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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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Why so many methods of computing PSD?

Welch's method has been my go-to algorithm for computing power spectral density (PSD) of evenly-sampled timeseries. I noticed that there are many other methods for computing PSD. For example, in ...
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Variance of White Gaussian Noise

It could seem an easy question and without any doubts it is but I'm trying to calculate the variance of white Gaussian noise without any result. The power spectral density (PSD) of additive white ...
Mazzy's user avatar
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What is the difference between PSD and squared magnitude of frequency spectrum?

The power spectrum of a signal can be calculated by taking the magnitude squared of its Fourier transform. Being an audio person, the signal of interest for me would be a time series. How does this ...
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Power spectral density vs. FFT bin magnitude

What's the difference between these? Both are measurements of some form of signal power, but surely there's some difference between the power they are measuring?
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What is cross-spectral density- CSD?

I asked a question earlier but I didn't get any answer for it. So now I am simplifying it: what are Cross-Spectral Density (CSD) and Power-Spectral Sensity (PSD)? What is their application? How can I ...
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20 votes
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How do you calculate spectral flatness from an FFT?

Ok, the spectral flatness (also called Wiener entropy) is defined as the ratio of the geometric mean of a spectrum to its arithmetic mean. Wikipedia and other references say the power spectrum. Isn'...
endolith's user avatar
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PSD (Power spectral density) explanation

I'm trying to understand how the PSD is calculated. I've looked in a few of my Communication Engineering textbooks but to no avail. I've also looked online. Wikipedia seems to have the best ...
user968243's user avatar
12 votes
1 answer
16k views

Difference between power spectral density, spectral power and power ratios

What 'exactly' is power spectral density for discrete signal? I was always under the assumption that taking the Fourier transform of the signal, and then the ratio of desired frequency range ...
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12 votes
5 answers
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Inconsistency between the units of power spectral density and the definition that people often give

Perhaps someone can help me resolve something - this is my understanding: In deterministic signal analysis, for a continuous signal $x(t)$ the signal energy is defined by $$E_{\textrm{s}} = \int^{+\...
teeeeee's user avatar
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12 votes
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25k views

Power spectral density vs Energy spectral density

I read the following on Wikipedia: Power spectral density: The above definition of energy spectral density is most suitable for transients, i.e., pulse-like signals, for which the Fourier ...
Amelio Vazquez-Reina's user avatar
10 votes
4 answers
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When is it true that "the Fourier transform of the autocorrelation is the spectral density"?

I am currently struggling on the book "System Identification: Theory for the User" by Lenart Ljung (freely available here) about the definition of the spectrum (around page 33). As I have ...
NokiYola's user avatar
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What is the difference between the PSD and the Power Spectrum?

Can any one explain the difference in the amplitude between the two and what does each one represents? For example, when using the pwelch algorithm in MATLAB how ...
havakok's user avatar
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9 votes
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Spectral Entropy Calculation in MATLAB

How do I calculate the Spectral Entropy of a signal in MATLAB ? I know the basic steps but it would be nice if someone can help, Calculate the power spectrum of the signal using FFT command in MATLAB....
RRelan's user avatar
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1 answer
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Is autospectrum the same as power spectrum density?

In my slides about signal processing, there is one that mentions the same thing as the beginning of this and this answer, namely that the Fourier transform of a signal, squared is the power spectrum ...
Mien's user avatar
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8 votes
3 answers
16k views

What should be the correct scaling for PSD calculation using $\tt fft$

I would to calculate the PSD of a signal using FFT however the result do not match with periodogram command. What did was as follow : ...
justin's user avatar
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2 answers
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Interpretation of Clarke's Doppler power spectral density

What I understand of Doppler spread is that the relative motion between Transmitter (TX) and Receiver (RX) change the exposing time of signal. In rapport to a constant-distance TX-RX, a moving toward ...
AlexTP's user avatar
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7 votes
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Why the RMS of a PSD curve is the root of the area below

I will try to explain what is my level of understanding of this problem, please correct me if I'm wrong: RMS is the Root Mean Square, it represent the mean value of the input signal. PSD is the ...
Sturm's user avatar
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2 answers
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Variance of periodogram estimate of the power spectrum

I have been reading chapter 13.4. ("Power Spectrum Estimation Using the FFT") of the Numerical Recipies Book. Some things related to the expectation value of the "periodogram estimate of the power ...
Tobias's user avatar
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1 answer
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How to calculate the power of a discrete signal? / Clarification on PSD estimates

I want to calculate the channel power $ P_\mathrm{x}$ of a given discrete and complex signal $x[n]$ (with a length of N) in a given bandwidth $B$. I'm aware, that I could probably apply a sharp ...
Hemanti's user avatar
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1 answer
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How Exactly Does MATLAB Zero Pad Signal?

I am doing some massive number crunching in MATLAB which involves millions of PSD estimations. Each data segment has length 41. So I have been using the multi-taper method with ...
Fixed Point's user avatar
6 votes
2 answers
672 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 ...
Sadist_Tanmoy's user avatar
6 votes
2 answers
501 views

Modelling MEMS accelerometer noise

I am trying to compare two MEMS accelerometers in terms of their noise for ground motion monitoring applications. I would like to take some "clean" data (recorded by good quality ...
marco890's user avatar
6 votes
2 answers
1k views

Does PSD (dBm/Hz) of white noise depend on sampling rate?

I am confused about signal processing broadband noise like white noise and single-tone noise (sine wave) using FFT. As a starter, I am trying to understand how to normalize white noise properly after ...
anikap's user avatar
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6 votes
2 answers
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Am I supposed to normalize FFT in Python?

I'm sorry if this question is posed often, I can't seem to understand the answers already out there. I'm working with several forms of the Fourier transform, including the FFT, PSD, and spectrograms. ...
Petra's user avatar
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1 answer
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What is the relationship between the PSD of a continuous signal and the PSD of its periodically sampled one?

In Oppenheim's "discrete time signal processing", it says, How is the equation (10.65) derived? PS: you may try to derive it with Fourier transform of the original and the sampled signals. ...
fececagec812's user avatar
6 votes
3 answers
3k 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 ...
Jagerber48's user avatar
6 votes
1 answer
353 views

Example of non-equivalence of the two PSD definitions

According to the book Introduction to Spectral Analysis by P. Stoica and R. Moses, the power spectral density (PSD) $P(\omega)$ can either be defined as the discrete-time Fourier transform (DTFT) of ...
user32892's user avatar
6 votes
1 answer
445 views

Cross Power Spectral Density of Unevenly Sampled Data

Here's my problem. The input signals $x$ and $y$ will be having the time value aligned with each other. However, the data are not evenly sampled. I would like to calculate CPSD of both signals. The ...
SeeJay's user avatar
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6 votes
3 answers
1k views

Units of 6.02*N + 1.76 as an FFT noise floor

I'm working on estimating the FFT noise floor for a data acquisition system my colleagues and I are designing. I've read MT-001 several times. In general, I think I get it. However I'm a little stuck ...
FooAnon's user avatar
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6 votes
2 answers
2k 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.
Akanksha 's user avatar
6 votes
1 answer
698 views

Decorrelating Stationary Colored Gaussian Noise -- Effect On The Desired Signal

So given stationary colored gaussian noise $\mathbf{n}$, I know that I can decorrelate it by first finding it's autocorrelation $R_{nn}$ and performing $R^{-\frac{1}{2}}_{nn} \mathbf{n}$. In ...
The Dude's user avatar
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5 votes
4 answers
3k views

Numerically generating noise time series from spectral density

I'm trying to figure out a way to construct (numerically) time series of random variables given some spectral density $S_{xx}(f)$. I'm interested in various types of spectral densities (flat, ...
user129412's user avatar
5 votes
4 answers
647 views

What Is Continuous White Noise in The Context of Signal Processing and Broadly

How can one define Continuous White Noise in a coherent way? Is there a way to derive it Mathematically? Specifically, is there a way to define it which will works as the model in Signal Processing ...
Royi's user avatar
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5 votes
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340 views

Bandpass Stationary Stochastic Process

I was following this interesting post by a new user Rubem Pacelli and got stuck at Proakis' referenced definition (see Section 4-1-4 starting on page 159 here). The math, all repeated further below, ...
Dan Boschen's user avatar
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5 votes
2 answers
515 views

Why is PSD estimated, and not simply computed?

I apologize if this comes as a basic question, but I am struggling to understand why the PSD can only be estimated and not directly computed. For example, this thread discusses several such PSD ...
Josh's user avatar
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5 votes
1 answer
9k views

Is it only me or matlab's periodogram's function is confusing?

I am really confused with matlab's periodogram. First of all, it says in the documentation that its unit is "dB per unit frequency". What does that really mean? I just don't quite get it. Second of ...
Kevin.hammet's user avatar
5 votes
5 answers
14k views

Where does the delta function come from if we derive autocorrelation directly?

I am reading a book "Creating Noise" written by Hollos & Hollos and have a question about the autocorrelation function of the Gaussain white noise when reading the following passage: From the ...
user5280911's user avatar
5 votes
1 answer
5k views

Is the periodogram squared-magnitude DFT or squared-average DFT?

How is the periodogram defined? I have been searching the internet a lot, and I find two different definitions: periodogram is the squared magnitude of the DFT periodogram is the squared average of ...
user10826's user avatar
5 votes
1 answer
595 views

Do waterfalls generate pink (1/f) or brownian (1/f^2) noise?

Does anybody know if natural waterfalls generate pink noise or brownian noise? I have tried to search about this but the matches are non-scientific and contradictory. For example Livescience.com ...
Akseli Palén's user avatar
5 votes
1 answer
11k views

Working backwards from PSD to possible signal

I have been trying to reconstruct a random signal from its PSD and am running into trouble. I know that many different signals in the time or spatial domains can result in the same PSD-- I am ...
Mr. Squig's user avatar
  • 153
5 votes
2 answers
256 views

What happens to the 0 and Nyquist frequency when using Welch's method?

Welch's method is a way to get better power spectral density (PSD) estimations than simple, naive periodograms. It has two main components: Cutting the input into many segments and average their ...
dedebenui's user avatar
5 votes
3 answers
3k 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 ...
KBriggs's user avatar
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5 votes
1 answer
2k views

Producing Colored Noise from a given PSD Data

I need to estimate (extract/produce) the colored noise of a given PSD Data. I have the following procedure to get the desired results. First of all I calculate the filter coefficiencts using firls ...
technik_duck's user avatar
5 votes
3 answers
7k views

1/3 Octave Analysis

Good Morning! I am new in signal processing and I am trying to do a work in noise control of an electronic steering lock device (ESL). My aim is to calculate the loudness (Zwicker Method- ISO 532 B) ...
Alisson Vieira's user avatar
5 votes
0 answers
615 views

fit theoretical spectrum to simulated one

I have a bunch of simulated time series, for which I can compute the power spectrum. Generally, the simulated power spectrum can be sketched as follows: I now aim to calculate the features of the ...
fpe's user avatar
  • 627
4 votes
3 answers
3k views

How to interpret spectrogram correctly?

I have a pressure transducer signal from a reacting mixture available here, which has a sampling frequency of 50kHZ. I have also obtained the spectrogram of the signal with NFFT=256, noverlap=4 as ...
nxkryptor's user avatar
  • 143
4 votes
2 answers
3k views

Magnitude of Power Spectral Density with Different Sampling Frequency

For exponential signals (sine or cosine), if the sampling frequency $f_s$ is equal to the length of signal, $N$, the magnitude of psd for each sine signal is proportional to amplitude in time domain, ...
user avatar
4 votes
2 answers
780 views

signal of $\frac{1}{f}$ Noise

I am working on kind of signals that can be classified as 1/f Noise. In this article is explained that the time history of 1/f noise follows a power law proportional to $t^{-\alpha}$. I am very ...
user avatar
4 votes
1 answer
9k views

Understanding the Windowing Method in PSD Calculation

I have some issues understanding the use of a window (it doesn't matter which one) to calculate the Power Spectral Density of a signal. For example say I want to use the hann window, with $N = 1024$,...
Engine's user avatar
  • 409
4 votes
1 answer
857 views

How does SciPy's Welch function change the shape of the data?

I am working with some time series data with a shape of 8064. The data is actually the popular EEG data called DEAP. It basically is a 3D array of size (40, 40, 8064) and here is the link to the ...
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