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

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Steps for proofing Tweedie's Formula

Assuming that $f_{X|D}(x|d)=e^{\alpha d x - \psi(d)}f_0(x)$ for some constant $\alpha$ such that it is a valid pdf for every value of $d$, i want to establish that: $$\mathbb{E}[D|X=x]=\frac{1}{\...
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How multiple HT-LTF in 802.11n (MIMO-OFDM) standard is used to estimate the CSI

In the 802.11n preamble, the number of HT-LTF (High Throughput- Long Training Field) is equal to the number of spatial streams. Therefore, for a 2 by 2 MIMO system, there will be 2 HT-LTFs. These HT-...
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Calculations resettings and Overlapping estimation technique [closed]

Please, i need a helpful example to examine the issue of how and when to update, or re-initialize, the computations with SIMULINK or Matlab. For exemple, a first identifier is reinitialized when t1= 0 ...
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33 views

Get variance of white noise from Accelerometer data

i have a static accelerometer data. So i assume that all signal are from noise. So i model it like this, $$X(k) = X(k-1) + U(k)$$ But I plot the $U(k)$ autocorrelation function seems it is not white ...
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1answer
25 views

Question on Levinson's proposed discrete form of Wiener filter

The whole foundation of Levinson's discrete version of Wiener filter is based on the assumption of stationarity of a time series, and aims to predict a value based on the past observed values. Now, if ...
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19 views

how to robustly estimate low and up envelope of signal with trend, few level constant steps and noise

I am looking for robust estimation method of low and up envelope of the signal consisting from smooth trend component, constant steps between few fixed levels and additive noise (+ outliers of course)....
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1answer
61 views

YIN pitch estimation algoritm-simplified explanation [closed]

can someone please explain the steps of YIN pitch detection algorithm in a simple way "especially the last 3 steps". here is the research paper of YIN algorithm http://audition.ens.fr/adc/pdf/...
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3answers
69 views

Question on Wiener Filtering

I have read that a Wiener filter is a filter used to produce an estimate of a desired or target random process by linear time-invariant (LTI) filtering of an observed noisy process. Now, my doubt ...
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2answers
141 views

Extended Kalman Filter (EKF) for Non Linear (Coordinate Conversion - Polar to Cartesian) Measurements and Linear Predictions

I'm new to Kalman filtering and state estimation and I'd like some guidance on EKFs. Currently, I'm trying to use a linear prediction model coupled with nonlinear measurements to estimate the state ...
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26 views

Estimating a discrete summer with constrained input bandwidth

I have a discrete-time system which can be described as: $$ Y_m = \sum_{r=-N_g}^{R-1+N_g} c_r x[R(m-1) + r] $$ The unknowns are $c_k$ but I know that they have the following approximate behavior: $$...
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1answer
48 views

Estimating variance in arbitrary, periodic signal

I have a periodic signal $x[m], m \in [0;M-N+1]$ made of modulated templates $s[n],~ n \in [0;N-1],~ N \ll M = NK$ of finite energy and support (i.e. zero outside of its defined interval, which does ...
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1answer
79 views

Estimation of Two Closely Spaced Frequencies?

What is the best frequency estimation algorithm for two closely spaced frequencies in term of the minimum frequency spacing achieved?
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1answer
26 views

How to Realize the Sigma Point Sampling Function in Unscented Kalman Filter?

Recently I'm learning the unscented kalman filter (UKF). When designing the unscented kalman filter, it involves a non-linear function to generate the sigma points and then use the system non-linear ...
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1answer
37 views

Why Isn't the ML Estimator (MLE) in MIMO Spatial Multiplexing Obtained by the Least Squares Solution?

In the simplest scenario of MIMO spatial multiplexing: $$\mathbf{y} = H\mathbf{s} + \mathbf{n}$$ where: $\mathbf{s}=[s_0,s_1,...s_{M-1}] \\\mathbf{y}=[y_0,y_1,...y_{N-1}]$ $\mathbf{n}=[n_0,n_1,......
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1answer
44 views

Phase and Amplitude estimation

Context: I have used FFT many times, but for real, non-periodic signals I consider it a poor estimator. For most of my applications I am only interested on the power spectrum, so I use the Welch's ...
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29 views

Estimation of the frequency response data using Matlab command invfreqz?

I would like to determine frequency response and then impulse response of the displacement equation (eq. 1 please see screen shot of the task below). In this example we study a response of the finite ...
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1answer
73 views

Sample Dataset for Kalman Filter

I'm a newbie to Kalman filter. I have found the code online but I was wondering if there is any sample dataset available online to get hands-on with it (for example: CIFAR-10 for classification etc. )....
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1answer
65 views

how can I generate SIMO underwater acoustic channel

I'm working in underwater acoustic channel, then I need to generate SIMO channel to use it for simulation in MATLAB, how can I generate SIMO channel? thank you
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16 views

Estimating a distribution of feature of sound based on a factor

I am currently working on creating a model of sound of inside of a car based on speed. To be specific, making a Gaussian distribution of MFCC(13 dim) for each speed, i.e. car running at 30 kmph, ...
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71 views

Estimating frequency when there's little isolation between signal and noise frequencies

Say I have a signal which is guaranteed to have a frequency between 110-120 Hz but is corrupted by interference signals that're very close to this frequency range. For example, let the interference ...
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23 views

Estimating a Function from its Covariance Function

I am trying to solve this question: Suppose that $n(t)$, $−∞ < t < ∞$ is a stationary Gaussian random process with covariance function $E\{n(t)n(t-\tau)\} = \delta(\tau) + {5 \over 4}e^{-\left|\...
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EKF smoothing for prediction at t=0 when no there is no measurement

I have a simple first-order reaction batch system for which I have some discrete measurements ($0<t_{k}\le t_{endbatchsample}$). I have an initial guess for $x_0$ and $P_0$ and from here I ...
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2answers
94 views

Harmonics to Noise Ratio Estimation

I'm willing to estimate the Harmonics to Noise Ratio (HNR) of a speech signal x[k] and using autocorrelation method. Theoretically, HNR is given as, $\ HNR = \frac{R_{xx}[T_0] }{R_{xx}[0]-R_{xx}[...
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1answer
64 views

How to prevent Octave Jumping in ACF of Speech Signal?

I'm working with speech signals and my aim is to estimate the fundamental frequency $\ F_0$ of this signal often called as "pitch". The main idea is taking small blocks of the speech signal such ...
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2answers
62 views

Finding the Best Gaussian Smoothing Kernel to Minimize the Discrepancy Between Two Images

Suppose we have two grayscale images, $A$ and $B$. $A$ and $B$ very strongly resemble each other, such that the mean of the absolute difference $\lvert A - B\rvert$ is fairly small. Suppose further ...
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33 views

What is the difference between Statistical Signal Processing and Estimation and Detection?

Looking at the syllabus of Statistical Signal Processing in different university I see a lot of correlation with that of Estimation and Detection? In some universities, these are seen the same. For ...
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3answers
94 views

Least Squares with blocks/updates

I have a continuous-time system that I want to fit via least squares. I just send $N$ digital samples $x[n]$ through the system and receive (via analog signal chain, ADC etc) $N$ digital samples $y[n]$...
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16 views

mean shift with weights

Lets say I have a set of weighted 3D data points and I want to find all modes using mean shift: $$x_{t+1} = m(x_t)=\frac{\sum_i x_i G(x_t-x_i)}{\sum_i G(x_t-x_i)}$$ ($G$ is simply a Gaussian kernel) ...
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2answers
32 views

Estimation of step amplitude using the CUSUM algorithm

I used the CUSUM algorithm to detect steps in data. Basically the data looks like this, the data has a constant amplitude and then there is a rapid variation or a step. For example, the signal has a ...
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31 views

Acoustic Echo Cancellation with system identification

I just red about system identification and the book mentions the example of acoustic echo cancellation as an example for practical application (nothing more than that) and I'm trying to figure out how ...
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18 views

How to fit a constant acceleration model given a set of x,y,t point with nonuniform timestamp?

I have a bunch a point $(x,y,t)$ in 2D $(x,y)$ with their sampled timestamp t. assuming acceleration do not change. How can I estimate a model $(x^*, y^*, vx^*, vy^*, ax^*, ay^*)$ where $(x^*,y^*)$ ...
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38 views

Best equalizer for a perfect CSI

Assuming a MIMO system and a perfect CSI (the channel matrix is known), what can be the best equalizer? ZF or others?
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1answer
60 views

Correlated signals separation with reference

I have a signal S, which needs to be split into two components Sx and Sy. And I have a signal X, which is a reference signal corresponding to Sx. I need to perform this split of S and check that ...
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77 views

Parseval's Theorm and Effective Bandwidth

This question says that RMS bandwidth (effective bandwidth) is defined based on the carrier frequency of a signal. This makes intuitive sense to me that the carrier frequency shouldn't determine the ...
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1answer
135 views

How channel state information is calculated from Sounding Packet

What I understand is for Explicit Transmit Beamforming scenario, the Transmitter sends an NDP packet(aka HT Sounding) which consist of OFDM training symbols in packet preamble (HT-LTF) which are ...
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Sensor fusion under unknown correlations: can covariance intersection account for delays?

Of late, there has been some interest in cooperative estimation algorithms in robotics, where the information sources are usually sensors such as cameras. When multiple robots observe surrounding ...
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2-D parameter vector: Cramer Rao lower bound

Given a 2-D parameter vector, $\mathbf{X} = [x_1, x_2]$, let the corresponding $2\times2$ Fisher Information Matrix be $\mathbf{F}$. The Cramer-Rao Lower Bound (CRLB) is the inverse of the FIM. I ...
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1answer
34 views

Deriving the CRLB for an active system with non-square shaped bandwidth

I'm attempting to calculate the CRLB for a bandlimited time-delay system which has a triangular shaped signal spectrum, instead of the usual square one. Currently I'm working on an active system. ...
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2answers
73 views

Estimate sampling frequency given an array of values

Given an array x of size 2000, is there any way to calculate (or estimate) the sampling frequency using Matlab? The values are the only information I have about the signal. I know the signal has been ...
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71 views

Why does noise prevent a (kalman) filter from diverging?

I'm using a filter (not exactly kalman) of the following form to estimate angles by fusing gyroscope with accelerometer and gyro with magnetometer: $(1)\quad \hat{\theta}_k = \hat{\theta}^-_{g,k} + \...
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1answer
88 views

Received signal error vs. BER

It is my understanding that the least squares algorithm (e.g., in equalization) minimizes the received signal error. However, minimizing the received signal error does not necessarily equate to ...
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2answers
30 views

Is it possible to estimate variance of noise for a step answer signal?

I know there is not possible to find the true noise of a measured signal. The only way to "find" the noise is to estimate the noise. Noise has the mean 0, but the variance varies. So assume that we ...
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1answer
87 views

Estimation of filter response

If I have samples of input say x(1:500) and it passes through FIR filter with 9 taps and some unknown coefficients. The output y(1:508) is also known. The aim is to estimate the filter response in ...
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1answer
232 views

Cramer Rao Lower Bound for Cross Correlation (Time Shift Estimation)

UPDATE 2 Okay, I think I understand now why the defined CRLB is not applying to my use case. In my use case, we have very high SNR, and the the first signal $x_1$ is always the same. So the classical ...
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75 views

Finding the parameters and endpoints of a sinusoid

Suppose I have some signal $$ s(t) = n(t) + \left\{\begin{aligned} &0 &&: t < t_0\\ &A e^{i (2 \pi f t + \theta_0)} &&: t_0 \le t \le t_1\\ &0 &&: t > t_1 \...
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149 views

Channel Estimation Interpolation in OFDM Signal

I am currently working on capturing the signal from the PXI Generator by using LTE Signal with 2x1 MISO, 64 QAM, cell-ID = 0. I am trying to decode the signal after capture it until I got the CRC Pass ...
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3answers
132 views

error variance of frequency and phase estimation using DFT

What is the error variance of estimating the (frequency) and (initial phase) of a sinusoid using DFT. please provide references if possible.
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2answers
65 views

Why use parametric based estimation methods - confusion regarding terms

Using the probability density function (pdf) we can estimate an unknown parameter using methods such as Maximum Likelihood estimation. If the pdf is not available, then Least Squares can be used. ...
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2answers
39 views

Is there any information we can extract from the residual

The residual in estimation is the difference between the measurement and the previous estimate. My question is when I plot this quantity, what is ,if any, information I can extract or infer from this ...
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2answers
88 views

MMSE - How to minimize a complex error with respect to a set of real parameters

Suppose there's a complex signal $X(k)$ (where $k \in \{0, 1, 2,...,N - 1\}$) corrupted by additive complex noise. Its estimate $\hat{X}(k)$ is a linear combination of a set of real parameters $A_r$ ($...