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Questions tagged [power-spectral-density]

The Power Spectral Density (PSD) is the distribution of signal power over frequencies.

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Question on the definition of one-sided PSD in AWGN channel

I am currently simulating the following in a telecommunications exercise in Python: Consider a binary sequence $m[n]$ that is being modulated with QPSK (Gray-mapped) that is being transmitted via ...
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113 views

Filter away sinusoidal noise properly

I have a stereo music signal corrupted by strong sinusoidal noise that varies over time. Here is the spectrogram of Left channel I plotted with Matlab. As you can see there are 3 or 4 strong ...
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425 views

Power Spectral Density of Digital Modulations

I want to simulate the power spectral densities of different modulations in MATLAB (without Simulink). Unfortunately I have only very basic understanding of signal processing, hence I struggle with ...
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95 views

Spectral density interpolation: Applications?

Let $\Phi_1$ and $\Phi_2$ be two matrix-valued power spectral densities. I wonder whether the problem of interpolating $\Phi_1$ and $\Phi_2$ has been studied in the literature and/or applied in ...
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337 views

What is the difference between the PSD of a deterministic and stochastic signal?

I am learning about stochastic processes and I don't get one thing: What is the advantage of calculating the PSD of a signal using the Wiener-Khinchin theorem $\Phi(\omega) =\mathcal{F}\{R_{xx}\}$ ...
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365 views

Trying to implement MATLAB $\tt pwelch$ in Python

I'm implementing an existing MATLAB script in Python and noticing some differences in the behaviour of MATLAB's pwelch function compared to ...
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172 views

MATLAB's $\tt cpsd$ and $\tt pwelch$ - different results for cross spectral power density

I am wondering why the following code does not yield the same results for Sxy1 and Sxy2, where ...
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551 views

Power Spectral Density of Brownian Motion despite non-stationary

Note: I originally asked this on Physics Stack Exchange but haven't attracted any interest there so I'm asking here where it may be more relevant. A white noise process, $\xi(t)$ with delta ...
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43 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) ...
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230 views

How to Estimate a Normalized PSD Using the Burg’s Method in MATLAB?

I'll try to be most sintetic as I can. I'm using an EEG system and I want perform an frequency analisys of the brain waves. I found this interesting article which describe how is possible to discern ...
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69 views

Harmonics after sinusoidal subtraction

I have an electrophysiological recording with a large sinusoidal artefact (from AC stimulation). If I subtract a template of this sinusoid, the power spectrum shows peaks at 2F, 3F, 4F, etc. Why might ...
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Is power density invariant to Fourier Transform? Does it hold through derivation?

Assumptions We have a finite discrete measurement. Introduction I had some troubles determining a power spectral densities needed for Wiener deconvolution. Looking through the continuous equations ...
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251 views

“Noise Spectral Density” a.k.a “Power Spectral Density” in datasheets

In the case of statistics, there are two terms: "Variance" and "Standard Deviation" to - for in the latter case - have one to note the case in which the units are without squares. Am I correct to ...
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102 views

Why MATLAB only allows cpsd and mscohere between vectors with the same length?

I am studying the applications of finding coherence in the frequency spectrum between two signals for pattern recognition. I have a recording that is way longer than the sampled signal that I want to ...
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210 views

$|X(e^{jω})|^2$ - Power or Energy Density?

If $x(n)$ is an aperiodic signal and $X(e^{jω})$ its DTFT, then, what is $|X(e^{jω})|^2$? Power or Energy Spectral Density? My understanging of Fourier transforms so far tells me that its energy ...
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Bandwith of the Gaussian Random Process

$X(t)$ is a zero-mean WSS Gaussian random process. Its power spectral density is $$S_x(f)= (4 \times 10^{-5}) \text{tri}(\frac{f}{10^{5}})$$ Where $\text{tri}$ is the triangle function. What is the ...
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367 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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47 views

How do I improve the SNR of my signal given a noise profile (additive noise)?

From an iPhone microphone, I have a background recording of 5s(fs = 44.1 Khz), and immediately after that, I have a voice recording of a person saying 'aaa...' for 10s(fs = 44.1 Khz). How can I use ...
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119 views

Methods of scaling FFT power

I wanted to know what are the well-known methods of scaling the FFT power of a signal? I am referring to EEG signal but this should apply to all signals I guess. I need to plot the powerspectrum/PSD ...
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44 views

AR filter length

I need to use the AR filter for pre-whitening a time series data to do multi taper spectral analysis on them, . How can I choose the AR filter length?
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399 views

Blackman-Tukey periodogram?

I have been reading about the non-parametric estimation of the spectral density, and I'm particularly interested in the Blackman-Tukey method. If we take the rectangular window we will have the ...
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126 views

What is the power spectral density after filtering?

Consider a signal $x(t)$, which is input to a pulse shaping filter with transfer function $g_t(t)$: $$x(t) = \sum_n d_n \delta(t-nT_s)$$ with $n$ an index from negative to positive infinity and $...
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319 views

Why does increasing FFT length (narrowing bandwidth) not decrease Noise Power per bin?

I was under the impression that zero-mean white guassian noise had a constant Power Spectral Density which means that smaller bandwidths should decrease the power in that band. I'm getting surprising ...
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313 views

DOA estimation; Music (Multiple Signal Classification) algorithm

Why do we say that signal subspace and noise subspace are orthogonal in e.g. MUSIC algorithm? precisely, Suppose we have 2 sources (signals) which are WSS, in WGN in a uniform linear array. After ...
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658 views

Show That the Power Spectrum Density Matrix Is Positive Semi Definite (PSD) Matrix

Given a Wide Sense Stationary Multi Variate (Vector) Random Process $ \boldsymbol{x} \left[ n \right] $ it Auto Covariance Matrix Function is given by: $$ {R}_{x, x} \left[ m \right] = \mathbb{E} \...
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228 views

Power Spectral Density of a WSS Random Process with 2D Discrete Fourier Transform

I'm trying to understand how the random process (RP) signal in discrete time domain is related to its power spectral density (PSD) in frequency domain if the signal is wide sense stationary (WSS). If ...
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88 views

Energy Detection Algorithm Uncertainty

I'm currently working on a project to perform energy detection of an IEEE 802.15.4 using the block diagram illustrated below. However, I do have a little uncertainty about the algorithm. I'm wondering ...
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270 views

PSDs and Parseval's theorem

OK, I have been banging my head for quite a while trying to make sense of this simple equation: The $1/T$ is what is causing me all the grief. I assume that the square of the Fourier transform of ...
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102 views

Response of Linear System to Stochastic Process

Somehow I am getting the variance{u(n)} equal to '0' !! This is the case when I take the coefficient 'a' as real. As it is not mentioned in the question I need to find the solution to this question ...
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760 views

Pa^2/Hz to dB/Hz conversion

I have PSD data from an computational aeroacoustics analysis, which is in the units of Pa^2/Hz. I want to convert this to dB/hz; would it be correct if I use PSD[in dB/Hz] = 10log10(PSD[in Pa^2/Hz]) ...
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7k views

dB/hz to dB Conversion

I'm have a PSD graph of dB/hz vs. frequency in hz. I want to convert the dB/hz unit to dB, but I can't find any way of doing it. Help would be much appreciated!
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determine dominant natural frequency of signal

I have a problem using Matlab's pmusic function (the syntax is pmusic(x,p,nfft,fs,nwin)). How are the nwin and ...
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Power Spectrum of Linear Mixtures of Processes

Suppose we have $n$ WSS stochastic processes $x_i(t)$ , and we construct another process from them using a linear mixture, $y(t) = (\sum_{i=1}^n w_ix_i(t)) + b$. If these were deterministic, then the ...
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424 views

Clarification concerning power spectral density

Many books in signal processing, e.g. Papoulis [1], define power spectral density (PSD) as: $$S(\omega)=\sum_{k=-\infty}^{\infty}R_{xx}(k)e^{-j\omega k}$$ Which is the fourier transform of the ...
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247 views

Vibration Analysis by using FFT

I have 6 column vectors $(\mathbf A_x,\mathbf A_y, \mathbf A_z, \mathbf G_x, \mathbf G_y, \mathbf G_z)$ taken by accelerometer to analyze the vibration of a construction. Each column is a $64998\times ...
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509 views

Calculating power in frequency band using power spectral density

In a text I am using it states: The fourier transform $F(\omega)$ has both positive and negative frequencies and $F(\omega) = F^*(-\omega)$. The power spectral density $S(\omega)$ is similarly ...
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Interpretation of steady state sensor signal

I try to understand some measurement results of an accelerometer MEMS sensor. I used a mikrocontroller which is sampling an accelerometer's analog signal with the built in analog-digital-converter. ...
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153 views

Reason for decrease in the PSD gain with increase in the number of FFT points

what is the reason for that? The gain should increase ideally I guess. This is the code I tried. As I increase the length of F by zero padding,the gain of PSD reduces. ...
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480 views

Average Power Spectral Density of PAM signals

I am reading through the PAM transmission scheme and about the power spectral density of the signals. Given that the Average Power Spectral Density of PAM Signals is: $$ \Phi_{ss}(f)=\Phi_{aa}\left(e^...
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123 views

AWGN Build vs Randn noise do not match

I am generating noise in two different cases with the same SNR once using AWGN command which is a built in command and second time using randn function with the correct scaling however I am getting ...
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184 views

Compute Power Delay Profile (PDP) from Delay Spread

I have data pertaining to channel obtained from measurements. In order to make use of this data, I need to convert it into a form as follows: ...
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270 views

Why use cross-spectral density to calculate frequency response?

I am taking a class about system identification and currently learning about cross-spectral density. My textbook says that the frequency response, G, of a system can be determined as $$G=\frac{S_{uy}}...
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41 views

How to transform flat-field corrected spectra to those under Standard illuminant E (ideal equal energy illuminant)

My ultimate goal is to convert a flat-field corrected hyperspectral image of reflectance (360nm-780nm) to corresponding CIEXYZ image and thus device-independent color image. By flat-field correction, ...
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2answers
383 views

Cross Power Spectrum

Is it necessary that cross power spectrum (CPSD) should always be between power spectrum (PSD) of individual signals, irrespective of the method we compute it? The images are shown below.
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148 views

Is there an equivalent time-domain operation to the spectrum averaging in Welch's method?

In Welch's method a time-series is segmented and then the subsequent FFTs of the segments are averaged. Is there an equivalent time-domain operation? I guess doing the the Welch estimate and ...
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459 views

How do I modulate complex time domain signal to a carrier frequency?

I want to modulate a complex time domain signal to a carrier frequency 1880MHz but the sampling frequency is 30M which is smaller than Fs. I did upconversion using ...
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294 views

Determining power spectral density from a sample

To start, I have absolutely no background in electrical engineering, I am a computer scientist by trade. I'm currently working on a project where I am attempting to code a function that uses the ...
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525 views

How to evaluate Spectral Density of DC component vs. AC component during computing PSD?

When computing the PSD, how to manipulate the DC component?  PSD integral is the total signal power, does it include the power of DC component? In other words, if there is one signal with DC value ...
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238 views

Calculate the harmonics in the power supply of $50\textrm{ Hz}$ using FFT

I need to calculate the harmonics in the power supply of $50\textrm{ Hz}$. If suppose I need to calculate up to 20 harmonics. Then my sampling frequency by Nyquist criteria should be : $$f_s \ge 2 ...
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202 views

Do I need to bandpass filter the signal before applying the Zoom FFT algorithm?

Let's say I have an acoustic signal that I want to make a spectrogram of filled with broadband noise and tonals, sampled at oh, $44100\textrm{ kHz}$, and I want to zoom in on the band between $2600\...