Efficient parametric coding of transients

Abstract

In this paper, methods for improved parametric coding of transients are presented. We propose a signal model for coding of transients consisting of a sum of sinusoids each being amplitude-modulated by a different gamma envelope. These envelopes are characterized by an onset time, an attack and a decay parameter. An efficient method for estimating these parameters is presented. Further, methods are proposed that combine this transient model with a constant-amplitude sinusoidal model in order to achieve efficient coding of both stationary and transient signal parts. By rate-distortion optimization using a perceptual distortion measure we combine variable rate bit allocation and segmentation in an optimal way. Formal as well as informal listening tests show that significant improvements can be achieved with the proposed model as compared to a state-of-the-art sinusoidal coder by the combination of optimal segmentation and amplitude modulated sinusoidal audio coding.

On perceptual distortion minimization and nonlinear least-squares frequency estimation

“…A recently published psychoacoustic masking model for audio coding has been shown to form a distortion measure [30], [31], and this distortion measure has been applied successfully to the sinusoidal estimation problem in [15], [23], [32], [33]. Based on this we define the perceptual frequency estimation problem and its optimal solution.…”

Bayesian Interpolation and Parameter Estimation in a Dynamic Sinusoidal Model

“…To better model these signals, the model in (2) has been modified in various ways. Typical modifications comprise amplitude and/or phase modulation [32], [33]. the representation of the amplitudes and/or phases as a linear combination of atoms from a suitable basis [34], and autoregressive (AR) frequency parameters [10].…”

“…The distribution for is a bivariate normal distribution and the product over of of these can therefore be written as (32) In order to write this distribution in a useful way in terms of the frequency parameter and the damping coefficient, we rewrite into (33) where is obtained by a 90 clockwise rotation of and…”

Variable Dimension Trellis-Coded Quantization of Sinusoidal Parameters

“…Assuming a sufficiently large window length N , or statistical independence between the components, the total expected distortion can be approximated as the sum over the L expected distortions for the individual components denoted E[D], with E[·] being the expectation operator. Therefore, we will in the rest of this letter be concerned with the quantization of a single set of parameters (a, φ, ν) and drop the subscript l. A perceptual distortion that has proven successful for audio coding applications (see, e.g., [1], [4], [5], [11], [12]) was introduced in [13], and is defined as…”