Questions tagged [power-spectral-density]

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

Filter by
Sorted by
Tagged with
21
votes
3answers
63k views

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 ...
55
votes
2answers
28k views

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 ...
1
vote
1answer
387 views

Power Spectrum: Definition

I am new to the study of time series. Recently I have asked a question about the covariance of real and imaginary part of a real(in time domain) stochastic time series and I have received an answer ...
22
votes
1answer
27k views

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 ...
12
votes
1answer
14k 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 ...
3
votes
2answers
5k 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 : ...
17
votes
4answers
9k views

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'...
4
votes
1answer
4k 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 $N = 1024$,...
8
votes
2answers
47k views

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?
15
votes
2answers
29k views

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 ...
16
votes
2answers
31k views

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 ...
10
votes
1answer
20k 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 ...
6
votes
5answers
454 views

Inconsistency with the units of power spectral density and the definition the people often give

Perhaps someone can help me resolve something - this is my understanding: In deterministic signal analysis, for a signal $x(t)$ the signal energy (as opposed to the real physical energy) is given by $...
3
votes
2answers
357 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 ...
2
votes
1answer
967 views

Dividing Audio signals into Barks Bands

I want to apply the following steps in matlab 1) Read the audio data 2) Apply window function on that data 3) Apply fft on the result of window function 4) Make power spectrum of fft 5) divide ...
1
vote
1answer
752 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 ...
2
votes
2answers
112 views

Power spectral density: Why are these two methods equal?

The power spectral density can be calculated in two ways: 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 ...
1
vote
1answer
135 views

Spectral density of modulated noise process

Suppose we have a noise process $F(t)$. Suppose $F$ is stationary and we know its autocorrelation function $$\rho_F(\tau) \equiv \langle F(0)F(\tau) \rangle$$ where the average is over realizations of ...
1
vote
2answers
173 views

Help with obtaining the power spectral density of a simple continuous cosine (using both forms of the definition for PSD)

I am trying to go through a simple example to teach myself about Parseval's theorem and calculating power spectral density (PSD) in practice and would be very grateful if someone could check my ...
0
votes
2answers
39 views

How can I shape my time channel response, in order to have Gaussian shaped Doppler Spread?

I know how to generate a Rayleigh fading channel but I have no clue how I can shape the Doppler spectrum to be Gaussian. Any help will be really appreciated. ps: I am coding on matlab
5
votes
1answer
7k 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 ...
5
votes
2answers
13k views

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 ...
2
votes
1answer
5k 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, ...
5
votes
1answer
7k 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 ...
7
votes
1answer
9k views

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 ...
4
votes
2answers
901 views

Properties of Up- and Downsampling

Given a gaussian white noise with mean 0 and $\sigma = 1$. I'm interested in the PSD (power spectral density), when the signal is plain up- or downsampled. No interpolation, no filtering nothing. ...
3
votes
1answer
3k views

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. But i ...
0
votes
2answers
558 views

Frequency magnitude distribution of noise

By the Wiener-Khinchin theorem, we have a straightforward way to calculate the power spectral density for stationary noise. If we know the bandwidth of a system, we can further calculate the variance ...
3
votes
1answer
660 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^...
3
votes
5answers
10k 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 ...
2
votes
1answer
165 views

Segmenting a frequency series: do we need band-pass filtering?

I am trying to implement what's called the "second spectrum". Basically, you do this: Take a time series of length $N$. Divide it into $m$ segment, each of length $N'=N/m$. For each segment $m$, do a ...
2
votes
2answers
3k views

White noise vs. delta pulse and Ultraviolet catastrofe

Everybody explains that white noise has all frequencies equally strong. But, this immediately means that Ultraviolet catastrofe inevitably happens if power > 0 stays constant at any frequency and, ...
2
votes
2answers
949 views

What does PSD represent in the spatial domain?

People use FFT methods to analyze topographic features in the spatial domain, such that the signal varies over (x) rather than (t). If a PSD curve characterizes amplitude versus frequency of an ...
2
votes
1answer
3k 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 ...
1
vote
1answer
647 views

Finding the right measure to compare sound signals in the frequency domain

I am comparing the spectral contents of some sound signals with MATLAB. I have quite a few measures but wanted one that represents the centre of gravity of the spectrum. I used ...
1
vote
1answer
288 views

Why do we need the power spectral density?

Since the power spectral density is just the squared of the fourier transform, why is it useful ? Can't I just replace every solution that requires the psd with the fourier transform ?
0
votes
2answers
4k views

PSD of sine wave

I'm learning some basic signal processing to use in my research. So I'm trying to understand the pwelch function in MATLAB to calculate the PSD. My understanding ...
0
votes
1answer
368 views

A query on Power spectral density (PSD)

Say a narrow band signal $n(t)$ has Power Spectral Density (PSD) $S(f)$. If the signal $n(t)$ got multiplied by $\cos(2\pi Ft)$, then what will the PSD of resulting signal in terms of $S(f)$ be? Will ...
0
votes
1answer
28 views

Signal Timing Recovery, Loop Bandwidth and SNR

As explained in the answer here, for the symbol timing recovery loop we need to keep loop bandwidth sufficiently below the modulation bandwidth of the signal so as to avoid the filtering of the signal ...
-1
votes
1answer
77 views

Spectral structure of sinusoidal model

Let us consider the following code: ...
4
votes
1answer
867 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 ...
4
votes
2answers
672 views

What assumptions should be used to invert spectrum into time domain data?

This question comes from a realistic problem that how to obtain a time domain wind pressure from known wind spectrum. Or similarly, gets rail surface curve from spatial rail spectrum. Obviously, ...
3
votes
1answer
1k views

How to average coherences estimated using Welch's method in MATLAB

I'm trying to estimate the average coherence of discontinuous snippets of a signal in MATLAB. For Welch's spectrum estimates, the following works: ...
3
votes
1answer
323 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 ...
2
votes
1answer
1k views

Phase difference between two sinuisoidal signal

Currently, I have two signals, the main components of both signals are 60Hz, but both also have weaker response at 180Hz + small amount of noise. As shown in the photo below, I want to find the phase ...
2
votes
1answer
86 views

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 ...
2
votes
2answers
4k views

Root mean square bandwidth of a signal with flat spectrum

I am trying to derive a simple expression for root-mean-square bandwidth $B_{\rm rms}$ for a signal that has flat spectral density over its entire bandwidth $B$. The expression for the $B_{\rm rms}$ ...
2
votes
1answer
2k views

Implementing Welch's method for Power Spectral Density

I want to implement Welch's method for PSD calculation in MATLAB. I do not want to use built in MATLAB cpsd function, such that I can change the FFT implementation ...
2
votes
1answer
509 views

PSD scaling due to the windowing

I am struggling with the following problem for a while: If I have signal of duration N and I apply window (assume rectangular window) of size M < N how will this influence PSD of that signal after ...
1
vote
1answer
290 views

Modified Periodogram function in MATLAB

Given below is a function written in MATLAB for computing the modified periodogram, taken from Hayes, Statistical Digital Signal Processing and Modeling ...