MATLAB编程实现码激励线性预测算法详解

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MATLAB®软件在编码激励线性预测（CELP）算法中的应用是本篇论文的核心主题。CELP是一种广泛应用于语音编码、通信系统以及信号处理领域的高效算法，它结合了预测编码与激励信号，以减少所需比特率并提高语音信号的质量。在本文中，作者Karthikeyan N. Ramamurthy和Andreas S. Spanias深入探讨了如何利用MATLAB这一强大的数值计算工具来实现和编程CELP算法。首先，MATLAB作为一个功能丰富的环境，提供了可视化编程和交互式开发的便利性。对于线性预测，用户可以使用其内置的信号处理工具箱，如`filter`函数和相关的窗口函数，来设计预测滤波器和实现自回归模型。通过MATLAB，开发者能够轻松地进行滤波器系数的计算、误差预测、激励信号的选择以及整个编码过程的仿真。论文可能详细介绍了以下步骤： 1. **预测模型设计**：通过理解语音信号的统计特性，构建自回归模型，MATLAB允许创建递归滤波器，用于预测信号的未来样本。 2. **误差计算**：利用预测结果与实际信号的差异，计算出预测误差，这是CELP算法的关键部分。 3. **激励信号生成**：通过激励信号减小误差，可以选择合适的激励序列，如最小均方误差准则或谱峰减小准则。 4. **编码过程**：对预测误差进行编码，通常采用诸如脉冲编码调制（PCM）或子带编码（Subband Coding）等方法，进一步压缩数据。 5. **解码与重建**：解码得到的信号通过逆向过程进行重建，以恢复原始语音质量。同时，文章可能会讨论MATLAB中的特定工具和函数，如`lpc`（线性预测编码）和`cepstral`函数，它们对于实现CELP算法至关重要。此外，由于联邦标准1016的提及，论文可能还涵盖了算法的标准化实践，确保了代码的兼容性和互操作性。这篇论文不仅关注理论分析，还提供了实用的编程指导，使得读者能掌握如何在MATLAB中有效地实现和优化CELP算法。它对于从事信号处理、通信工程或音频编码研究的工程师和学生来说是一份宝贵的资源，能够帮助他们提升技术能力，将理论知识转化为实际应用。

1.1. LINEAR PREDICTIVE CODING 5

speech compression systems for encoding vocal tract parameters. A lattice structure is shown in

Figure 1.3.

s(n)

()

− 1

−

s(n)

()

− 1

−

ΣΣ Σ

ΣΣΣ

Figure 1.3: Lattice structure for linear prediction and reﬂection coefﬁcients.

1.1.2 EXCITATION, GAIN AND PITCH PERIOD

The residual signal e(n) given in (1.2) forms the optimal excitation for the linear predictor. For

low-rate representations of speech, the residual signal is typically replaced by a parametric excitation

signal model. Many of the early algorithms for linear prediction used the two-state excitation model

(impulses/noise) shown in Figure 1.1. This model is parameterized in terms of the gain, the binary

voicing parameter and the pitch period. The gain of voiced and unvoiced segments is generally

determined such that the short-term energy of the synthetic speech segment matches that of the

analysis segment. For unvoiced speech, the excitation is produced by a random number generator.

Since unvoiced segments are associated with small energy and large number of zero crossings, voicing

can be determined by energy and zero-crossing measurements. Pitch estimation and tracking is a

difﬁcult problem. Some of the well-known algorithms for pitch detection were developed in the

late sixties and seventies. A straightforward approach to pitch detection is based on selecting the

peak of the autocorrelation sequence (excluding r(0)). A more expensive but also more robust

pitch detector relies on peak-picking the cepstrum. The Simpliﬁed Inverse Filter Tracking (SIFT)

algorithm is based on peak-picking the autocorrelation sequence of the prediction residual associated

with downsampled speech. Post-processing algorithms for pitch smoothing are also used to provide

frame-to-frame pitch continuity. Current pitch detection algorithms yield high-resolution (sub-

sample) estimates for the pitch period and are often speciﬁc to the analysis-synthesis system. In

many Analysis-by-Synthesis (A-by-S) linear predictive coders, the pitch is measured by a closed-

loop process which accounts for the impact of the pitch on the overall quality of the reconstructed

speech.

6 1. INTRODUCTION TO LINEAR PREDICTIVE CODING

1.1.3 LINEAR PREDICTION PARAMETER TRANSFORMATIONS

One of the major issues in LPC is the quantization of the linear prediction parameters. Quantization

of the direct-form coefﬁcients a(i)is generally avoided.The reﬂection coefﬁcients k

are by-products

of the Levinson algorithm and are more robust for quantization. The reﬂection coefﬁcients can also

be quantized in an ordered manner, i.e., the ﬁrst few reﬂection coefﬁcients can be encoded with a

higher precision. Transformations of the reﬂection coefﬁcients, such as the Log Area Ratio (LAR),

i.e.,

LAR

(

)

= log



1 + k

1 − k



, (1.8)

have also been used in several LPC algorithms. Another representation of Linear Prediction (LP)

parameters that is being used in several standardized algorithms consists of Line Spectrum Pairs

(LSPs). In LSP representations, a typical tenth-order polynomial,

(

)

= 1 + a

−1

+···+a

−10

, (1.9)

is represented by the two auxiliary polynomials P

(

)

and Q

(

)

where,

(

)

= A

(

)

+ z

−11



−1



, (1.10)

(

)

= A

(

)

− z

−11



−1



. (1.11)

P(z)and Q(z) have a set of ﬁve complex conjugate pairs of zeros each that typically lie on the unit

circle. Hence, each polynomial can be represented by the ﬁve frequencies of their zeros (the other

ﬁve frequencies are their negatives). These frequencies are called Line Spectral Frequencies (LSFs).

If the polynomial A(z) is minimum phase, the roots of the polynomials P(z)and Q(z) alternate on

the unit circle.

1.1.4 LONG-TERM PREDICTION

Almost all modern LP algorithms include long-term prediction in addition to the tenth-order short-

term linear predictor. Long Term Prediction (LTP) captures the long-term correlation in the speech

signal and provides a mechanism for representing the periodicity of speech. As such, it represents

the ﬁne harmonic structure in the short-term speech spectrum. The LTP requires estimation of two

parameters, i.e.,a delay τ and a gain parameter a(τ). For strongly voiced segments,the delay is usually

an integer that approximates the pitch period. The transfer function of a simple LTP synthesis ﬁlter

is given by,

(z) =

1 − a(τ)z

−τ

. (1.12)

The gain is obtained by the equation a(τ) = r(τ)/r(0). Estimates of the LTP parameters can be

obtained by searching the autocorrelation sequence or by using closed-loop searches where the LTP

lag that produces the best speech waveform matching is chosen.

1.2. ANALYSIS-BY-SYNTHESIS LINEAR PREDICTION 7

1.2 ANALYSIS-BY-SYNTHESIS LINEAR PREDICTION

In closed-loop source-system coders, shown in Figure 1.4, the excitation source is determined

by closed-loop or A-by-S optimization. The optimization process determines an excitation se-

quence that minimizes the perceptually-weighted MSE between the input speech and reconstructed

speech [1, 2, 3]. The closed-loop LP combines the spectral modeling properties of vocoders with

the waveform matching attributes of waveform coders; and hence, the A-by-S LP coders are also

called hybrid LP coders.The term hybrid is used because of the fact that A-by-S integrates vocoder

and waveform coder principles. The system consists of a short-term LP synthesis ﬁlter 1/A(z) and a

LTP synthesis ﬁlter 1/A

(z) as shown in Figure 1.4.The Perceptual Weighting Filter (PWF) W(z)

shapes the error such that quantization noise is masked by the high-energy formants. The PWF is

given by,

W(z) =

A(z/γ

)

A(z/γ

)

1 −



i=1

(i) a(i) z

−i

1 −



i=1

(i) a(i) z

−i

; 0 <γ

<γ

< 1 , (1.13)

where γ

and γ

are the adaptive weights, and m is the order of the linear predictor. Typically, γ

ranges from 0.94 to 0.98; and γ

varies between 0.4 and 0.7 depending upon the tilt or the ﬂatness

characteristics associated with the LPC spectral envelope [4, 5].The role of W(z)is to de-emphasize

the error energy in the formant regions [6]. This de-emphasis strategy is based on the fact that, in

the formant regions, quantization noise is partially masked by speech. From Figure 1.4, note that a

gain factor g scales the excitation vector x and the excitation samples are ﬁltered by the long-term

and short-term synthesis ﬁlters.

The three most common excitation models typically embedded in the excitation generator

module (Figure 1.4) in the A-by-S LP schemes include: the Multi-Pulse Excitation (MPE) [2, 3],

the Regular Pulse Excitation (RPE) [7], and the vector or Code Excited Linear Prediction (CELP) [1].

A 9.6 kb/s Multi-Pulse Excited Linear Prediction (MPE-LP) algorithm is used in Skyphone airline

applications [8]. A 13 kb/s coding scheme that uses RPE [7] was adopted for the full-rate ETSI

GSM Pan-European digital cellular standard [9].The standard was eventually replaced by the GSM

Enhanced Full-Rate (EFR) described brieﬂy later.

The aforementioned MPE-LP and RPE schemes achieve high-quality speech at medium

rates. For low-rate high-quality speech coding a more efﬁcient representation of the excitation

sequence is required. Atal [10] suggested that high-quality speech at low rates may be produced by

using non-instantaneous (delayed decision) coding of Gaussian excitation sequences in conjunction

with A-by-S linear prediction and perceptual weighting. In the mid-eighties, Atal and Schroeder [1,

11] proposed a CELP algorithm for A-by-S linear predictive coding.

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