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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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Power spectrum density and frequency

if i have some random signals (sampling rate = 10Hz, 0.1s per data) Using python library i transformed it to power spectral density power spectral density forms = f, psd (using mlab.psd) I'm really ...
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Is there a criterion that says at what point you can distinguish 2 partially overlapping Lorentzian peaks?

If you have 2 Lorentzian peaks that partially overlap and you have some frequency resolution df (your points in frequency space are separated by df) and both Lorentzian peaks have FWHM $\Gamma$ is ...
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63 views

How to choose the right segment length for a given signal?

Im working on plotting the power spectral density of a random time series measured. I know the target spectrum.The idea is check the measurement vis-a-vis the target spectrum. However, I get slightly ...
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72 views

Simple tests for normalisation of power spectra

I am trying to compute power spectra of multidimensional (2d, 3d) arrays. In particular, I want to compute radially averaged power spectra $P(k) = P(|\mathbf{k}|)$ using FFTW, where $P(\mathbf{k}) = |\...
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Correctly scaling Power Spectrum and Correlation Function of Galaxies from Mock Catalogues

I'm currently writing a code to compute the two-point correlation function of a set of galaxies. As I work with a loooot of galaxies, it was suggested to me not to do it in real space, but to compute ...
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189 views

How to interpret Discrete Wavelet Transform Coefficients?

I want to extract features from DWT coefficients like Power Spectral Density, Max frequency, Min frequency etc. After taking DWT, we get coefficients D1, D2, A2 etc. But my question is, Are D1, D2, ...
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134 views

Understanding PSD: Why Does Power at High Frequencies Affect Low Frequencies?

I'm trying to wrap my head around power spectral density on a conceptual level, but I am having some difficulty. Suppose I have a communication system where I am receiving and sampling white Gaussian ...
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57 views

non-negative FFT spectrum, subtlety

definations $x(t)$ is a function of time. Physically, it can be voltage, displacement, magnetization and so on. It can be real, complex, vectors or more fancy numbers. $C(t)$ is the auto correlation ...
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How to Update Power Spectral Density Function Estimation of a Dataset in Moving Average Sense

Assume we have a dataset containing 1000 floating-point numbers. Its power spectral density function (PSD) can be estimated using various methods, e.g. Welch's method. Unlike above, please consider a ...
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130 views

frequency spectrum of a sampled signal, PSD and power discussion

Before I go into my question, I first want to review the basics of sampling a signal and at the same time I build the basics of my questions so that they make more sense. I know I have asked couple of ...
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404 views

How Does the RMS of White Noise Change with Sampling Frequency?

There is an analog system which includes the continuous-time linear equalizer (CTLE). With some .noise analysis the power-spectral density (PSD) of the noise in that system is provided. So let's not ...
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Understanding Jakes Doppler Spread [duplicate]

I'm trying to understand why the doppler spread leads to a U-shaped spectrum shown below. From what I learn, Doppler spread is caused by the aggregate of Doppler effect on all multipath components of ...
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How to generate the amplitude of a signal with a certain power spectral density?

I am a newbie. If I posted a question someone else already asked, please forgive me. Thank you! Now, I have a power spectral density named $P(f)$ as a function of $f$. Let's say this function is ...
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41 views

Detection over a few number of bins

In Periodogram Can I take only few frequency bins (nFFT bins) , sum and compare it with threshold in stead of whole bins . if yes why? with knowledge I pass the data through the window before fft ...
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42 views

Isolating frequency-specific oscillation from transient

I am performing time-frequency analysis on electrophysiological data with complex morlet wavelets. Each decomposition in the attached figure shows total power following the onset of a stimulus (top ...
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40 views

psd of an ac voltage signal

In an lab class experiment who's subject of interest was Johnson's noise I measured the ac voltage of a battery. Now I wish to find the psd of the measurement and show that it is constant. 1.Is such ...
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122 views

Should scipy.signal.coherence be 1 for single input and output signals?

I am trying to calculate the coherence between input and output signals. I thought I could work with a single input and a single output time series and calculate the coherence $\gamma^2$ between them. ...
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Computing Power spectral Density

Acronyms: Power spectral density, PSD Autocorrelation, AC Hey so I'm in my first ever DSP class and thoroughly enjoy the material, but absolutely suffer in the HW. I have this question ...
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Obtaining $x[n]$ from its periodogram [duplicate]

I'm trying to work out the following problem, but I'm missing something I hope I can get your support. I'm using Matlab, and currently trying the following simple task: We have sampled discrete ...
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225 views

Condition for modelling noise as white noise

I am reading a book on Communication System by Simon Haykin. In the topic of white noise there is a paragraph "We may state that as long as the bandwidth of noise process at input of a system is ...
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196 views

Amplitude of signal and PSD peak height

So, suppose you have a superposition of cosines of the same magnitude: $\sum_{i}\cos[\omega_i t]$ When you take the Fourier transform, theoretically you'd expect to find $\delta$-like peaks of the ...
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35 views

How to calculate Normalised PSD?

I have calculated psd of a signal using periodogram. I followed this guide. ...
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1answer
62 views

Octaves vs Decades Fractions

At this USGS very good site about rms noise in sensors, a phrase regarding third octave bands (the original topic) appeared. The figure displays the minimum vertical seismic noise directly as rms ...
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Synthesizing a band limited noise from time samples of white noise and the relation to sampling frequency

I wan't to synthesize a colored noise of Bandwidth of 40Mhz around some carrier (say 2.5Ghz) from samples of WGN. So, I sample in matlab using randn(1,10000) samples of normal distribution. Now, ...
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PSD using short time fourier transform

I am trying to calculate power spectral density over frequency bands (eg. alpha beta, gamma etc.). To do so I have been asked to apply 512 point short-time Fourier transform with 1s long window and ...
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389 views

Calculating average noise power

Our professor assigned us homework in one of my grad courses: Assume a white noise source with a single-sided power spectral density of 100pW/Hz is put into a bandpass filter having an absolute ...
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Random Vibration Parameters & Values

I have been searching similar questions and am not having much luck. I currently have a program setup for random vibration already and a request for random vibration to different settings.(chart and ...
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158 views

Applications of Power Spectral Density [closed]

I have a class covering Power Spectral Density but I have no idea why it matters. Could someone provide some examples of its use? Thanks
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270 views

Quantify the difference between two audio spectrograms

I have two speech signals of the same length. They contain the exact same speech content but are recorded from two different microphones. I want to compare the differences between them. 1) Assuming ...
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542 views

Comparing Welch and FFT power spectrum density

Based on previous answers from the forum, I implemented a function to compute the Power Spectrum of a 1D time series. ...
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15 views

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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Why look at power spectral density for stochastic processes?

I have been told that for deterministic signals, it makes sense to look at their respective Fourier transforms/spectra. For stochastic processes on the other hand, I am supposed to work with power ...
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111 views

Phase information from product of complex conjugate transfer functions

For an input signal $x(t)$ and output signal $y(t)$ through an LTI system I $H(t)$ I have found and interesting property that concerns signals' power spectral densities: $${\lvert H(\omega)\rvert}^2 =...
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Estimating number of sinusoid from spectral estimation

Suppose I am given a data X0 that have 50 realizations of a sum of an unknown number of sinusoids in additive white Gaussian noise. I plotted the Spectral estimate as attached. How do I estimate the ...
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What is the relationship between image spatial domain and FFT powerspectrum?

I am trying to perform contrast-transfer-function for pictures which were recorded in defocus. To do so, I have to calculate the contrast-transfer function from the Thon rings and fit the function to ...
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3answers
368 views

Generating a timeseries with an arbitrary power spectrum

I need to generate random numbers with a given PSD. To do so, I found this recipe. In case it's behind a paywall, here's now it works: Given your power spectrum $P_k$ with $0\leq k<N$ points ...
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506 views

Calculating and plotting Wavelet Power Spectral Density

I would like to calculate the power spectrum of the wavelet coefficients for an observed signal and compare it with the Fourier power spectrum of the same signal. I want to do this to show how the ...
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1answer
1k views

Converting PSD to dB scale

I am taking the PSD of the output of an RTL-SDR with Welch's method. The output is an array like: [1.34225796e-07 1.37964799e-07 1.24558405e-07, ....]. I'd like to convert this array to dB, so ...
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1answer
122 views

Wiener Filter Additive Noise Uncorrelated

I have been trying to understand for a while now why a non-causal Wiener filter that has a frequency response of the type H(jω)=S_yx(ω)/S_xx(ω) where ...
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242 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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Cross-pol discrimination measurement

I have 2 antenna feeds that have orthogonal polarizations. There is a signal in one feed with about 10 dB SNR. How do I measure the cross-pol discrimination of the signal? Is the cross power spectrum ...
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393 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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234 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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341 views

How to compute Power Spectral Density?

If I wanted to do a power spectral density (PSD) of my FFT results, would the following be a well-accepted means to do so? (SOURCE: Based on the Matlab code shown here) Assuming ...
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54 views

How to plot PSD (dB) vs FT_b? What am I doing wrong in these plots?

I am trying to plot PSD (dB) for CPM (continuous phase modulation) signals. I want to produce something like this. I generated a CPM signal and tried to plot PSD for L = 1 but I get this. My code is ...
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110 views

What would you call a power spectrum which has been normalized to another

Let's say I have the FFT derived power spectrum of a signal measured at time 1 ($P_{xx,1}$) and of the same signal measured at time 2 ($P_{xx,2}$). If I want to demonstrate how the frequency content ...
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1answer
2k 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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2answers
76 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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742 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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172 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{...