Questions tagged [estimation]

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

Filter by
Sorted by
Tagged with
9
votes
1answer
4k 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 ...
9
votes
2answers
818 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(\...
4
votes
2answers
2k views

How Is the Formula for the Wiener Deconvolution Derived?

Wikipedia - Wiener Deconvolution shows this formula: $$ \ G(f) = \frac{H^*(f)S(f)}{ |H(f)|^2 S(f) + N(f) } $$ Could someone explain the derivation? Specifically, where does the squaring ($|H(f)|^2$) ...
11
votes
2answers
18k 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: ...
4
votes
4answers
996 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 ...
3
votes
2answers
9k 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
votes
1answer
351 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 (...
5
votes
1answer
530 views

Estimate the Discrete Fourier Transform / 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 Transform / Series. Now, assume I'd like to estimate its Discrete Fourier ...
12
votes
7answers
5k 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 ...
1
vote
3answers
443 views

Understanding the Difference Between MAP Estimation and ML Estimation

There are a number of possible criteria to use in making decisions. Can someone elaborate on the difference between ML and MAP for a sequence of BPSK symbols impaired by Gaussian noise ?
9
votes
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 ...
4
votes
1answer
5k 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 ...
3
votes
2answers
101 views

Estimating a Signal Given a Noisy Measurement of the Signal and Its Derivative (Denoising)

I have a signal and its derivative simultaneously measured, both including additive noise. The measurement is completed before the analysis, so it can be looked ahead. Now I want to reconstruct a less ...
5
votes
2answers
974 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
votes
1answer
5k 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
votes
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
votes
3answers
438 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 ...
4
votes
1answer
107 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 ...
4
votes
4answers
167 views

Estimation of Amplitude, Frequency and Phase of Linear Combination of Harmonic Signal Beyond the Leakage Resolution of DFT

How can I find a rough ( as accurate as possible) Amplitude of each frequency when there is spectral leakage. Currently, I am dealing with a system that contains special leakage which seems ...
3
votes
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)...
3
votes
1answer
342 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
votes
1answer
124 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 $\frac{\mathrm{units}^2}{\mathrm{Hz}}$: $$...
2
votes
2answers
5k 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 ...
2
votes
1answer
74 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", ...
1
vote
1answer
95 views

KLT vs DCT basis restriction error

I want to implement 8x8 DCT and 8x8 KLT matrices to the 8-length vectors of 256x256 Lena image (e.g. each row of image there is 32 vectors 256/8 = 32 and for all rows 256x32 = 8192). I do the eigen ...
1
vote
2answers
283 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 \cos(\...
1
vote
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 ...
-1
votes
1answer
464 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: $y_2[n]=y_1[n]\exp(...
5
votes
0answers
164 views

Residual error when setting measurement matrix in compresssive sensing

I have an issue when implementing compressive sensing to recover sparse vector. Assume I have sparse vector $x$ of length, for example, $(256,1)$. $x = [x_1,x_2,.....x_{256}]$. This vector is ...
5
votes
1answer
116 views

On the Measurement Matrix Used for Compressing Sensing

Assume we have a matrix $x$ of size $(8,8)$ where each column is considered to be sparse with degree of sparsity equals to $4$. it means that every column can have $4$ zeros and $4$ non-zeros values ...
4
votes
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
votes
3answers
316 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: ...
3
votes
2answers
98 views

How to Pick a Journal for Publishing a Research Work?

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 ...
3
votes
1answer
690 views

Estimating a Low Frequency Signal Corrupted by High Frequency Noise

This is a follow up to the question How to Pick a Journal for Publishing a Research Work? question. Suppose we take discrete samples of a low frequency signal corrupted by high frequency noise. We ...
3
votes
1answer
231 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 ...
2
votes
0answers
96 views

Find the Autocorrelation and Cross Correlation of The Wiener Filter

I am dealing with a problem with Wiener filter. Assume the original function is $s(t)$ with observation $x(t) = s(t) + n(t)$. And $s(t)$ and $n(t)$ are WSS (wide sense stationary) and they are ...
2
votes
2answers
1k 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
votes
1answer
180 views

Kalman Filter | Difference Between Minimizing the Mean Square Error (MMSE) & Maximizing Likelihood Value in Bayesian Estimation

I am going through data assimilation slides on Multi Sensor Data Fusion by Hugh Durrant Whyte and it mentions: The Kalman Filter, and indeed any mean-squared-error estimator, computes an estimate ...
1
vote
1answer
95 views

How to calculate time domain SNR using known sequence

I am using the following formula to calculate SNR of a real world complex baseband signal sampled at 1x Nyquist. ...
1
vote
1answer
40 views

Channel estimation using bit reversed order of FFT matrix

Is it possible to use the bit-reverse order of FFT instead of FFT to estimate the channel? Based on my reading, I found that bit reversed order of FFT matrix can diagonalize the channel, but ...
1
vote
1answer
86 views

Estimation / Reconstruction of an Image from Its Missing Data 2D DFT

Given the 2D DFT of an image i.e. a NxM matrix of complex numbers, with some missing lines (or even partial lines), considering we have zeros in the missing positions. Any suggestions for an ...
1
vote
1answer
188 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 (...
1
vote
0answers
51 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 ...
0
votes
0answers
75 views

Estimating a Filter's Envelope

Are there any established techniques for estimating the envelope of a swept filter? I tried a first order piece-wise polynomial approximation using the SHGO global minimizer algorithm (Python code ...
0
votes
1answer
111 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
votes
1answer
1k 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
votes
1answer
1k 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} ...
0
votes
0answers
122 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 ...
-2
votes
1answer
225 views

Zero forcing vs matched filtering vs LMMSE

In what scenarios would you choose each of Zero forcing, LMMSE and matched filtering receivers: Possible points to consider are: Receiver SINR, High Interference levels, Low interference levels, ...