In signal processing, estimation is a technique for approximating an unobserved signal from an observed signal containing noise.

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91 views

How to understand the type of noise

Suppose that I am receiving RF signals contaminated with noise through antenna. This signal is digitally sampled. How can I understand the type of noise(Gaussian,Uniform etc). Any algorithm is there ...
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1answer
38 views

Using a Wiener Filter to Estimate a Transfer Function

As a follow-on to this question about estimating a transfer function of an unknown system using a Wiener filter, How would you put a minimum MSE criteria on how well the estimated filter weights ...
3
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2answers
119 views

Estimate the transfer function of an unknown system?

Suppose you have a system, H, that you want to estimate its transfer function. You have a finite number of complex input samples, x, and noisy complex (magnitude and phase) output samples, y: In ...
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1answer
37 views

Minimum Mean Square Estimator - Equivalent Expressions to Minimize

Given $ M \in {R}^{NxN} $ Positive Definite Matrix. Let $ \hat{x} $ the MMSE of $ x $ given $ z $. How come the following are equivalent of minimizing $ E[{(\hat{x} - x)}^{T}(\hat{x} - x)] $: $ ...
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0answers
45 views

Confusion regarding Dimension of AR model

I have a confusion regarding what is meant by dimension of AR,ARMA,MA model? Considering an AR model $x(t) = a1*x(t-1) + a2*x(t-2)$ is a 2 order AR model with $a1,a2$ as the parameters. This equation ...
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0answers
14 views

Relationship between phase space volume and entropy minimization

I would like to know if there is any analytical proof or relationship which can show that for a dynamical system in presence of chaos signal, if the phase space volume (PSV) minimization leads to the ...
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0answers
24 views

Minimizing the sum of squares of autocorrelation function of residuals instead of sum of squares of residuals

I am trying to fit my model to some experimental data and I am using a simulated annealing algorithm. My objective function has so far been the sum of squares of the residuals: $\sum_{i=1}^n (y_i - ...
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1answer
87 views

Carrier frequency offset (CFO) estimation based on Symbols

In (1), it's said that: If two identical training symbols are transmitted consecutively, the corresponding signals with CFO of $\epsilon$ are related with each other as follows: ...
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0answers
22 views

Estimating Model Weights for Point-Process Input/Output Systems using Probability Theory

Problem: I have a point-process input & output, x & y and I am attempting to estimate a 2nd order nonlinear Volterra-like model for them in the form: $$ Eq. 1: y[t] = k_0 + ...
2
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2answers
80 views

minimum SNR requirements for maximum likelihood frequency estimation

In certain applications, you have enough SNR available to, for example, perform an FFT and identify peak location and hence the signal frequency. If my understanding is correct, parameter estimation ...
2
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2answers
224 views

Carrier frequency offset (CFO) estimation using cyclic prefix

I understand the cyclic prefix, but in (1) it's said that: "If we consider that the channel effect is minimal and can be neglected. then the phase difference of the CP and the OFDM symbol which the ...
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0answers
39 views

What are variance and bias in spectral estimation (specifically periodogram spectral estimation)?

So far, I have read that all the non-parametric estimation techniques decrease the frequency resolution in order to decrease the variance in the spectral estimate What is the general "overview" ...
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0answers
62 views

Prony method for undamped signal

i have one question related to sinusoidal model,as i know Prony's method for parameter estimation is used for damped signal,when amplitude of signal decreases as time varies,but is it relevant to ...
3
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3answers
92 views

How to determine, calculate and plot a probability distribution for a given set of numbers?

A device is rotating with a particular wind speed and producing such pulse frequencies in a minute: ...
0
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2answers
59 views

Estimating the amplitude of a particular frequency

I am relatively new to DSP and have been reading a lot on the internet. I have a couple of questions. I have a signal in the form of a function $$ f(x) = A_0 + A_1 \cos(\omega_1 x) + A_2 ...
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0answers
28 views

Kalman Filter Properties with Biased (By Constant) Measurements

Assuming I have a filter with the following form: $$ \begin{bmatrix} {r}_{k} \\ {\dot{r}}_{k} \end{bmatrix} = {F}_{k} \begin{bmatrix} {r}_{k - 1} \\ {\dot{r}}_{k - 1} \end{bmatrix} + {v}_{k} $$ $$ ...
2
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0answers
25 views

If test statistic is $T(\textbf{Y})=\frac{1}{N}\sum\limits_{n=1}^N |Y[n]|^2$ then what is $T(\textbf{Y}|H_1)$?

There are two hypothesis: $H_0:Y[n]=W[n]$. $H_1:Y[n]=X[n]+W[n]$. $X[n]$ and $W[n]$ are independent of each other. $W[n]$ is zero mean Gaussian with variance = $\sigma^2$; however we only know the ...
2
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0answers
76 views

4th order cumulant of signal

I'm trying to implement some code for watermarking on audio based on a scientific paper. I'm stuck in the part of the pseudo code where they calculate the fourth order cumulant of the approximation ...
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0answers
37 views

Incorporating delayed data in Kalman filter

my guide has told me to get familiarized with state estimates and kalman filter ....the problem is that: 1) I am totally new to this topic and finding it really difficult to understand due to lack of ...
0
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2answers
62 views

DFT detemine frequencies

I am just begining learning about DFT and I am bit unsure on what is happening mathematically during DFT. I've sampled a signal , a sine wave sin(1000*2*pi*t). And performed DFT to calculate the ...
0
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1answer
37 views

How to identify stable deltas in a noisy signal

This is a problem I have had to deal with in several different contexts now. Given a real time signal which you expect to act as a noisy step function (periods of stability separated by quick changes ...
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1answer
31 views

inquires for prony estimation method

I want to estimate the frequency components of a time series by prony method, Is there any matlab routine for this purpose? tnx
2
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1answer
43 views

What is the set of most predictable or in other words most self-correlated signals?

Which signals or set of signals is the most predictable or in other words most self-correlated (autocorrelation)? I think one of them is $x(t)=c$, for all $t$, where $c$ is a scalar constant. The ...
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0answers
50 views

Sampling Clock Offset estimation

I want to estimate sampling clock offset. I am currently referring this paper " CRAMER-RAO BOUNDS FOR DATA-AIDED SAMPLING CLOCK OFFSET AND CHANNEL ESTIMATION ". Is there any other method to estimate? ...
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28 views

MMSE Estimation of Noise Corrupted Signal

I just learnt the MMSE (minimum mean square estimate) in my stochastic processes course and I am experimenting it on matlab. So I have a noise corrupted signal Z. ...
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7answers
497 views

Obtain a signal's peak value if it's frequency lies between two bin centers

Please suppose the following: The frequency of a signal's fundamental has been estimated using FFT and some frequency estimation methods and is lying between two bin centers The sampling frequency ...
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0answers
56 views

Symbol timing recovery algorithms

I am trying to implement the symbol timing recovery loop and for that I have chosen two algorithm to compare my results one is feedforward and Gardner TED. One thing that is confusing me is smoothing ...
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0answers
51 views

Questions regarding the Yin algorithm

I decided to implement the Yin algorithm for pitch estimation in monophonic music as a school project. I have studied the paper, but I don't understand some parts of it: In Step 3 - Cumulative mean ...
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0answers
53 views

Estimating Position Based on Range Measurement

I want to present Kalman Filter problem. For simplicity I'd assume the simplest dynamic model - Piece Wise Constant Velocity. The state vector and dynamic model are given by: $$ \begin{bmatrix} ...
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2answers
80 views

Relation between Kalman filter and Sequential linear MMSE estimation

Are the results of applying Kalman filter and recursive linear MMSE estimation process the same ?
4
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2answers
96 views

Why is PSD estimated, and not simply computed?

I apologize if this comes as a basic question, but I am struggling to understand why the PSD can only be estimated and not directly computed. For example, this thread discusses several such PSD ...
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0answers
52 views

Cleaning accelerometer output

I am working on an accelerometer on a mobile device. When an event occurs, I record around 30 acceleration values. The accelerometer, being extremely noisy is very unreliable. What makes it worse is ...
5
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1answer
176 views

How to detect specific behavior in time series?

I was not quite sure what the right SE for this was, so I posted this also here on SciComp. Please tell me which one to remove :) Problem statement I have a few hundred unrelated time series, say ...
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93 views

Stochastic process inference from partial observations

Consider a set $U$. My signal is a piece-wise constant "function" $Sig: t \mapsto s$, i.e. the signal at time $t$ equals to some subset $s \subset U$. One can see $Sig(t)$ as a stochastic process. ...
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1answer
117 views

Estimation of the amplitude of a frequency component in a signal

I'm working on a device that produces a signal with sampling rate of 100 kHz. Every 40 ms, I receive 16000 points, from which I have to extract a frequency close to 3.55 kHz. I have developed a method ...
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0answers
34 views

Issue in applying Kullback divergence metric

This is in application to blind signal separation in communication. I have an observation modelled as $x(t) = \sum_{i=1}^p a_p*x_{t-i} + noise(t)$ where noise is AWGN. At the receiver end an inverse ...
0
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1answer
62 views

Estimation of input signal to obtain the desired output signal for an unknown filter

Suppose $h(n)$ is a finite impulse response which is unknown. We can feed any input signal $x(n)$ into the system and observe the corresponding output signal $y(n)$. From this, is it possible to ...
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2answers
171 views

Conceptual question on least square estimation method

What is meant by Least square plus Gaussian method of estimating the parameters of an unknown system? I am aware of least squares in general but some works refer it as least square+gaussian method. ...
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2answers
190 views

Given an experimental FFT plot, how to find the best match from a set of generated FFT plots?

What I'm trying to do is, given some experimental data and it's (magnitude normalized to 1) FFT, match the FFT with one of say 1000 other (magnitude normalized to 1) FFT plots. Please note that the ...
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0answers
48 views

White Gaussian Noise: a reality or fantasy? [duplicate]

White noise has infinite variance, whereas Gaussian random variable must have some finite-variance to exist. How do two disjoint phenomena co-exist? Help will be highly appreciated.
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0answers
47 views

Iterative Auto and Cross Correleation Estimates

I'm looking for literature or other information that covers iteratively estimating the auto- and cross-correlation vectors and the auto-correlation matrix. Initially, I can assume the signal is ...
3
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2answers
178 views

How do you combine 2 least squares estimates?

Say you want to compute the least squares estimate of $w$ from a data-set: $$ \begin{bmatrix}d_1 \\d_2 \\\vdots\\d_N \end{bmatrix} =\begin{bmatrix} x_1 \\x_2 \\ \vdots \\x_N\end{bmatrix}w + ...
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1answer
171 views

Estimating Filtered Noise Variance

Assuming I have samples of a colored noise. I know the empirical Variance of those samples. I also know the bandwidth of the filter which colorized the noise (Only the bandwidth, not the actual ...
3
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1answer
75 views

Fitting fixed number of complex exponentials to complex signal

I have a complex data series, and I would like to fit a fixed number (in this case, two) of complex exponentials of the form $Ae^{jBn}$, where A, B are complex. Not interested in the phase (i.e. arg ...
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0answers
548 views

Prony method for frequency estimation in matlab

i am interested if where can i find matlab code for Prony method for frequency estimation.there is pdf article about prony ...
6
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2answers
1k views

have position, want to calculate velocity and acceleration

This is simple i thought, but my naive approach led to a very noisy result. I have this sample times and positions in a file named t_angle.txt: ...
4
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2answers
151 views

Is there a way to reduce the covariance matrix of several source signals to the dominant source signal?

The problem I have can be seen in the context of DoA estimation or blind source signal separation and similar fields, where several source signals are observed by several antennas (or by an antenna ...
5
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1answer
499 views

Measuring time delay of audio signals

Before anyone yells at me I fully realize that this question has been asked numerous times. I assure you that I've read through the existing questions and answers but I am still confused about part of ...
2
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0answers
108 views

Estimating Plane Pose Without Knowledge of Intrinsic Camera Parameters

Assume a camera has no skew, and has square pixels, that is, its camera-calibration matrix, $K$, looks like: $$ K = \left[\begin{matrix} \alpha&0&u_x\\0&\alpha&u_y\\0&0&1 ...
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0answers
100 views

How to model/estimate channel in discrete time with different sampling time?

I want to estimate a channel based on LTE 3GPP EVA with given power delay profile (set of average power and delay of channel taps). ...