The autoregressive model is one of a group of linear prediction formulas that attempt to predict an output y[n] of a system based on the previous outputs ( y[n-1],y[n-2]...) and inputs ( x[n], x[n-1], x[n-2]...).
Deriving the linear prediction model involves determining the coeffiecients a1,a2,.. and b0,b1,b2,... in the equation:
ye[n] (estimated) = a1*y[n-1] + a2*y[n-2]... + b0*x[n] + b1*x[n-1] + ...
Note the REMARKABLE similarity between the prediction formula and the difference equation used to describe discrete linear time invariant systems. Calculating a set of coefficients that give a good prediciton ye[n] is tantamount to determining what the system is, within the constraints of the order chosen.
A model which depends only on the previous outputs of the system is called an autoregressive model (AR), while a model which depends only on the inputs to the system is called a moving average model (MA), and of course a model based on both inputs and outputs is an autoregressive-moving-average model (ARMA). Note that by definition, the AR model has only poles while the MA model has only zeros.
Several methods and algorithms exist for calculating the coefficients of the AR model, all of which are implemented by the matlab command 'ar'. We use the default setting ('forward-backward') to calculate the AR model for the vocal tract, with the following justifications:
The simplest model for the vocal tract, consisting of linked cylindrical tubes, produces an all-pole transfer function.
Only the outputs of the system are available to us.
Note that the AR model is based on frequency-domain analysis and should be windowed. (We use the hamming.)
The order of the system: We are using the AR model to determine the characteristics of the vocal system and from this system model evaluate the formants, or resonant frequencies of the vocal system.(i.e. the peaks in the frequency response) One conjugate pole pair is required to produce each formant, and one formant is expected in each 1kHz band or so. Therefore the order of the model is a function of the sampling frequency: fs/2 + 2 (the added 2 being the 'empirically determined adjustment factor')
All our autoregressive matlab techniques are in the function formants.m.(or see the attachement)
There is TONS of material about autoregressive models. Check out your library...
From: http://www.owlnet.rice.edu/~elec431/projects96/digitalbb/autoregression.html
分享到:
相关推荐
Bayesian prediction in threshold autoregressive models with exponential white noise
• Autoregressive Models • Latent Variable Models • Deterministic Generative Models • Generative Adversarial Nets • Flow-Based Generative Models • Bayesian Generative Models • Bayesian Inference...
摘要:为提高烧结混合料加水控制的智能程度,针对烧结生产线现场的实际情况,提出了一种非线性自回归 (nonlinear autoregressive models
D2D信道阴影衰落相关性的自回归移动平均建模,李金兴,赵友平,D2D系统能够提高网络吞吐量与能源利用效率,已得到广泛研究。由于收发端天线高度均降低且均可移动,D2D无线信道的衰落特性与传统蜂
CHAPTER 12: SEASONAL AUTOREGRESSIVE INTEGRATED MOVING AVERAGE MODELS CHAPTER 13: DESEASONALIZED MODELS CHAPTER 14: PERIODIC MODELS CHAPTER 15: FORECASTING WITH SEASONAL MODELS PART VII: MULTIPLE ...
matlab代码影响自回归模型的网络推理 介绍 该存储库包含用于在高维自回归模型中对网络参数进行估计和测试的代码。 高维线性AR(p)模型的假设检验 文件夹线性测试包括用于对高维AR(p)模型中的自回归参数进行假设...
Moreover, two drawbacks have been found in many of the past forecasting models: (1) statistical assumptions about variables are required for time series models, such as the autoregressive moving ...
R语言MSwM包说明文档。 Univariate Autoregressive Markov Switching Models for Linear and Generalized Models by using the EM algorithm.
Historically, traditional methods such as Autoregressive Integrated Moving Average (ARIMA) have played an important role for researchers studying time series data. Recently, as advances in computer ...
technique, based on a Generalized Likelihood Ratio Test (GLRT), for detecting and estimating mean shifts in autocorrelated processes that follow a normally distributed Autoregressive Integrated Moving...
R语言实现包括时间序列arima模型等内容,具体有Simple time series models, ARIMA, Wavelets, Digital Signal Processing (DSP) Modeling volatility, GARCH models (Generalized AutoRegressive Conditionnal ...
The book then moves on to discuss the mathematics of counting processes and autoregressive conditional duration models, which are quite common modeling tools for high frequency tick data. At the end ...
log-normal, and K-distribution models. Finally, a new modified Kolmogorov—Smirnoff (KS) goodness-of-fit test is proposed; this modified test guarantees good fitting in the distribution tails, which ...
石油和天然气行业是著名的行业之一,从生产和经济角度来看,对必要的石油统计数据进行预测和预测都很重要。 人工举升方法被用于提高生产率。 即使底部井口的自然压力合适,我们也确实依靠人工举升机制,如游梁泵、...
This paper focuses on the parameter estimation problems of output error autoregressive systems and output error autoregressive moving average systems (i.e., the Box–Jenkins systems). Two ...
我们提供了基于高斯过程回归 (GPR) 的随机波动率 (SV) 的公式。 预测样本外波动率,模拟和实证分析表明,我们基于 GPR 的随机波动率 (GPSV) 模型明显优于 SV 和 GARCH 基准,尤其是在长期范围内。...
4.2 Concept of Cointegration and Error-Correction Models . . . . . . . 75 4.3 Systems ofCointegratedVariables ......................... 78 Summary ................................................... ...
张量流和pytorch中的变体自动编码器 TensorFlow和PyTorch中可变自动编码器的参考实现。 我建议使用PyTorch版本。 它包括一个更具表达性的变分族的例子,。 变分推断用于使模型适合二值化MNIST手写数字图像。...