Questions tagged [power-spectral-density]

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

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359 views

Estimating the bandwidth of various signals

I am trying to estimate the bandwidth of different signals, with different modulations, as seen in a PSD graph. I've heard about a "$3\ \rm dB$ rule" in this context. I don't need extreme accuracy. ...
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772 views

Calculating SPL from pressure signal - Amplitude vs Power method

I have a pressure signal from a Fluent FFowcs-Williams Hawkings acoustics analysis. I converted this pressure signal into the frequency domain in order to get SPL values, using Matlab. I used the ...
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445 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 ...
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4k views

variance in the time domain versus variance in frequency domain

Hi All: I'm trying to better understand the connection between variance of a time series and the integral of the spectral density over all frequencies. Rather than going through all of the relations, ...
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97 views

Approximate the change in perceived gain from applying transfer function to audio signal

I have an audio signal that I am applying an analogue transfer function $H(s)$ to. I would like to approximate the change in gain ($\Delta \text{ Gain}$) as perceived by the listener for an arbitrary ...
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2answers
1k views

Definition of average power?

There are two kind of average power I encountered in random signal class and textbook: definition 1: average power =$$E[|x(t)|^2]=R_{xx}(0)=\int^\infty_{-\infty} S_{xx}(f)\,df$$ definition 2: average ...
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234 views

Autocorrelation and PSD

Let $X(t)$ and $Y(t)$ be two orthogonal processes with power spectral densities $$S_{xx}(f) = S_{yy}(f)=\begin{cases} 1-\lvert f\rvert, & \lvert f\rvert<1 \\[1ex] 0,& \text{otherwise} \end{...
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1answer
581 views

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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2answers
142 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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1answer
632 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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121 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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454 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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616 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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1answer
228 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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1answer
917 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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69 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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336 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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48 views

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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349 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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1answer
158 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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284 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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1answer
516 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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51 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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1answer
196 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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1answer
668 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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188 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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1answer
474 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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1answer
464 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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943 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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309 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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1answer
117 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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442 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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1answer
131 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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2answers
1k 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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1answer
10k 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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487 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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313 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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899 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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41 views

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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1answer
202 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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573 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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183 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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1answer
281 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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392 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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1answer
50 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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671 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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209 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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1answer
634 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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1answer
391 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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698 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 ...