The FFT is used widely in signal processing for efficient computation of the Fourier transform (FT) over a set of uniformly spaced frequency locations. However, in many applications, one requires nonuniform sampling in the frequency domain, i.e., a nonuniform FT. Several papers have described fast approximations for the nonuniform FT based on interpolating an oversampled FFT. This paper present...

In this paper, a recursive computation method is developed to derive the multiple reflections of nonuniform transmission lines. The true impedance profiles of the nonuniform transmission lines are then reconstructed with the help of this method. This method is more efficient than other algorithm. To validate this method, two nonuniform microstrip lines are designed and measured using Agilent ve...

This paper studies the covolumes of nonuniform arithmetic lattices in PU(n, 1). We determine the smallest covolume nonuniform arithmetic lattices for each n, the number of minimal covolume lattices for each n, and study the growth of the minimal covolume as n varies. In particular, there is a unique lattice (up to isomorphism) in PU(9, 1) of smallest Euler–Poincaré characteristic amongst all no...

We introduce the notion of nonuniform coercion, which is the promotion of a value of one type to an enriched value of a different type via a nonuniform procedure. Nonuniform coercions are a generalization of the (uniform) coercions known in the literature and they arise naturally when formalizing mathematics in an higher order interactive theorem prover using convenient devices like canonical s...

A novel linear transform (LT) is proposed for frequency warping (FW) with standard filterbank based MFCC features. Here, we use the idea of spectral interpolation of [9] to perform a continuous warping in the log filterbank output domain, and incorporate both interpolation and warping into a single warped IDCT matrix. The new transformation matrix is thus mathematically simpler than in [9], and...

This paper establishes a new coherent framework to extend the class of unitary warping operators [1] to the case of discrete–time sequences. Providing some a priori considerations on signals, we show that the class of discrete– time warping operators finds a natural description in linear shift–invariant spaces. On such spaces, any discrete–time warping operator can be seen as a non–uniform weig...

Image-based rendering (IBR) techniques produce realistic-looking 3D graphics at a relatively low cost. The 3D image warping technique is particularly appropriate for such an implementation, because it requires a relatively small input data set. In this paper, we propose a computationally efficient framework for 3D image warping technique. This includes a function that maps the visible points in...

Music alignment links events in a score and points on the audio performance time axis. All the parts of a recording can be thus indexed according to score information. The automatic alignment presented in this paper is based on a dynamic time warping method. Local distances are computed using the signal’s spectral features through an attack plus sustain note modeling. The method is applied to m...