scholarly journals Audio Codec Using Legendre Functions for Simplified Digital Telephony

2021 ◽  
Author(s):  
Sabapathy Ananthi ◽  
Ananthanarayanan Arun ◽  
Sivakannan Subramani ◽  
Krishnasamy Padmanabhan
Keyword(s):  
Legendre Functions ◽  
Audio Codec ◽  
Digital Telephony

scholarly journals Superwideband Bandwidth Extension Using Normalized MDCT Coefficients for Scalable Speech and Audio Coding

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Young Han Lee ◽  
Seung Ho Choi
Keyword(s):  
Discrete Cosine Transform ◽  
Audio Coding ◽  
Bandwidth Extension ◽  
Spectral Parameters ◽  
Cosine Transform ◽  
Modified Discrete Cosine Transform ◽  
Audio Codec ◽  
Speech And Audio Coding

A bandwidth extension (BWE) algorithm from wideband to superwideband (SWB) is proposed for a scalable speech/audio codec that uses modified discrete cosine transform (MDCT) coefficients as spectral parameters. The superwideband is first split into several subbands that are represented as gain parameters and normalized MDCT coefficients in the proposed BWE algorithm. We then estimate normalized MDCT coefficients of the wideband to be fetched for the superwideband and quantize the fetch indices. After that, we quantize gain parameters by using relative ratios between adjacent subbands. The proposed BWE algorithm is embedded into a standard superwideband codec, the SWB extension of G.729.1 Annex E, and its bitrate and quality are compared with those of the BWE algorithm already employed in the standard superwideband codec. It is shown from the comparison that the proposed BWE algorithm relatively reduces the bitrate by around 19% with better quality, compared to the BWE algorithm in the SWB extension of G.729.1 Annex E.

scholarly journals Derivatives of addition theorems for Legendre functions

1995 ◽  
Vol 37 (2) ◽  
pp. 212-234 ◽  
Author(s):  
D.E. Winch ◽  
P.H. Roberts
Keyword(s):  
Spherical Harmonics ◽  
Chebyshev Polynomials ◽  
Legendre Polynomials ◽  
Addition Theorem ◽  
Legendre Functions ◽  
Addition Theorems ◽  
Associated Legendre Functions ◽  
Tensor Spherical Harmonics ◽  
Derivatives Of

AbstractDifferentiation of the well-known addition theorem for Legendre polynomials produces results for sums over order m of products of various derivatives of associated Legendre functions. The same method is applied to the corresponding addition theorems for vector and tensor spherical harmonics. Results are also given for Chebyshev polynomials of the second kind, corresponding to ‘spin-weighted’ associated Legendre functions, as used in studies of distributions of rotations.

scholarly journals ROLES OF LOG-CONCAVITY, LOG-CONVEXITY, AND GROWTH ORDER IN WHITE NOISE ANALYSIS

2001 ◽  
Vol 04 (01) ◽  
pp. 59-84 ◽  
Author(s):  
NOBUHIRO ASAI ◽  
IZUMI KUBO ◽  
HUI-HSIUNG KUO
Keyword(s):  
White Noise ◽  
Noise Analysis ◽  
Holomorphic Functions ◽  
Legendre Transform ◽  
Legendre Functions ◽  
Growth Order ◽  
White Noise Analysis ◽  
Systematic Method ◽  
Growth Functions ◽  
Natural Way

In this paper we will develop a systematic method to answer the questions (Q1) (Q2) (Q3) (Q4) (stated in Sec. 1) with complete generality. As a result, we can solve the difficulties (D1) (D2) (discussed in Sec. 1) without uncertainty. For these purposes we will introduce certain classes of growth functions u and apply the Legendre transform to obtain a sequence which leads to the weight sequence {α(n)} first studied by Cochran et al.6 The notion of (nearly) equivalent functions, (nearly) equivalent sequences and dual Legendre functions will be defined in a very natural way. An application to the growth order of holomorphic functions on ℰc will also be discussed.

The Legendre Functions P v (x) and Q v (x)

2008 ◽  
pp. 611-626
Author(s):  
Keith B. Oldham ◽  
Jan C. Myland ◽  
Jerome Spanier
Keyword(s):  
Legendre Functions

scholarly journals Spatially Restricted Integrals in Gradiometric Boundary Value Problems

2009 ◽  
Vol 44 (4) ◽  
pp. 131-148 ◽  
Author(s):  
M. Eshagh
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Legendre Functions ◽  
Gravity Gradiometry ◽  
Satellite Gravity Gradiometry ◽  
Satellite Gravity ◽  
Earth’S Gravity Field ◽  
Associated Legendre Functions ◽  
Tensor Spherical Harmonics ◽  
Slepian Functions

Spatially Restricted Integrals in Gradiometric Boundary Value ProblemsThe spherical Slepian functions can be used to localize the solutions of the gradiometric boundary value problems on a sphere. These functions involve spatially restricted integral products of scalar, vector and tensor spherical harmonics. This paper formulates these integrals in terms of combinations of the Gaunt coefficients and integrals of associated Legendre functions. The presented formulas for these integrals are useful in recovering the Earth's gravity field locally from the satellite gravity gradiometry data.

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