Questions tagged [power-spectral-density]

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

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psd in matlab, problem with the coefficient $\frac{1}{2\pi}$

Using the fft to mimic the Fourier Transform I have this question. The definition that I use for the PSD $S(f)$ is: $S(f)=\frac{1}{2\pi}\int_{\infty}^{\infty}exp(-i\tau2\pi f)r(\tau)d\tau$ where r(t)...
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How can we prove that Spectral density of In-Phase component and Quad-Phase component of a sample function of narrow-band noise have same definition?

Suppose we have a narrow-band noise $N(t)$. We analyse this to In-Phase and Quad phase components by the equation: $$N(t) = N_I(t) \cos(2\pi f_c t) - N_Q(t) \sin(2\pi f_c t)$$ Now a book (by Simon ...
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Question regarding AC power of ergodic process

We know Ergodic process is the subset of Weakly stationary process which permits us to substitute time average for ensemble Average My teacher said If $X(t)$ is Ergodic random process then following ...
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1answer
50 views

limit of the integral in the anti-transform

if I have an autocorrelation on a limited domain r($\tau$)=$\lim_{T \to \infty}\frac{1}{T} \int_{0}^{T} u(t)u(t+\tau)dt$ The power spectral density, obviously will have an infinitive domain: S(f)=...
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how to cut off frequencies above 10 Hz with Welch method

This is the first time I have worked with any code so I am rather unfamiliar with all the lingo and processes involved. I am trying to convert a signal to the frequency domain and want to find the ...
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1answer
32 views

demonstration using parseval

I have to do a demonstration. If we do the Parseval identity of the signals $x(t)$, $y(t)$ and $z(t)$ that go from $0$ to $T$ and that are real, we have: $\int_{0}^{T} x(t)^2dt=\int_{-\infty}^{\...
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22 views

Power Spectral Density vs Energy Spectral Density for Discrete Signal

I'm sure this is a silly question but reading a bit about the PSD vs ESD for continuous signals, I'm a bit confused how that applies to discrete signals. Usually people seem to be using the PSD when ...
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what is equal to the FT of the Autocorrelation function

I am trying to make my own demonstration in order to find what is equal to the FT of the Autocorrelation function. The autocorrelation function in some book about turbulence is defined as: r($\tau$)=...
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39 views

Filter before or after multiplication of two signals?

I have two signals and want to multiply them, e.g. voltage and current are multiplied to get power. The result (e.g. power) shall be a filtered result, e.g. to see the average. Is it better to filter ...
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1answer
29 views

power spectrum -PSD

I was wandering if someone can help me to understand if there is difference between power spectrum and power spectral density. Looking here I found that there are differences https://www.quora.com/...
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1answer
23 views

Power contained in a random process $X(t)$

How do we calculate the AC and DC power of random process $X(t)$ , provided we have $R_x (\tau)$, and $S_x(f)$ ?
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the demonstration that states that the FT of the ACF function is the square of the DTFT of the signal

I am following the book The Intuitive Guide to Fourier Analysis & Spectral Estimation with MATLAB. I am trying to selflearn the fourier analysis in matlab. I got lost in one passage in the ...
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Power spectral density: why this 2 method are equal

the Power spectral density can be calculated in two way: by doing the fourier transform of the autocorrelation by doing (abs(X(f)).^2 where X(f)=fft(x(t)) Can you explain me passage by passage why ...
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How does spectral density of a power signal change when it is multiplied by $\cos(2\pi f_ct)$?

Suppose we have a power signal $n(t)$ whose power- auto-correlation function is: $R_{n}(\tau)$. Now we multiply the signal by a cosine as $$\cos(2\pi f_ct) \cdot n(t)$$ whose auto-correlation is $R_{...
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Expectation of power spectrum for nonorthogonal wavelets

I'm working through "A Practical Guide to Wavelet Analysis" by Torrence and Compo, and I am confused about section 3d ("Wavelet Power Spectrum"). Let $x_n$ denote the signal, sampled at increments $\...
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Changing power of an audio signal to a specific dB

Suppose I have an audio signal with power 31dB. I want to change the signal power to 24dB. How can I change the power of that signal from 31dB to 24dB?
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1answer
38 views

Fourier transforms and time shift

There is probably something trivial behind this, but I am missing something. I need to create a stationary random time series data v(t) which is the the sum of another time series u(t) and u(t) with a ...
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1answer
29 views

Time derivative of signal - effect on noise distribution

I have an angular velocity measurement that has a certain amount of ripple that yields an histogram shaped like a gaussian curve. I quantify that ripple using a standard deviation. I am interested in ...
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28 views

Comparison of results own implementation and python signal.welch

I am trying to replicate the output of Python's signal.welch function to make an estimate of the PSD from an FFT calculation. I don't want to use the built-in function to understand better what is ...
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51 views

How to normalize PSD to get the same magnitude as FFT peak

I am trying to use FFT and power spectra density estimation with python (np.fft.fftand scipy.signal.periodogram). And trying to ...
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24 views

Correlation/anticorrelation as a function of frequency

I am tracking the values of two fluctuating quantities as a function of time and am trying to analyze possible correlations between the two as a function of frequency. The application is experimental ...
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Morlet-based Cross Spectral Density vs Wavelet Transform

I am interested in the frequency distribution and power of neural alpha waves (8-12Hz), and have been using WT to examine them. I am quite new to the techniques involved, however, and have noticed ...
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61 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: $$x[n] = 3 \cdot \sin(ω_1 \cdot n + ϕ_1) + 5 \cdot \cos(ω_2 \cdot n + ϕ_2) + 2 \cdot \sin(ω_3 \cdot n + ϕ_3) + v[n]$$...
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1answer
45 views

Signals Cross Correlation from Their Power Spectral Densities?

For two real valued signals $f$ and $g$ with their corresponding power spectral densities $|F(k)|^2$ and $|G(k)|^2$ Is there a way to get an intuition of how correlated $f$ and $g$ are just by looking ...
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136 views

Cross Correlation, how can any signals except the trivial cases be uncorrelated?

I have been working on a problem where I am trying to subtract two Power Spectral Densities (PSD's) from one another in the following way. $$|F(k) - G(k)|^2 = |F(k)|^2 - |G(k)|^2$$ Which is only ...
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26 views

What is the physical meaning of the cross-spectrum of two signals measured at two locations and different moment?

I am working with steady state pressure field measurement where sound pressure at multiple locations in the field needs to be measured. In my case, more than one microphone existing in the field at ...
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How to find spectral density of a signal whose correlation depends on time?

Suppose we have two uncorrelated, real white noise $\xi_1(t)$ and $\xi_2(t)$, with zero mean, and equal variance. Now, I create the signal $\xi(t) = a\xi_1(t)\cos(\omega_0 t) + b\xi_2(t) \sin(\...
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66 views

What kind of power spectrum implies uncorrelation in time?

I am new in signal processing field, and actually I just need some basic tools for what I am working on. I've learnt that the autocorrelation function is the inverse Fourier transform of the signal's ...
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1answer
104 views

Calculating Data Rate using Bandwidth, Transmission Power, Noise Power Spectrum Density and Channel Gain

I'm a Software Engineering student researching on Load Balancing in IoT and I need to calculate data rate. However, I don't know how to use these values to attain data rate despite searching on the ...
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Relation between power spectral density and mean absolute value

The root mean square $$\sigma_{x} = \sqrt{\frac{1}{T}\int_0^T x^2(t) \, \mathrm{d}t}$$ of a finite zero-mean random signal $x(t)$ in the range $0 < t < T$ is related to the signal's power ...
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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 $\...
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Analytical spectral density of a On/Off modulation defined by a Bernoulli process

Consider a narrow band signal (laser) that I can modulate digitally with a on/off switch controlled by a digital pseudo random number generator. The resulting signal features a linewidth broadened by ...
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How to choose the order of the filter - Capon's method

I am studying power-spectra and I want to find the best estimation method for my problem. I stumbled upon Capon's method (sometimes also called minimum variance), which on paper looks very nice. On ...
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1answer
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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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Binary vs 4-PAM PSD

I'm struggling to understand how you would form an expression for the PSD of a 4-PAM signal which is using rectangular pulse shaping. I understand for binary the likelihood of +/1 is equal so the ...
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How to get PSD from frequency domain representation of time-series data [duplicate]

Let's say we have a realization (time-series data) of a random process. I take fft() of that to get its frequency domain representation. Then how can I estimate the PSD of this random process by ...
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1answer
62 views

Units for a PSD from square of FT?

If I am looking to do a PSD plot on a signal $x(t)$ with units $m$ then the units I am expecting in the PSD would be $\frac{m^2}{Hz}$ but I can't seem to get this result from the following reasoning: ...
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Losing lowest Frequencies in frequency modulated signal, rest of spectrum is fine

For several reasons I am attempting to re-modulate a de-modulated FM (as in WFM Radio) signal using python. Demodulating the initial signal goes well, it produces the PSD chart below which looks just ...
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1answer
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MATLAB & Power Spectral Density - Error - Getting the same range of values regardless of sound type?

I wrote code [attached at end of question] to take .wav files of child vocalizations and tried to see if there are valid ranges for the formants F1:F2:F3 for the 5 ...
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Is it possible to approximate given skewness and kurtosis values using an IFFT?

I have time domain data for a signal that behaves randomly but has non-random (non-Gaussian?) skewness and kurtosis values of ~0.9 and ~7.4, respectively. The FFT of the signal shows that it's not ...
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1answer
115 views

QPSK Data Rate vs Bandwidth at Passband: Why can it only transmit 1 bit per Hz and not 2 bits per Hz?

1) This is a follow up question to the most up-voted answer to this question. 2) The accepted answer is that "QPSK transmits 1 bit per Hz at passband". 3) The theory found in books seems to agree ...
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PSD subtraction

I am interested seeing the difference between two power spectral densities (PSD) as a noise reduction exercise The blue line is the psd of my signal, and the the orange line is the psd of the ...
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How to relate power spectral density with the number of resource blocks in LTE?

I am running a simulation with 100 Resource blocks for LTE OFDM and I plotted a PSD for it. Now I am able to bring down the out of band emissions when I perform an algorithm on it. Based on the ...
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Why does power spectral density of OFDM signal changes with number of zero subcarriers

I am trying to plot the power spectral density (PSD) of an OFDM signal with $N_{dsc}$ subcarriers and $N_{zeros} = N_{fft}-N_{dsc}$ zero subcarriers. I am using the matlab function pwelch() to plot ...
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Normalizing vectors to be the same size to retain PSD data

Context: PSD=periodogram(y) in MATLAB gives the PSD (power spectral density) estimate of a sound-source signal. I want to find the local maximum within 3 different ...
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Help obtaining the variance of a signal from a power spectrum?

I have been reading this. The paper presents a power spectrum (attached). The power spectrum shows the power spectrum of velocity perturbations, $v$, in the solar atmosphere. If I want to obtain the ...
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Equivalence of the Power Spectral Density definitions

I am trying to show the equivalence of the following Power Spectral Density definitions in Matlab: Definition 1: $$ P(\omega) = \sum_{k=-\infty}^{\infty} r(k)e^{-j\omega k} $$ Definition 2: $$ P(\...
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27 views

Chi-squared distribution variable spectral analysis

I an interested in spectral analysis of a random signal. Assume the signal $n(t)\sim\mathcal{N}(0,\sigma^2)$ is followed by the white Gaussian noise with zero mean and $\sigma^2$ variance. The test ...
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1answer
45 views

When a stochastic process would be a beneficial model in terms of noise

Let's say we have an image/signal with some noise in it. When would it be beneficial to model the signal as an outcome of a stochastic process? More specifically: How significant would noise have to ...
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38 views

Interpreting Auto correlation results

I used xcorr function in Matlab to compute the autocorrelation of my signal. I obtained a graph, which is shown below. How to interpret this? I read that autocorrelation helps in finding the patterns ...