I want to know the exact meaning of power spectral density, by a suitable real life example. There are a lot of definition but how can I correlate it with real experiences?

Power spectral density function (PSD) shows the strength of the variations(energy) as a function of frequency. In other words, it shows at which frequencies variations are strong and at which frequencies variations are weak. The unit of PSD is energy per frequency(width) and you can obtain energy within a specific frequency range by integrating PSD within that frequency range. Computation of PSD is done directly by the method called FFT or computing autocorrelation function and then transforming it.

Power spectral density can be obtained computing autocorrelation function in Fourier space. From physical point of view, high frequency wavenumber of the Power Spectral Density of a 2D image, can be related to sharp variations in intensity values of the pixels in the image domain. Such variations occur in pixels near to an object edge in the image.

Jul 16, 2013

Nirav Desai · Institute of Electrical and Electronics Engineers

Power Spectral Density is the Fourier Transform of the autocorrelation function of a signal. First compute the auto correlation function and then compute its Fourier Transform.

Jul 16, 2013

Nirav Desai · Institute of Electrical and Electronics Engineers

White noise will give a flat power spectral density (White)

Nirav Desai · Institute of Electrical and Electronics Engineers

If you get into the computation of the Fourier Transform of the auto correlation funciton, you will find that you can do a 2-sided or a 1-sided Fourier Transform and they both give different results. The 2-sided Fourier Transform of the ACF is called a correlogram and the 1-sided Fourier Transform of the ACF is periodogram. Usually, the correlogram is more accurate than the periodogram. A good book to learn the applications of this would be Spectral Analysis of Signals by Petre Stoica and Randolph Moses. Usually the EEG of nerve signals gives strong cross-correlations during neural activity and weak cross-correlations during lack of neural activity. This property is used in prosthetic devices to identify the activity the brain wishes to perform.

Jul 16, 2013

Nirav Desai · Institute of Electrical and Electronics Engineers

For a 2-sided Fourier Transform (correlogram), the index at 0 delay is taken as the midpoint and the summation goes from -N/2 to N/2.

Jul 16, 2013

Nirav Desai · Institute of Electrical and Electronics Engineers

I hope that clarifies things better.

Jul 16, 2013

Nirav Desai · Institute of Electrical and Electronics Engineers

Ok....thanks to both of you...ultimately our target is to convert any signal to its sine and cosine term, as in nature all signal are sinusoidal, psd is an anathor form or i can say a kind of representation....m i correct????

Jul 17, 2013

Nirav Desai · Institute of Electrical and Electronics Engineers

Hi Nisha. The Fourier Transform theorem states that only periodic signals have a Fourier Series representation. When we do a Discrete Fourier Transform, we are assuming the signal to be periodic outside the sampling period. It does not make any errors in the process and is the function mapping can be inverted to get the original signal back.

What are negative frequencies? Do they really exist or used in mathematical formulas only?

Jul 27, 2013

Daoud Berkani · National Polytechnic School of Algiers

Negative frequencies are required to complete Fourier integral. Negative frequencies correspond to the negative time. They are also called mirror frequencies : you cannot get (modify) your mirror image as you cannot modify these frequencies as you can get negative time (= to modify pass time or action).

Power spectral density describes the signal power distribution over the frequency.

Jul 21, 2014

Aasim Khurshid · Universidade Federal do Rio Grande do Sul

Power spectral density is distribution of power, and it can be calculated by Fourier Transform of auto-correlation function of the signal. You can test this to better understand. Take a signal/image, find auto-correlation and take FFT, plot it.

Feb 16, 2015

Taha A. Ali · Arab Academy for Science, Technology & Maritime Transport

Power spectral density function (PSD) shows the strength of the variations(energy) as a function of frequency. In other words, it shows at which frequencies variations are strong and at which frequencies variations are weak. The unit of PSD is energy per frequency(width) and you can obtain energy within a specific frequency range by integrating PSD within that frequency range. Computation of PSD is done directly by the method called FFT or computing autocorrelation function and then transforming it.

Daoud Berkani · National Polytechnic School of Algiers

The power spectral density shows how the energy of a signal is distributed. That can allow us to make some decisions or operations on a considered signal. The important thing is that the DSP can be obtained from the function of auto correlation without signal priory knowledge (Wiener-Khintchine theorem 1929). What makes the valid FT for a signal is random or real.

Mar 14, 2015

Ahmed Guerine · Institut National des Sciences Appliquées de Rouen

Hi

I advice you to see these documents. You will find what you need with some examples.

Chirag Pallan · Indian Institute of Technology Madras

when you measure the signal it will be having the various frequency components in it, since the power contained in each signal with different frequency will be different so the psd is the graph of power vs frequency.

also the main application of the psd plot is that it will give the range of the frequency where the power density is high

Power spectral density function (PSD) shows the strength of the variations(energy) as a function of frequency. In other words, it shows at which frequencies variations are strong and at which frequencies variations are weak. The unit of PSD is energy per frequency(width) and you can obtain energy within a specific frequency range by integrating PSD within that frequency range. Computation of PSD is done directly by the method called FFT or computing autocorrelation function and then transforming it.

S. Bali Reddy · Indian Institute of Technology Guwahati

Power spectral density function shows the energy with frequency. It will useful when you want check the signal is week or strength.

May 22, 2015

Yves Chapron · Alpine Institute of Environmental Dynamics

What is the difference between a PSD = f( Hz) and the square of energy (E^2) = f(Hz)? When a domain in Hz is changing in energy (increase of E^2) maintained along all the signal following. In other words what is the difference in the meaning of density (PSD) versus only the square of E (E^2) = Hz? What is lost in the information relatively

May 27, 2015

Ahmed Guerine · Institut National des Sciences Appliquées de Rouen

Hi

Power Spectral Density ou PSD is the square of the Fourier transform module, divided by the integration time T (or, more strictly, the limit as t goes to infinity of the mathematical expectation of the square of the Fourier transform module signal - this is called average power spectral density). Thus, if x is a signal X and its Fourier transform, the spectral power density is:

I have the a similar question, I'd like to add more questions, anyone had experienced to analyze the from Z-accelerometer to PSD and road roughness (IRI). Thanks

## Popular Answers

Light Coherence· Indian Institute of TechnologyPower spectral density function (PSD) shows the strength of the variations(energy) as a function of frequency. In other words, it shows at which frequencies variations are strong and at which frequencies variations are weak. The unit of PSD is energy per frequency(width) and you can obtain energy within a specific frequency range by integrating PSD within that frequency range. Computation of PSD is done directly by the method called FFT or computing autocorrelation function and then transforming it.

Go here for more...

http://www.cygres.com/OcnPageE/Glosry/SpecE.html

## All Answers (28)

Andrea Aprovitola· Scuola Politecnica e Delle Scienze di BaseNirav Desai· Institute of Electrical and Electronics EngineersNirav Desai· Institute of Electrical and Electronics EngineersAndrea Aprovitola· Scuola Politecnica e Delle Scienze di BaseNirav Desai· Institute of Electrical and Electronics EngineersAndrea Aprovitola· Scuola Politecnica e Delle Scienze di BaseNirav Desai· Institute of Electrical and Electronics EngineersNirav Desai· Institute of Electrical and Electronics EngineersNirav Desai· Institute of Electrical and Electronics EngineersNirav Desai· Institute of Electrical and Electronics EngineersNisha Bhatt· Amrapali Group of InstitutesNirav Desai· Institute of Electrical and Electronics EngineersNisha Bhatt· Amrapali Group of InstitutesNisha Bhatt· Amrapali Group of InstitutesDaoud Berkani· National Polytechnic School of AlgiersFouad Abbou· Al Akhawayn UniversityPower spectral density describes the signal power distribution over the frequency.

Aasim Khurshid· Universidade Federal do Rio Grande do SulPower spectral density is distribution of power, and it can be calculated by Fourier Transform of auto-correlation function of the signal. You can test this to better understand. Take a signal/image, find auto-correlation and take FFT, plot it.

Taha A. Ali· Arab Academy for Science, Technology & Maritime TransportPower spectral density function (PSD) shows the strength of the variations(energy) as a function of frequency. In other words, it shows at which frequencies variations are strong and at which frequencies variations are weak. The unit of PSD is energy per frequency(width) and you can obtain energy within a specific frequency range by integrating PSD within that frequency range. Computation of PSD is done directly by the method called FFT or computing autocorrelation function and then transforming it.

http://www.cygres.com/OcnPageE/Glosry/SpecE.html

Daoud Berkani· National Polytechnic School of AlgiersThe power spectral density shows how the energy of a signal is distributed. That can allow us to make some decisions or operations on a considered signal. The important thing is that the DSP can be obtained from the function of auto correlation without signal priory knowledge (Wiener-Khintchine theorem 1929). What makes the valid FT for a signal is random or real.

Ahmed Guerine· Institut National des Sciences Appliquées de RouenHi

I advice you to see these documents. You will find what you need with some examples.

Best regards

Chirag Pallan· Indian Institute of Technology Madraswhen you measure the signal it will be having the various frequency components in it, since the power contained in each signal with different frequency will be different so the psd is the graph of power vs frequency.

also the main application of the psd plot is that it will give the range of the frequency where the power density is high

hope this will satisfy your question

Light Coherence· Indian Institute of TechnologyPower spectral density function (PSD) shows the strength of the variations(energy) as a function of frequency. In other words, it shows at which frequencies variations are strong and at which frequencies variations are weak. The unit of PSD is energy per frequency(width) and you can obtain energy within a specific frequency range by integrating PSD within that frequency range. Computation of PSD is done directly by the method called FFT or computing autocorrelation function and then transforming it.

Go here for more...

http://www.cygres.com/OcnPageE/Glosry/SpecE.html

S. Bali Reddy· Indian Institute of Technology GuwahatiPower spectral density function shows the energy with frequency. It will useful when you want check the signal is week or strength.

Yves Chapron· Alpine Institute of Environmental DynamicsWhat is the difference between a PSD = f( Hz) and the square of energy (E^2) = f(Hz)?

When a domain in Hz is changing in energy (increase of E^2) maintained along all the signal following. In other words what is the difference in the meaning of density (PSD) versus only the square of E (E^2) = Hz?

What is lost in the information relatively

Ahmed Guerine· Institut National des Sciences Appliquées de RouenHi

Power Spectral Density ou PSD is the square of the Fourier transform module, divided by the integration time T (or, more strictly, the limit as t goes to infinity of the mathematical expectation of the square of the Fourier transform module signal - this is called average power spectral density). Thus, if x is a signal X and its Fourier transform, the spectral power density is:

PSD=ІXІ^2/T

Best regards

Sumit Balguvhar· Indian Institute of Technology DelhiPSD means how the strength of a signal is distributed in the frequency domain.

Yusuf Adinegoro· Queensland University of TechnologyI have the a similar question, I'd like to add more questions, anyone had experienced to analyze the from Z-accelerometer to PSD and road roughness (IRI). Thanks

Can you help by adding an answer?