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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9
votes
1answer
3k views

What is an AMDF?

The wikipedia page for Average Magnitude Difference Function/Formula (AMDF) appears to be empty. What is an AMDF? What are AMDF's properties? What are AMDF's strengths and weaknesses, as compared ...
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2answers
15k views

Given Position Measurements, How to Estimate 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: ...
3
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2answers
7k views

Hermitian symmetry in OFDM systems

I am trying to understand the usage of Hermitian symmetry in OFDM systems and have a couple of questions regarding this. What is the reason of using the Hermitian symmetry in OFDM? How can we arrange ...
4
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1answer
310 views

Direct Correlation (DC) Time Delay Estimation: Variance Keeps Decreasing for Increasing SNR?

I'm trying to reproduce the results from this paper "Discrete time techniques for Time Delay Estimation" doi:10.1109/78.193195, for both the correlation and Least Squares. I've generated a random (...
12
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7answers
4k 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 is ...
8
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2answers
658 views

Duration of unknown rectangular pulse with additive white Gaussian noise

Problem. There is a discrete signal $f[i]$ (example below). It is known, that $f[i]$ have a form of rectangular pulse with additive white Gaussian noise. $f[i] = s[i] + n[i]$, $s[i] = \alpha(\...
9
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1answer
6k 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 ...
3
votes
1answer
3k views

What would be the variance for complex number?

When $x$ is a zero mean random variable then $$\sum_{n=1}^N x_n x_n^T = N \sigma^2_x\,\text,$$ where the variance is $\sigma^2_x$. I'm considering Complex Normal Distributions where the real and ...
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4answers
474 views

Sequential Form of the Least Squares Estimator for Linear Least Squares Model

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 ...
4
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2answers
3k 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 ...
4
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1answer
4k views

Tracking a Sine Wave with Kalman Filter - How to Account for Offset (DC Signal)?

I am attempting to create a Kalman filter to track a sine wave (I am using a linear Kalman filter example assuming I already know the frequency of the sine wave) - the example I am using is derived on ...
4
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1answer
59 views

Amplitude Estimating Using a Windowed DFT

Let's say we want to estimate the amplitude A of a mono-frequent signal using a windowed DFT. The frequency of the signal is unknown, and the frequency resolution of the DFT is limited, thus it cannot ...
3
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1answer
198 views

How does this FLL work?

I'm trying to get my head around how band-edge frequency locked loops work. In particular, a diagram from this paper: Specifically, what does the Tanh() function and the conjugate product of the two ...
2
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1answer
57 views

Amplitude estimation of sinusoid in known spiky spectral noise

What is the "best" way to estimate amplitude of a known-frequency sinusoid in the presence of known spiky spectral noise (i.e. noise comprising a few spectral peaks at known frequencies)? By "best", ...
2
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1answer
1k 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 filter)...
2
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1answer
117 views

Quantifying goodness of amplitude estimation

Assume you have a single sinusoid in bandlimited Gaussian noise with unknown amplitude $A$, known frequency $f_0$, and known noise spectral density $S(f)$ in $\frac{\mathrm{units}^2}{\mathrm{Hz}}$: $$...
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3answers
2k views

FFT bin interpolation for low frequency with DC offset

I have a noisy signal in I/Q format with a peak frequency that constantly changes between 0.5Hz and 4Hz. The sample rate is 64Hz. I want an output showing the current peak frequency with a maximum lag ...
5
votes
1answer
840 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 \end{...
4
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1answer
416 views

Estimate the Discrete Fourier Series of a Signal with Missing Samples

Assuming we have a discrete signal $ { \left\{ x \left[ n \right] \right\}}_{n = 1}^{N} $. Which has a Discrete Fourier Series. Now, assume I'd like to estimate its Discrete Fourier Series ...
4
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1answer
3k views

What Is Uncorrelated Noise

In many applications such as estimation theory, when we need to estimate a parameter then we usually consider in presence of white gaussian noise of zero mean and some standard deviation. During ...
3
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1answer
207 views

Help in understanding from book expression of variance of an estimator : PRBS vs real valued input

The question is based on Book : Fundamentals of Statistical Signal Processing by Steven Kay, Chapter 4 : Eq(4.21). The expression for the variance of the estimated coefficients when the input is PRN ...
3
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3answers
275 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: ...
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2answers
86 views

Novice researcher aims to get published… How to pick a Journal?

I got my MS in EE way back in 1994 and have not presented at a conference, or published in a journal before, but I had and still have an intense interest in the applied math that I learned. I have ...
2
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2answers
868 views

Determining channel frequency response from measured data via IFFT

I've been working on a small system that transmits a linear chirp over the 35Hz-20kHz frequency range in a room and simultaneously records the transmitted signal with echoes (from the floor, walls, ...
2
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1answer
589 views

Estimating a low frequency signal corrupted by high frequency noise

This is a follow-up to this question. Suppose we take discrete samples of a low frequency signal currupted by high frequency noise. We know the signal has no frequencies higher than 20% of the ...
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1answer
170 views

Equalization knowing the Channel State Information

I am trying to simulate a simple communication system using channel estimation. I was able to estimate the channel response using the Least Squares channel estimator, and it is working properly (...
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1answer
966 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 ...
0
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1answer
74 views

Correlation between frequency and initial phase estimates using FFT

Why is there a high negative correlation between frequency estimation errors and initial phase estimation errors when measured using FFT? I have a simple code showing this negative correlation. is ...
0
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1answer
961 views

minimizing the mean squared error?

I'm reading this book "Applied Optimal Estimation" by A. Gelb. In the example 1.0-1, there are two measurements $z_{1}$ and $z_{2}$ with some noise for measuring $x$ as following $$ z_{1} = x + v_{1} ...
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0answers
103 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 ...