Questions tagged [linear-prediction]
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52 questions
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Proof that the order of a linear prediction model cannot be reduced by analysing non-adjacent points
I have a signal, for which a linear prediction model of order $M$ can be constructed. This means, that a system of the shape
$$
\begin{bmatrix}
s_0 & s_1 & \cdots & s_M \\
s_1 & s_2 &...
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1
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145
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How to mitigate floating point error in recursive DSP calculations
I have implemented a modified linear prediction coding function like this:
...
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2
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2
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276
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Design of digital filters with negative group delay
I am currently working on digital filters that can predict my input signal(assume that input signal is bandlimited). In other words, I want my filter to have a flat magnitude response in bandwidth of ...
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3
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326
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Why use an ARMA process theory instead of just performing linear regression?
I am studying ARMA processes. At the end of the course the professor told us that estimating the next sample in an arma process using past of length $p$ (so performing a projection of $X_t$ on $\text{...
2
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1
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251
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How were the coefficients for polynomial linear predictive coding derived?
FLAC uses linear predictive coding (LPC) as one of its central compression steps. While it allows for arbitrary LPC coefficients in the "FIR Linear prediction" subframe compression type, ...
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0
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41
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Strange result in simple LPC simulation of a sinus
I'm trying to understand how Matlab LPC function works. So I made a little example script : I generate a real cosinus, calculate the LPC coefficients of this signal and then I try to predict the ...
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1
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1
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65
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Can Goodness-of-fit increase while noise also increases?
I saw a tweet with a good slide. It has a Goodness-of-fit curve that goes up with Model Complexity. There is a Generalizability curve. Noise is cited as the difference between the GOF and ...
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Does the Wiener Filter Achieve the Cramer Rao Lower Bound (CRLB)?
I have been told (Wikipedia agrees) that the Wiener filter is optimal when signal and (additive) noise are WSS. Optimal in the sense that it minimizes the mean-square error.
The Cramér–Rao bound is ...
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483
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How to select the order of LPC to model formants?
I am having some difficulties understanding LPC and speech processing in general. The professor asked us to provide an heuristic way to select the order of LPC? For example if I wanted to model 3 ...
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1
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What do coeffcients mean from Matlab?
I ask for a brief explanation of each coefficient and their sources of related information. Thank you very much in advance.
The coefficients comes from this code below:
I've got a robust linear ...
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190
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Finding the linear prediction coefficients for a sampled sinusoid
I am unable to work my way through this problem -
A sinusoid with random phase is given as 𝑦(𝑛) = 2 sin(0.25π𝑛 + 𝜃). If this signal is sampled at 10
KHz, estimate the coefficients of a second ...
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1
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381
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Estimate Instantaneous Frequency Using LMS Algorithm
I hope someone can help me with the following problem:
I want to estimate the frequency of a sound file that is composed of a sinusoidal with varying frequency and additive white noise:
$$ x \...
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1
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137
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Linear prediction and filter stability
I am currently trying to implement an iterative block-wise algorithm in which AR coefficients are computed for each block.
There is a issue with my code where values get too large, and I was ...
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4
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1
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997
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Learning the Coefficients of Auto Regressive (AR) Model Using Least Mean Squares (LMS) Filter for Signal Prediction
I want to do two things.
Estimating Coefficients of AR model using LMS
Using Coefficients found in step 1 and predict future samples of a signal using AR equation.
I don't have a desired signal so I ...
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309
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Can Temperature Data be Predicted Using Adaptive Filter (Such As LMS) Algorithm?
I am working on a project which requires me to implement adaptive filter as a predictor.
I have just started on adaptive filter and I intend to use least mean square algorithm for weight adjustment.
...
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436
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AR Modeling: Why residual is white noise?
I was going through AR modeling.
The AR model of a covariance stationary process can be expressed as:
$$x[n]=\sum\limits_{i=1}^{p} \alpha_i x[n-i] + \epsilon[n]$$
where $p$ is the model order and $...
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Adaptive Predictive Coding: Transmit signal AND prediction coefficients
I'm not well versed in the literature so please forgive/inform me if my terminology is wrong:
I have a bounded real-valued, discrete-time signal $x_n \in \mathbb [0, 1]$, and I want to (lossily) ...
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Practical insightful time domain functions [closed]
This question might be a little bit different, but i am having hard time to find some sort of a list/book/website/advice, with very practical time domain functions that provides useful insgihts for a ...
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Linear Predictive Coding example in MATLAB
I have some data that is highly correlated and I wanted to see if I could try and encode it using linear predictive coding (LPC). Here is how I've been understanding the process:
Encoding
Generate ...
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223
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Understanding linear predictive coding in MATLAB
I want to test my understanding of linear prediction by running it on some test data in MATLAB. The way I understand it is if I have some data that is correlated, I can encode the signal with linear ...
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555
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Linear Predictive Coding for general signals
I have a signal that's monotonic and roughly linear and have been looking at using Linear Predictive Coding to encode information and compress my signal. I guess my first general question is if this ...
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3
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591
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Is Linear Prediction ever exact?
I'm just learning about linear prediction and was wondering whether or not there are any signals that would produce no error if run through a linear prediction algorithm. I was thinking (maybe naively)...
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2
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147
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Image Interpolation Using the Yule Walker Equations
I have been studying about the Yule-Walker equations for prediction of a time series data from knowledge of past values of the series. Is there any way I can use the same in an image to exploit the ...
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Autoregressive modeling (linear prediction) of electrical transmission lines?
I've read that the reflection coefficients in speech processing (as computed by the Levinson-Durbin algorithm for solving the Yule-Walker equations) "represent the fraction of energy reflected back" ...
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Pre-emphasizing in speech recognition
Usually, in speech recognition, the techniques that are used are based on the linear prediction model (Fant, 1960).
Parallel to this, the human speech production mechanism causes energy to drop ...
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340
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Intuitions on Kumaresan-Tufts algorithm for exponential fit
I am analyzing a transient signal presumably consisting of superposed exponentials. Such a case is indicated for the Prony analysis, but my data aren't noiseless enough, so I have turned to the ...
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2
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982
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How do I go from LPC coefficients to a filter polynomial?
I've recently begun experimenting with LPC, and while I understand that it works, I'm still slightly lost on why it works.
Specifically, I understand that LPC involves finding coefficients $a_1, a_2, ...
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2
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827
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Predicting account balance based on historical data
Given the values of a bank account balance over time (see figure below as an example), how can one predict the account balance at a given date in the future ?
Should I just fit one linear regression ...
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2
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0
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414
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How to use linear predictive coding to compress voice diphone samples?
I'm working on an experimental diphone / unit selection speech synthesizer for my native language which lacks good speech synthesizer for blind people.
The problem is that recorded unit library can ...
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Variance and Co-variance of a Linear Forecast
Consider a linear forecasting problem where all shocks $\{\epsilon_i\}_1^n$ are independently distributed with $\epsilon_i\sim N(0,\sigma_i^2)$ for all $i$. Suppose you want to forecast $\theta = \...
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Compression algorithms specific to complex signals
I am looking for (lossy or lossless) compression algorithms dedicated to complex signals. The latter could be composite data (like the left and right for stereo audio), a Fourier transformation or an ...
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392
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Prediction-error filter for images
I am interested in studying local pixel value dependencies in images and I am wondering if it exists a general form of prediction-error convolutional filter that is able to suppress the image's ...
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Linear prediction (LPC) of Sine wave samples around maximas
I think I missed class when this was explained ...
Anyway as part of a bigger project I have to implement a LPC to predict 2-3 future values of a sinusoidal process. I wrote a small Matlab m-file to ...
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What is the need for prediction filter in PCM and DPCM?
The DPCM works by the difference between actual samples and predicted samples.
If we already have the actual samples, we can quantize it and encode it later.
But why we use prediction filter?
And ...
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How is cross-correlation related with orthogonality?
In linear prediction we can say that in case of optimum linear predictor the error with be orthogonal to data. And when we derive minimum mean square error for $\underline{y} = \mathbf{a}\underline{x} ...
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Sample-By-Sample Linear Prediction
As I understand it and have it currently implemented, linear prediction [via Burg's method or the autocorrelation method] is a block algorithm. Hence, there will be latency involved because one must ...
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Noise Robust Linear Prediction
So it appears that Linear Prediction as performed via Durbin Recursion is sensitive to additive noise. What are some techniques for linear prediction that may be more robust? Can anyone supply a link ...
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100 samples ahead signal prediction [duplicate]
I have a signal sampled at 100 sample per second. After low pass filtering of 200 order and some calculation such as zero crossing detection, I am getting around 1 second delayed signal. I want it in ...
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Turn a decision problem into a linear filter problem
Let $x[n]$ be a time-series, and two filters:
$A[n] = a_0 x[n] + a_1 x[n-1] + ... a_q x[n-q]$
$B[n] = b_0 x[n] + b_1 x[n-1] + ... b_r x[n-r]$
I think the answer is No, but is there a way to have ...
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1
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437
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Linear Prediction of AR Process
A discrete signal x is generated by the recursive process
$$
x_n = x_{n-1} - 0.2 x_{n-2} + w_n
$$
where $w_n$ is white noise with zero mean and unit variance. What is the optimum order of a linear ...
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1
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984
views
Division by zero in Levinson–Durbin recursion?
I am doing a LPC analysis of a speech signal using the autocorrelation method. To calculate the LPCs I am using the Levinson–Durbin recursion. In my literature the error is initialized with the first ...
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276
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Spectral Whitening: Approches
Given the absence of information about the algorithms of spectral whitening functions in software packages:
How many ways do you know for doing spectral whitening?
What are the differences?
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pitch extraction for speech
I am building an LPC analysis tool, and am at the point of needing to do pitch period analysis. I was initially interested in using the Gold & Rabiner algorithm for this, and got a hold of a ...
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Linear Predictive Coding and Block Size
I'm experimenting with linear predictive coding as a low-complexity audio compression method, and I'm observing something very odd. I'm compressing a 20 MB mono 16-bit PCM song in different block ...
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Is there any relationship between the FFT and linear prediction?
Is there any relationship between the FFT and linear predictive methods? Can an FFT result or the input to an FFT be modified to do non-circular prediction/extrapolation from the FFT results.
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150
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Adaptive calculations of Wiener filter coefficients
Suppose,I have an input of length of lenght 100. data=[x0...x99];
I take a window of lenght 11 from x0 to x10.
windowed data=[x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10],
now, I compute 7 wiener coefficients ...
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Adaptive Wiener Filter Coefficients Calculation
I want to extrapolate a signal X of length 11, using the weiner filter coefficients W of length 7. The procedure I am using is as follows:
Compute the autocorrelation matrix upto lag 8 .
Using ...
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1k
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Derivation of Yule-Walker Equation for LPC
I have derived the Yule-Walker equation as shown below.
\begin{align}
\hat s(n) &= -\sum_{k=1} ^ p a_k s(n-k)\\
e(n) &= s(n) - \hat s(n) = s(n) + \sum_{k=1}^pa_k s(n-k)
\end{align}
In order ...
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Voice sample prediction scheme
I have some telephone voice audio with occasional "blips" in the audio. The blips appear to come from an IP link buried in the PSTN (this is a conceptual explanation, so don't worry about things like ...
- 2,188
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2
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Linear predictive model convolution
Accidentally asked this question in the general area and was told to ask here, so...
I've been trying to develop a lightweight, relatively-fast-to-decode sound compression format for use in my gaming ...
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