Questions tagged [spectrum-estimation]

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1answer
76 views

Is there an efficient algorithm to precisely find the spectrum of a finite discrete signal consisting of incommensurable frequencies?

If we periodically sample a continuous band-limited signal at a sufficient sampling rate, we can estimate its spectrum by using Discrete Fourier transform (DFT). DFT of a finite discrete signal sample ...
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1answer
27 views

Noise Power Spectrum from Log Video Amplifier

I know that if I use a square law detector on band limited noise - let's assume it's rectangular - the noise power spectrum becomes the convolution of the input power spectrum. After lowpass-...
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2answers
65 views

Computable Time-Frequency Distribution without Cross-Terms

Context: I have a single receiver that is receiving multiple signals. Each signal has a few strong harmonics, but I don't know the fundamental frequency. I would like to display them on a spectrogram ...
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0answers
75 views

Wrong amplitude in the FFT for 10 seconds measured signal

I measured a signal with the Osziliscope that I generated with a signal generator. The signal is a pure sine wave with a frequency of 1 kHz and a peak amplitude of 2.5 V, I measured the signal for ...
3
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0answers
46 views

Running window design for irregular or nonuniform time series

I have to deal with multiple time series $X_n$ that are non-uniformly or irregularly sampled at increasing times $\Theta=\{t_k\}_{k\in \mathbb{Z}}$ ($ t_k<t_{k+1}$). In case this could help, this ...
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1answer
51 views

Number of antenna to perform MUSIC algorithm

When the MUSIC algorithm is used for direction of arrival (DOA) estimation it can identify up M-1 signals, where M is the number of array elements. MUSIC can also be used for spectral frequency ...
2
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0answers
196 views

Welch Method FFT Python - Scaling factor?

I've been implementing a Welch method FFT and I am trying to work out the correct scaling factor that should be applied to the output of the function so the PSD is accurate because at the moment it's ...
0
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1answer
64 views

Spectral peak location estimation using complex DFT

In this paper a simple method to estimate a spectral peak is proposed, by using quadratic interpolation between three samples of the DFT of the signal. Namely, the position of the peak relative to the ...
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2answers
39 views

Difference in signal Spectrum

[ Here are two figures from the same signal, the 2nd one(B) is after digital predistortion at transmitter end. How can you describe it? What are the improvements and advantages of this technique? Much ...
0
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1answer
90 views

Sub-Band Extraction Techniques for Complex (I/Q) Signal

There is an application which processes Complex I/Q signal of 100 MHz bandwidth and it is required to extract independent sub-bands from this bandwidth at different center frequencies and bandwidths. ...
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0answers
51 views

Interpreting scipy spectrum from audio signal

I have recorded some audio and would like to obtain a spectrum from it. As the audio is a real valued signal, I figure that I could perform a FFT with some window and obtain a spectrum for that period....
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1answer
202 views

Carrier frequency offset estimation for QPSK and asymmetrical spectrum

I am working on estimation of carrier frequency offset for QPSK data from a satellite. From my understanding, there are two main approaches: either remove data from the carrier (by taking the fourth ...
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2answers
276 views

Power Spectral Density units

I am trying to compare power spectral density values (obtained from dsp.SpectrumAnalyzer) with PSD values obtained from hardware which has a VSA. MATLAB's documentation says that " The power spectral ...
0
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1answer
41 views

what is the best technique to detect a given signal : energy detection, autocorrelation, and matched filter based sensing, CRC?

In order to detect the presence of a signal impaired by noise, what is the best technique (best metrics) one can use ? energy detection, autocorrelation, matched filter based sensing, CRC data ...
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0answers
2k views

Power spectral density vs. Fourier Transform

I am trying to understand the difference between the Power Spectral Density and the Fourier transform. Specifically, I am trying to understand why the power spectral density is useful and in what ...
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1answer
44 views

Finding the phase and frequency of a tone with Doppler. What is wrong in the code?

I am trying to find the phase and frequency of a single tone having a small Doppler (10 Hz). I have the following code. The integration time for the operation (the length of the time vector) is ...
2
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1answer
158 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
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1answer
134 views

Power Spectrum Estimation of three sinusoids in white noise

Let's assume we have a random process consisting of three sinusoids in white noise: $$x[n] = 3 \cdot \sin(ω_1 \cdot n + ϕ_1) + 5 \cdot \cos(ω_2 \cdot n + ϕ_2) + 2 \cdot \sin(ω_3 \cdot n + ϕ_3) + v[n]$$...
2
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2answers
180 views

How exactly does one apply a Hanning Window for a spectral estimate?

PREAMBLE I am a graduate student researching evolutionary ecology. My supervisor and I have been trying to learn how to simulate colored noise, discretely, by the $\frac{1}{f^\alpha}$ power law for $\...
0
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1answer
73 views

frequency/phase offset estimation in satellite DOA beamforming applications

In satellite QPSK demodulation, we first estimate and remove the phase offset introduced by the channel. Then, we demodulate the baseband information bits (I & Q channels). In satellite DOA ...
0
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1answer
351 views

What are some of the disadvantages of parametric PSD estimation methods?

Roughly speaking, the methods of power-spectra estimation can be divided in two categories : parametric and non-parametric. From what I understood, parametric methods assumes that the signal can be ...
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0answers
40 views

Complex Spectral Phase Evolution (CSPE) Performance depending on signal windowing?

I am look into CSPE. "Signal Analysis Using the Complex Spectral Phase Evolution (CSPE) Method" The method is simple. It compares the original signal's FFT and shifted signal FFT in phase domain so ...
0
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1answer
2k views

Spectrum Inversion Problem

For a signal with $f_c$ (Centre Frequency) $=1200MHz \,\,$ and $BW= 100MHz$ ,which of the following Sampling Frequency ($f_s$) will cause spectrum inversion: A)$\, 287.5MHz \quad$ B)$\,575MHz \quad$...
4
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1answer
273 views

Example of non-equivalence of the two PSD definitions

According to the book Introduction to Spectral Analysis by P. Stoica and R. Moses, the power spectral density (PSD) $P(\omega)$ can either be defined as the discrete-time Fourier transform (DTFT) of ...
1
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1answer
106 views

Explanation of Spectral Line Splitting when AR process is overmodeled

In the book Statistical Digital Signal Processing and Modeling by Monson Hayes, it is shown (in section 8.5.1) that when an AR(2) process described by the following difference equation $$x(n) = 0.9x(n-...
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1answer
2k views

Simplest way to generate AR(2) process on MATLAB

As part of a project I need to use autocorrelation method of estimating model paramters of an autoregressive process on MATLAB. Can anyone tell me the simplest way to generate an AR(2) process on ...
0
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1answer
238 views

Defining frequency axis for periodogram

I am trying to simulate example 8.2.2 from Hayes, Statistical Digital Signal Processing and Modelling, on MATLAB. Let $x(n)$ be a WSS process consisting of random phase sinusoid in unit variance. $$ ...
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1answer
43 views

An equality in DOA estimation

Suppose we use a uniform linear array for DOA estimation. Assuming neither of the signals and noise are correlated, and the noise power on each sensor is equal, it's well known that the covariance of ...
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2answers
1k views

Why averaging in Spectral magnitude domain not in complex domain to estimate spectrum of a process

Consider we need the magnitude spectrum of the signal. Signal is recorded in $N$ trials to a certain stimuli. Signal varies from each trial because of noise. So, to estimate the actual magnitude ...
2
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0answers
259 views

How to derivate in the frequency domain

I have two Time Domain functions, $f_1(t)$ and $f_2(t)$. I have both Fourier Transforms, $F_1(\omega)$ and $F_2(\omega)$. Functions $f_1$ and $f_2$ are not independent and, in fact, $f_1$ is also a ...
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0answers
130 views

Second moment properties (covariance) of lag window estimator

We know that the lag window estimator of the spectral density is defined as: $$S^{(lw)}(f)=\int_{-f_{(N)}}^{f_{(N)}}W_m(f-\phi)\hat{S}^{p}(\phi)d\phi=\sum\limits_{\tau=-(N-1)}^{\tau=N-1}w_{\tau,m}s^{(...
0
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1answer
118 views

Welch's overlapped method for amplitude by frequency estimation

pwelch is a useful matlab function for computing real/magnitudes for power using WOSA method, but I'd like to apply the same thinking in order to output complex pairs for amplitude (not power) ...
3
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1answer
133 views

Are there algorithms to invert a magnitude spectrum?

I have a speech signal and have calculated the magnitude spectrum for the signal. Is it possible to get a good estimate of the original signal from the magnitude spectrum, seeing that phase ...
1
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1answer
253 views

Periodogram Averaging

FOR CONSISTENT ESTIMATION OF PSD Let, $x_i(n)$ be a sequence of random variables for $i=1,2, ... , K$ uncorrelated realizations and $\widehat{P}_{(i)}^{per}(e^{jω})$ is their corresponding ...
2
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1answer
748 views

Estimating the PSD (Periodogram): How do you find the Expected Value

The periodogram $\widehat{P_x}(e^{jω})$ is an estimate of PSD $P_x(e^{jω})$ and for mean-square convergence - $\lim_{N \rightarrow \infty}E\left\{\widehat{P_x}(e^{jω})\right\}=P_x(e^{jω})$ My ...
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1answer
75 views

Anyone know what algorithm the Spice AC Noise Analysis uses?

Anyone know what algorithm the Spice AC Noise Analysis uses? http://vision.lakeheadu.ca/eng4136/spice/noise_analysis.html Is it some spectral modeling synthesis? I.e. that it estimates the main ...
1
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1answer
55 views

Proving Convergence of a limit related to Cross-Spectrum Estimation

Proving asymptotic covariance of Cross-Spectrum Estimation I came across this mathematical problem: Consider two constants $M,L$ such that $M\to \infty, L \to \infty \hbox{ and } \frac{L}{M} \to 0$, ...
5
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2answers
249 views

Detecting Pattern from Signal Data by Gaussian Mixture Model?

I'm a machine learning newbie. I have sensor data which is generated by several sensors. The data is a series of 'time's. (it is not labeled, in other words, I cannot know which sensor generates ...
0
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1answer
593 views

Identify the frequency spectrum of an audio file by using matlab [closed]

I need to identify the first few harmonics of a audio file by cancelling the noise of the specific signal. So I have partitioned the signal into 1024 Hz sample blocks and then took the FFT values of ...
4
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1answer
6k views

Calculate 1D Power Spectrum from 2D Images

Imagine satellite images, these are irregular sampled in X and Y direction and the shapes are of course are oddly off. We now want to estimate a 1D power spectrum from the whole image to estimate the ...
3
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1answer
715 views

Practical cross-spectrum estimation using Blackman-Tukey approach

I would like to estimate the cross-spectrum of two signals using the (lag-windowed) Blackman-Tukey approach but I'm having difficulties with proper practical implementation. As defined in equation 2.8....
2
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1answer
662 views

What is the computational complexity of Spectrum Estimation Algorthms and What they depend upon?

There are lots of spectrum estimation techniques, each with some pros and cons. Algorithms like: Music Welch's method Yule-Walker AR method Periodogram modified covariance method multitaper method (...
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2answers
117 views

The frequency spectrum of a static non-linearity driven by colored noise

Does there exist any straight-forward theory that can explain what happens to colored noise that passes through a static non-linearity? That is, if you have colored noise $$v = H u \, , \; u \sim N(0,\...
2
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1answer
581 views

A few questions about the output value of dsp.SpectrumAnalyzer

I am testing the output values of dsp.SpectrumAnalyzer for a sine wave mixed with white noise. The $\sigma^2$ of the white noise is 1e-4, so I use 0.01*randn(1024,1)...
2
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1answer
170 views

Estimation of occupied frequency bins (location of non-zero fourier coefficients)

I'm working in circuits fields and I am not very familiar with spectrum sensing techniques. Is there a method to identify location of non-zero Fourier coefficients of a signal (just locations, not ...
3
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2answers
4k views

An explanation of parts of the MUSIC Algorithm for someone without a background in signal processing?

I've been looking at every tutorial and paper I can find, but I keep losing the intuition behind what's going on when they get into the matrix operations. There is a step in which the signal vector ...
4
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1answer
6k views

Understanding the Windowing Method in PSD Calculation

I have some issues understanding the use of a window (it doesn't matter which one) to calculate the Power Spectral Density of a signal. For example say I want to use the hann window, with $N = 1024$,...