Signal Processing

Questions tagged [linear-prediction]

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23 views

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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1answer
31 views

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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1answer
53 views

Kalman Filter implementation is too slow

I have implemented with a simple code a Kalman Filter for time domain, based on these: KG = error_est / (error_est+error_measurment) estimate = estimate_prev + KG ( measurment - estimate_prev) ...
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21 views

Filtering relationship for sources propagating over a sensor array

A sensor array $y$ measures the superposition of $N$ sources $s$, at time $t$ and position $x$ we have : $$y(t,x)=\sum_{i=1}^{N} s_i(t,x)$$ The sources $s$ travel at constant speed over the array of $...
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0answers
11 views

Interactive Multiple Model Likelihood Calculations

I'm writing an Interacting Multiple Model tracking filter for the first time. I understand that the reported state is a blending of the states of the individual states of the individual filters based ...
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0answers
80 views

Is the Wiener filter operating at the Cramér–Rao bound?

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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1answer
28 views

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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1answer
31 views

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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1answer
103 views

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 ...
4
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1answer
154 views

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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1answer
81 views

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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0answers
369 views

How to find Coefficients of Autoregressive (AR) model using least means square (LMS) Algorithm without having future signal?

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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1answer
191 views

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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1answer
171 views

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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1answer
59 views

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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1answer
36 views

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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0answers
2k views

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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0answers
125 views

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 ...
2
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1answer
339 views

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 ...
4
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3answers
465 views

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)...
4
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2answers
107 views

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 ...
2
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1answer
260 views

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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0answers
2k views

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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0answers
246 views

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 ...
2
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2answers
669 views

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, ...
2
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1answer
717 views

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 ...
2
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0answers
363 views

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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0answers
53 views

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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4answers
1k views

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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0answers
325 views

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 ...
2
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1answer
1k views

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 ...
4
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3answers
8k views

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 ...
4
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1answer
1k views

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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0answers
112 views

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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0answers
94 views

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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1answer
239 views

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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0answers
47 views

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 ...
2
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1answer
381 views

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 ...
1
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1answer
807 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 ...
2
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0answers
242 views

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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2answers
437 views

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 ...
-1
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2answers
224 views

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 ...
0
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2answers
142 views

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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0answers
140 views

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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1answer
1k views

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 ...
0
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1answer
1k views

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 ...
2
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0answers
121 views

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 ...
3
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2answers
354 views

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 ...
8
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1answer
3k views

Speech Compression - In LPC how does the linear predictive filter work on a general level?

Hi I'm taking a multimedia systems course and I'm preparing for my exam on tuesday. I'm trying to get my head around LPC compression on a general level, but I'm having trouble with what is going on ...
9
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1answer
1k views

Theory behind Linear Predictive Coding (LPC)

What is the theory behind LPC? Why are(were) certain implementations of LPC said to be more tolerant of transmission or encoding errors quantization than other compressed voice encoding schemes? ...

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