Showing papers on "S transform published in 1979"

Coherent Optical Implementation Of Generalized Two-Dimensional Transforms

Abstract: A coherent optical method capable of performing arbitrary two-dimensional linear transformations has recently been studied, in which transform coefficients are given by two-dimensional inner products of the input image and a set of basis functions. Since the inner product of two functions is equal to the value of their correlation when there is zero shift between the functions, it is possible to use an optical correlator to solve for the coefficients of the transform. By using random phase masks in the input and the filter planes of the correlator, we have been able to pack many coefficients close together in the output plane, and thus take better advantage of the space-bandwidth product of the optical system. Both the input random phase mask and the spatial filter are computer-generated holographic elements, created by a computer-controlled laser beam scanner. The system can be "pro-grammed" to perform arbitrary two-dimensional linear transformations. For demonstration, the set of two-dimensional Walsh functions was chosen as a transform basis. When the resolution of the Walsh functions was limited to 128 x 128, up to 256 transform coefficients were obtained in parallel. The signal-to-noise and accuracy of the transform coefficients were compared to the theory.

Coefficient extrapolator for the Haar, Walsh, and Hadamard domains

Abstract: In a data compression system utilizing the Haar, Walsh or Hadamard transformation, a machine which operates in the transform domain to obtain approximations to the higher order transform coefficients by means of extrapolation from lower order transform coefficients. The extrapolation of the higher order transform coefficients is approximately equivalent to either a linear or to a quadratic interpolation within the spatial or time domain.

Rate/Pitch modification of speech using the constant-Q transform

Abstract: Modification of the rate of occurrence of acoustic events without altering frequency content, and modification of pitch without changing time scale are presented as equivalent problems. While the short-time Fourier transform has been used to solve the rate modification problem, it is not a natural tool. It lacks the scaling property of the Fourier transform. The constant-Q transform, on the other hand, exhibits this property. A more natural rate/pitch modification system using the constant-Q transform is presented which performs well with rate/pitch changes by factors of between one-third and three.

Qualitative and semiquantitative Fourier transformation using a noncoherent system.

Abstract: A number of authors have pointed out that a system of zone plates combined with a diffuse source, transparent input, lens, and focusing screen will display on the output screen the Fourier transform of the input. Strictly speaking, the transform normally displayed is the cosine transform, and the bipolar output is superimposed on a dc gray level to give a positive-only intensity variation. By phase-shifting one zone plate the sine transform is obtained. Temporal modulation is possible. It is also possible to redesign the system to accept a diffusely reflecting input at the cost of introducing a phase gradient in the output. Results are given of the sine and cosine transforms of a small circular aperture. As expected, the sine transform is a uniform gray. Both transforms show unwanted artifacts beyond 0.1 rad off-axis. An analysis shows this is due to unwanted circularly symmetrical moire patterns between the zone plates.