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Questions tagged [estimation]

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

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Recovering signal statistics from non-uniform sampled signal

I'm interested in estimating the mean and standard deviation of a signal that was sampled non-uniformly. Assuming I have an estimate of the signal bandwidth, what algorithms would provide estimates of ...
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34 views

Equivalence of ML and FFT peak finding for Single-Tone estimation

My understanding is Maximum Likelihood and FFT peak finding for a single tone produce the same results assuming the ML is restricted to the same frequencies as the FFT. I was wondering if there was ...
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2answers
99 views

Solving a Linear Mean-Square Estimation the easy way

I have an exercise which is quite trivial. However I got stuck and I'm not sure if this the end-result. I assume there has to be a way to get this result much quicker. Given are two randomly ...
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34 views

Transfer function estimation of a noisy system

Overall description I am trying to estimate a filtering system’s transfer function, given its input and output. This system takes $x$ as input . This signal is low pass filtered and added to a WGN by ...
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1answer
18 views

Square of the ratio of errors in power quantities in decibels

A ratio of amplitude quantities $A$ and $B$ can be expressed in decibels as: $$20 \log_{10}\left(\frac{A}{B}\right) \text{ dB}.$$ A ratio of power quantities $A^2$ and $B^2$ can be expressed in ...
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245 views

Estimators for improved spectral subtraction of noise

Real zero-mean Gaussian white noise, independent of a clean signal $x$ and of known variance is added to $x$ producing a noisy signal $y.$ Discrete Fourier transform (DFT) $Y$ of the noisy signal is ...
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1answer
48 views

number of samples and Amplitude accuracy,what's the solution to this problem

I'm colleceting data samples from a device (temporal signal) in order to analyze it with FFT function in MATLAB R2015b,first i get N=4063 data points with (delta_t=0.000015s) so my frequency ...
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1answer
31 views

Periodogram and Welch periodogram comparison

I'm trying to compute the PSD using the periodogram method. I have a signal that is periodical at 5kHz. The frequency resolution sought for is 1.221Hz. It's a PRBS signal that has its energy drop to ...
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4answers
62 views

Spectrum estimation

When calculating the spectrum estimation of a signal $x(t)$ with random noise, why do we use ($E$ for expectation) $$E[|X(\omega)|^2]$$ but not $$E[|X(\omega)|] $$ If it is because the random ...
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18 views

What is the method for calculating a “running” linear fit?

I'm currently working on a project in which I need to find the tilt of a surface. Let's assume I'm only concerned with a single dimension tilt (i.e. slope) to begin. I currently have the ability to ...
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30 views

Resolution of MUSIC algorithm

MUSIC algorithm has been known to provide super-resolution imaging capabilities, and it is implemented in target recognition radar system, however, I couldn't find a definite expression for its ...
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36 views

Advances in Blind SNR estimation beyond $M_2M_4$

In Pauluzzi and Beaulieu, various SNR estimation methods are compared. Among the blind methods considered, the $M_2M_4$ estimator seemed to be unambiguously the best. However, it has been shown that ...
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2answers
39 views

Summing over constants [closed]

I'm following some notes and I came across an example which said that for this x_n with a proposed estimator of the mean, that it is an unbiased estimator for the DC level. I'm trying to do it out ...
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1answer
146 views

Kalman Filter : How measurement noise covariance matrix and process noise helps in working of kalman filter , explain intuitively please?

How noise covariance matrix and process covariance matrix helps in improving the state estimate, can some one explain intuitively without mathematics ?
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1answer
45 views

Symbol Timing recovery for modulation producing ISI

I am interested in understanding why the common timing recovery algorithms function for modulation schemes which produce ISI. For example, suppose you are receiving at the output of a matched filter ...
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1answer
41 views

Estimation Theory - Basic Question

I'm just starting estimation theory for my DSP course and I'm a bit confused about the classic example given everywhere which aims to show that two unbiased estimators can have different variances. I'...
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1answer
58 views

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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1answer
31 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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24 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
260 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
122 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
536 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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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
73 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
97 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
62 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
50 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
69 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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0answers
59 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
179 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
113 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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17 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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81 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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24 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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27 views

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
161 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
98 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
101 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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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
97 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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17 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
52 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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36 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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19 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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46 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
63 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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101 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
365 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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64 views

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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56 views

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 ...