Questions tagged [power-spectral-density]
The Power Spectral Density (PSD) is the distribution of signal power over frequencies.
109
questions
3
votes
2
answers
781
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, ...
- 293
3
votes
1
answer
1k
views
How to generate time-series from a given one-sided PSD?
Generating time series from a given PSD has been discussed in this and some other forums already (which I've referred some of them below) but almost all of them are mostly descriptive and none of them ...
- 338
3
votes
1
answer
2k
views
PSD from autocorrelation in MATLAB
I am trying to simulate a simple stochastic process defined by the equation:
\begin{equation}
\frac{1}{v}\frac{db}{dt} +\Gamma_0 b= \sqrt{\sigma}R(t),
\end{equation}
where $R(t)$ is a zero-mean white ...
- 131
3
votes
1
answer
614
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 ?
- 193
3
votes
1
answer
294
views
Can I simplify $x=\frac{\ln(|\mathcal F((\mathcal F^{-1}(\sqrt{(f^{-5/3})}))^{2})|)}{\ln(f)}$
Given a variable in time $u_{k}$, and an other variable f which represents the frequencies in a range [a,b]:
$$|\mathcal F \left \lbrace u_{k}\right \rbrace |^{2}=f^{-5/3}\tag{1}$$
where $\mathcal F$ ...
anon
3
votes
1
answer
2k
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:
$$
\Phi_{ss}(f)=\Phi_{aa}\left(e^...
- 343
3
votes
1
answer
974
views
PSD scaling due to the windowing
I am struggling with the following problem for a while: If I have signal of duration N and I apply window (assume rectangular window) of size M < N how will this influence PSD of that signal after ...
- 181
2
votes
1
answer
9k
views
FFT and Power Spectrum Normalization
On many websites, including MathWorks, it was suggested to normalize the fft spectrum (MATLAB or numpy) by dividing it by the total number of samples ($N$). For a sinusoidal signal, for example:
$$x(...
- 175
2
votes
2
answers
392
views
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 $\...
2
votes
2
answers
4k
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, ...
- 1
2
votes
1
answer
2k
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 ...
- 23
2
votes
1
answer
150
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 ...
- 155
2
votes
3
answers
568
views
Making the units of a analytically calculated PSD consistent with the units of an FFT
One thing that has always puzzled me is making the units of an analytically derived Power Spectrum Density (PSD) consistent with the units of an FFT.
Let's say we record the output of a frequency ...
- 199
2
votes
1
answer
471
views
Why coherence function calculation needs averaging of different segments of the signal?
I am trying to understand coherence function calculation. I am working with a non-linear system without any noise. Coherence function is defined as:
I understand that coherence is 1 for N=1, but I ...
- 21
2
votes
2
answers
149
views
Contradictory results from power spectral densities and autocorrelation in shot noise
I have a white noise generator circuit which involves a Zener diode meant to undergo breakdown across a resistor $R1$, and am trying to compare power spectral densities and autocorrelation of the ...
- 121
2
votes
1
answer
2k
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 ...
- 21
2
votes
2
answers
7k
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 $B_{\rm rms}$ ...
- 97
2
votes
2
answers
2k
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 ...
- 123
2
votes
2
answers
1k
views
Signal power without FFT
I have an EEG signal thats about 1second long, sampling frequency of 256Hz, measured in microvolts, and I want to calculate the power of a specific frequency band (8-12Hz)
I believe the correct way ...
- 305
2
votes
1
answer
3k
views
PSD of a sum of two stationary real signals
I have 4 signals ($w_1(t),w_2(t),u_1(t),u_2(t)$ of which I know the power spectral densities (PSDs) $S_{w_1,w_1}(\omega),S_{w_2,w_2}(\omega),S_{u_1,u_1}(\omega),S_{u_2,u_2}(\omega)$ and the cross PSD $...
- 23
2
votes
2
answers
480
views
Band-limited random signal with arbitrary distribution?
I'd like to generate a random discrete-time signal that is band-limited to some bandwidth B (by means of a digital filter, ie in MATLAB). The catch is that I'd like this signal to have an arbitrary ...
- 29
2
votes
1
answer
4k
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 ...
- 23
1
vote
2
answers
4k
views
Pa^2/Hz to dB/Hz conversion
I have PSD data from an computational aeroacoustics analysis, which is in the units of Pa^2/Hz. I want to convert this to dB/hz; would it be correct if I use PSD[in dB/Hz] = 10log10(PSD[in Pa^2/Hz]) ...
- 71
1
vote
1
answer
231
views
Magnitude response of mirrored (with respect to unit circle) poles and zeros
I just want to check that my understanding about the following paragraph from Optical Filter Design
and Analysis by Christi K. Madsen, Jian H. Zhao is correct:
A filter’s magnitude response is equal ...
1
vote
2
answers
2k
views
Autocorrelation for periodic signals
Autocorrelation for power signals is defined by $$R_x(\tau)=\lim_{T\to\infty}\frac{1}{2T}\int_{-T}^Tx(t)x^*(t-\tau)dt\tag{1}$$ Is it true that for periodic signals $(1)$ can be computed by $$R_x(\tau)=...
- 726
1
vote
2
answers
7k
views
Parseval's theorem - Average Power
I want to calculate averaged power of a time-domain signal by means of its spectrum. I guess Parseval is the right tool.
So I sample a sinus of 100 Hz 10000x within one second.
Unfortunately the sum ...
- 133
1
vote
1
answer
201
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 ...
- 384
1
vote
1
answer
572
views
Oversampling while maintaining noise PSD
I'm designing a digital PID for control and stabilization of laser amplitude. The noise PSD of the laser intensity is around -140dB/Hz, and I want to servo that between DC and 100kHz. I think I've ...
- 113
1
vote
0
answers
332
views
Lost power while using FFT with apodizing mask
Previously I asked this question about FFT artifacts.
The solution that is most easily implemented is using an apodizing mask on the original image, tapering the borders to zero making the image left-...
- 263
1
vote
1
answer
626
views
Is there a simple way to determine the peak power spectral density values for a simple linear combination of sine functions?
I'm trying to acquire a better understanding of the heuristics behind power spectral density (PSD). In particular, for a very simple function, is it possible to determine the peak PSD values from ...
- 261
1
vote
2
answers
452
views
1
vote
1
answer
362
views
While calculating the power spectral density (PSD), why is there a roll-off at the end depending on the sampling rate?
In these power spectral density plots shown above (taken from the web 1,[2]), the spectra show a roll-off at the highest frequencies, as shown in the figure. For my own example, when I calculate PSD ...
- 33
1
vote
1
answer
855
views
Apply band pass filter (BPF) before calculating the power of a signal (PSD)?
From my understanding PSD tries to give a good estimation on the power each frequency attributes to the overall signal power.
If I am only interested in a frequency range $(\omega_0 \leq \omega \leq ...
- 113
1
vote
1
answer
619
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
...
- 383
1
vote
1
answer
996
views
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 ...
- 155
0
votes
3
answers
8k
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 ...
- 23
0
votes
1
answer
183
views
How to plot in MATLAB the PSD of two signals with different bandwidths
I would like to plot the power spectral density (PSD) of this signal
$$y(t) = x(t) + i(t)$$
where both $x(t)$ and $i(t)$ are binary phase shift keying (BPSK) signals with baseband bandwidths $W_x/2$ ...
- 141
0
votes
2
answers
2k
views
FFT of signal data with windowing, overlapping and averaging
This is my first ever question here so the help is really appreciated.
I am performing FFT on a signal. I want to perform windowing, 50% overlapping and averaging to the signal. There is a function <...
0
votes
0
answers
121
views
gmsk: suppression of higher-frequency spectral components
I study gmsk modulation and worked with gmsk implementation, BT = 0.5. I have decided to test with BT = 0.25, which is used for near Earth communicaiton.
Spectrum of output signal with BT = 0.5, ...
- 377
0
votes
2
answers
465
views
Measuring amplitude of a spectral component
I'm trying to measure the amplitude of a spectral component in a signal. The component's frequency is always known beforehand.
I take a given number of samples, apply the flattop window to reduce ...
0
votes
0
answers
77
views
MEMS Microphone Convert V to dBV and Performing FFT
At first is sampled data from the IMP23ABSU MEMS mic converted to V by multiplying each sample by the conversion factor $ \frac{1}{32786} $. Then i want to calculate the FFT and PSD after applying a ...
- 121
0
votes
1
answer
347
views
How to interprete the standard deviation of the psd in dB?
I have done a power spectrum density estimate using Bartlett's method. However, I was wondering if it is also possible to get a sense of the variation of the averaged spectra.
I have plotted the mean ...
- 109
0
votes
1
answer
807
views
what the difference between spectral density and the power spectral density?
What is the difference between the spectral density and the power spectral density,
Or they are the same thing?
In fact, I find this term in the book of GODA 2000.
- 3
0
votes
1
answer
102
views
Autocorrelation to diagnose faults
I'm attending a very practical course on signals and i have some doubts, i hope to receive answers in layman terms.
1) My prof said i can use the autocorrelation of the output of a process to ...
- 217
0
votes
2
answers
976
views
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 ...
- 555
0
votes
1
answer
492
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 ...
- 303
0
votes
1
answer
1k
views
Calculating Cross Power Spectral density between two complex signals
I have a small misunderstanding of cross power spectral density between two complex signals. I know that it is the Fourier transform of cross correlation between two signals. Let's say the complex ...
- 59
0
votes
1
answer
1k
views
Calculating PSD, Cross PSD by using FFT outputs
I am having the FFT results of two distinct voice signals. Let's say the FFT results of these two signals are of the form (a+ib) and (c+id). Now, I want to calculate the PSD of each signal and also ...
- 59
0
votes
1
answer
1k
views
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 ...
- 197
0
votes
0
answers
4k
views
Generate time-domain random signal from PSD
Given an analytical description of the PSD, for example (MATLAB "pseudocode"):
...
- 473