Questions tagged [power-spectral-density]

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

161 questions with no upvoted or accepted answers
Filter by
Sorted by
Tagged with
5
votes
3answers
5k 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) ...
5
votes
0answers
583 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 ...
3
votes
0answers
147 views

Physical significance of Power spectral density of sum of correlated random processes

For two processes $X(t)$ and $Y(t)$, PSD of $Z(t) = X(t) + Y(t)$ is $S_Z(\omega) =S_x(\omega)+ S_Y(\omega) + S_{XY}(\omega)+S_{YX}(\omega) $. If $X(t)$ and $Y(t)$ are orthogonal, PSD of the sum ...
3
votes
0answers
265 views

Noise PSD and sampling rate relation

Let's consider generating samples of a random process like white Gaussian noise (AWGN). Let's assume I am generating $N$ samples of AWGN with variance $\sigma ^2$ in MATLAB by using randn() funtion i....
2
votes
0answers
37 views

Relating Fourier and power-law descriptions of noise

I'm trying to understand this PDF, which is in English but has Polish authors, so there may be translation issues confusing me. The subject is the frequencies of sentence lengths in novels. Eq. (1), ...
2
votes
2answers
218 views

Frequency response of a microphone using a sine sweep

I want to determine the frequency response (magnitude, phase) of a microphone. I have another "good" reference microphone whose frequency response I know. I understand that I can use a good speaker ...
2
votes
0answers
50 views

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($\tau$)=...
2
votes
0answers
52 views

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 ...
2
votes
0answers
25 views

Proof that the Lomb-Scargle periodogram reduces to the classical periodogram when the sample is equally spaced

If we have a equally spaced sample, we can use the conventionally used periodogram: $$P_x(\omega) = \frac{1}{N_0}\left[\left(\sum_j X_j\cos \omega t_j\right)^2+\left(\sum_j X_j\sin \omega t_j\right)^...
2
votes
1answer
451 views

Confusion about PSD and RMS

Let's say I have a noise power-spectral-density (PSD) which is not flat and ranges from 0 to $f_1$ Hz in frequency. As we know, the total area under the PSD is equal to the total average power of the ...
2
votes
1answer
4k views

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 ...
2
votes
0answers
1k views

Yule-Walker PSD Estimate of an AR Process

I am trying to implement a Yule-Walker PSD estimation in Python but my results are not up to the expectations. In MATLAB, I would normally implement my functionality as follows: ...
2
votes
1answer
344 views

A few questions about the output value of dsp.SpectrumAnalyzer

I am testing the output values of dsp.SpectrumAnalyzer for a sine wave mixed with white noise. The $\sigma^2$ of the white noise is 1e-4, so I use 0.01*randn(1024,1)...
2
votes
2answers
122 views

Should I filter before calculating power, if I'm looking for relative changes in power?

I am building a "scanner" sort of program, which reads IQ samples from an rtl-sdr stick, and keeps track of the power on certain frequencies, in certain bands. I am interested in detecting activity ...
2
votes
0answers
40 views

Determining the point in a temporal signal when a periodic behavior begins to occur

I'm a newcomer to digital signal processing, so I'm looking for some general advice and direction on this problem I have. I have a signal like that shown below. Starting around x=40000, you can see a ...
2
votes
0answers
213 views

Noise analysis with periodogram. problem with different resolutions

I don't understand what happened in my simulation. I would like to perform a trade off between 2 ways to estimate power in frequency bands. I want to detect spurious frequencies. First method: I ...
2
votes
0answers
127 views

How to properly express periodogram over analog frequency?

Assume a signal $x[n]$ with $N$ samples and its $N$-point FFT $X[k]$. Assume also the simplest power spectral density estimator: $$ S_x[k] = \frac{\left| X[k] \right|^2}{N} $$ With this estimator, ...
2
votes
0answers
57 views

Stationary processes and their power

The top answer to this question: Power spectral density vs Energy spectral density states: However if random process is stationary, then it is for sure that it has some finite power over some ...
2
votes
0answers
892 views

Matlab: Estimating power spectral density of an experimental data?

How do I estimate PSD in matlab ? There are lots of methods to estimate, depending on application. I am using an experimental data to identify faults ( e.g. interturn fault of electric motor), which ...
2
votes
0answers
250 views

Is there any problem with my FFT method?

I am trying to analysis a system by Fourier Transform. my system has 3 dominant modes. (1,0.05) (0.51,0.01),(0.46,0.01) the pairs are defined as (freq,damping_ratio) I've got those result with ...
2
votes
0answers
828 views

difference (or relationship ?) between power spectral density, power density function and periodogram

What exactly is the difference or relationship between power spectral density and power density function? I thought they referred to the same thing but one article I need says to calculate both of ...
2
votes
1answer
174 views

Most appropriate spectral analysis method for a recording of a saxophone note?

I'm currently doing an investigation where I am attempting to resonant frequencies of an Alto Saxophone at various different notes. I have taken audio recordings of the notes with a sample rate of $...
1
vote
1answer
80 views
+50

Power spectral density of a simple continuous cosine and checking the correct average power can be recovered, as it should according to Parseval

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 ...
1
vote
0answers
42 views

How to simulate (in matlab or c) power spectrum of random brownian noise signal?

I have a semi random noise signal, it does have some periodicity however. I can estimate the power spectrum (of the blue signal, I thought that it would be more clear, because white noise is flat, ...
1
vote
1answer
37 views

How to create a wide-sense stationary time series with a frequency of 40 Hz?

I want to create a time series in MATLAB which has a peak frequency of 40 Hz but is also a wide-sense stationary random process. I then want to use power spectral density estimation to recover the ...
1
vote
0answers
63 views

Power spectral density vs. Fourier Transform

I am trying to understand the difference between the Power Spectral Density and the Fourier transform. Specifically, I am trying to understand why the power spectral density is useful and in what ...
1
vote
0answers
25 views

How to find the solution of nonlinear least square (NLS) equation for freqeuncy estimation

I am struggling to understand the theory of parametric methods for power spectral estimations of line spectra. And I want to find the solution of nonlinear least square (NLS) method for estimating ...
1
vote
0answers
142 views

Definitions of PSD, ESD and Autocorrelation

This question is going to encompass multiple areas and may not have a single answer but here it goes. I'm trying to conceptualize 3 different concepts and how they relate to each other. These 3 ...
1
vote
0answers
34 views

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 ...
1
vote
1answer
117 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 ...
1
vote
0answers
14 views

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 $\...
1
vote
0answers
33 views

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 ...
1
vote
1answer
73 views

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 ...
1
vote
0answers
64 views

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(\...
1
vote
0answers
150 views

Power spectral density of a pulse

A little background: I am simulating the response of an antenna to a pulse. The pulse has a wide frequency range, but the antenna only responds to a fairly narrow frequency. I can extract voltage and ...
1
vote
0answers
66 views

PSD of randomly positioned dirac delta train

Let $s(t)= \sum_{i=0}^{T} \delta(t-\tau_i)$, where $ \{ \tau_{i} \}$ are random integers between $0,1,\cdots, T-1$. What is the power spectral density of the signal $s(t)$?
1
vote
1answer
99 views

Cross power spectral matrix from PSDs and coherence using matrix notation

I have a vector containing all the PSD of a series of signals $\underline{s} = \left[ |S_{x_1x_1}| |S_{x_2x_2}| |S_{x_3x_3}| ...\right]^T$ I also have a matrix $\gamma^2$ containing all the ...
1
vote
0answers
51 views

Efficient audio power spectrum estimation

I am working on a small personal project where I want to control a matrix of roughly 100 actuators with an audio stream. The goal would be that the user can see/feel the music features in the movement ...
1
vote
0answers
335 views

frequency spectrum of a sampled signal, PSD and power discussion

Before I go into my question, I first want to review the basics of sampling a signal and at the same time I build the basics of my questions so that they make more sense. I know I have asked couple of ...
1
vote
0answers
90 views

How to generate the amplitude of a signal with a certain power spectral density?

I am a newbie. If I posted a question someone else already asked, please forgive me. Thank you! Now, I have a power spectral density named $P(f)$ as a function of $f$. Let's say this function is ...
1
vote
2answers
835 views

Quantify the difference between two audio spectrograms

I have two speech signals of the same length. They contain the exact same speech content but are recorded from two different microphones. I want to compare the differences between them. 1) Assuming ...
1
vote
0answers
51 views

Is power density invariant to Fourier Transform? Does it hold through derivation?

Assumptions We have a finite discrete measurement. Introduction I had some troubles determining a power spectral densities needed for Wiener deconvolution. Looking through the continuous equations ...
1
vote
0answers
240 views

What is the power spectral density after filtering?

Consider a signal $x(t)$, which is input to a pulse shaping filter with transfer function $g_t(t)$: $$x(t) = \sum_n d_n \delta(t-nT_s)$$ with $n$ an index from negative to positive infinity and $...
1
vote
0answers
348 views

Power Spectral Density of a WSS Random Process with 2D Discrete Fourier Transform

I'm trying to understand how the random process (RP) signal in discrete time domain is related to its power spectral density (PSD) in frequency domain if the signal is wide sense stationary (WSS). If ...
1
vote
0answers
42 views

Interpretation of steady state sensor signal

I try to understand some measurement results of an accelerometer MEMS sensor. I used a mikrocontroller which is sampling an accelerometer's analog signal with the built in analog-digital-converter. ...
1
vote
0answers
209 views

AWGN Build vs Randn noise do not match

I am generating noise in two different cases with the same SNR once using AWGN command which is a built in command and second time using randn function with the correct scaling however I am getting ...
1
vote
0answers
80 views

Epoching Data with no Events in mne?

I am new to Python and signal processsing, and I'm trying to create a spectrogram of EEG data taken during a course of general anesthesia. I would like to use MNE's ...
1
vote
0answers
799 views

Relationship between Wavelet transform and Fourier Power Spectral Density

Is there anyway to obtain the Fourier Power Spectral Density from a wavelet transform of a time series? I am particularly interested in this problem because I was wondering if there is any ...