracings

Abstract: An optical Fourier transforming system is used to produce the transform of a one-dimensional signal recorded as a transparent oscillogram on an opaque screen. If the tracing is illuminated with light whose amplitude varies linearly perpendicular to the tracing axis, then the exact transform is obtained along one axis of the output plane. Spectra with small error terms are obtained by superimposing a phase plate, or a knife edge or a special binary mask over the line tracing. The theory of the methods is presented and verified experimentally. Multichannel operation is demonstrated.

Calculating Chebyshev shading coefficients via the discrete Fourier transform

Abstract: A previous technique for deriving Chebyshev shading coefficients using a cosine series is rewritten in the form of an inverse discrete Fourier transform (DFT) thus allowing one to take advantage of standard DFT algorithms. The reduced accuracy required for intermediate calculations is retained. Additionally, the fast Fourier transform can be used giving computational savings.

Extension of a radix-2 fast Fourier transform (FFT) program to include a prime factor

Abstract: A simple procedure is presented to develop a fast Fourier transform (FFT) program for PQ points starting from a program for Q points, with emphasis on Q = 2M. The transformation with respect to the factor P is followed by a transformation of P groups of Q points each using the existing subroutine, then the array is unscrambled with respect to P.