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Questions tagged [spectrum-estimation]

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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)$\,575MHz \quad$...
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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 ...
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Random sampling Bartlett spectrum estimation vs Welch

I'm trying to estimate the spectrum of a noisy time series and considering two approaches and their relative correctness. Let's say the time series is 800s long. Option 1 is to do a Welch spectrum ...
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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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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 ...
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Difference between power spectrum of NR signal as seen in Vector Signal Analyser and MATLAB pwelch method

My setup is as follows: I have an R&S SMW signal generator which generates a 100 MHz 5G New Radio signal. The signal is passed through a channel emulator which has components like Digital-To-...
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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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I get confused about the Power Cepstrum [duplicate]

I get confused about the power cepstrum .How we can estimate it? does it from taking the IFFT of the absolute power spectrum density or from IFFT of the absolute ( (power spectrum))?
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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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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 ...
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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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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^{(...
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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) ...
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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 ...
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68 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 ...
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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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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 ...
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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 $M\to \infty, L \to \infty \hbox{ and } \frac{L}{M} \to 0$, ...
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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 ...
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1answer
274 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 ...
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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 ...
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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....
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322 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
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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,\...
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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)...
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1answer
119 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 ...
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2answers
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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 ...
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1answer
3k 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 $N = 1024$,...