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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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Generate a Time Series from Power Spectral Density Python

I am trying to generate a time series from a defined PSD function, however i tried to do this in python , with the following steps: Define the Power Spectral Density Define the time parameters Define ...
zouatine mohamed's user avatar
3 votes
5 answers
250 views

Energy and Power: Power Spectral Density is units of Energy

To help focus answers: The following is specific to “Energy” and “Power” as used for signal processing, not physical units of energy and power (then to ask can units of “Watts” and “Joules” be used, ...
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Two meanings for "innovation" in Wiener filter are the same?

This is related question to A question about Wiener filter based on Linear Estimation by Kailath, based on the textbook Linear Estimation by Kailath. In that link I talk about how I first learned what ...
monad's user avatar
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A question about Wiener filter based on Linear Estimation by Kailath

In my linear estimation class based on the textbook Linear Estimation by Kailath, we went through the process of finding LLSE of $\hat{x}(t+\lambda)$ for fixed $\lambda$ given $\{y(\tau)|-\infty<\...
monad's user avatar
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Why is the sample spectrum considered inconsistent?

In multiple sources of the literature, e.g. here or here, it is stated that the sample spectrum (i.e. calculating the spectrum of an input signal by simply squaring the magnitude of the DFT) is ...
student1's user avatar
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Possible to combine and/or compare a swept Sine and a wide band noise signal?

I am working on a problem where two profiles need to be compared. One is a swept sine in $m/s^2$ (Acceleration) and the other is a sine-on-random signal composed of a swept sine $m/s^2$ and a random ...
SpillTheFFTea's user avatar
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Comparing custom Welch periodogram with Julia's Welch periodogram

I wrote my own PSD struct in Julia for practice purposes. It involves two type of constructors: a "direct" PSD and a <...
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How to find frequency , location and phase of two sinusoid signal buried in noise?

There is a data set which has two different sinusoids buried in noise. Data record has following properties: A data records with a total data length of 2048 points. The sampling frequency is 100 Hz. ...
Thouhidul Islam's user avatar
1 vote
1 answer
70 views

What factors could affect the scale of PSD estimation?

I was required to program a function in R to estimate power spectral density of EEG data. The function I created is, I think, rather standard, and estimates the PSD of a signal by computing $$ \frac{2|...
lafinur's user avatar
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Effects of Hanning window on power

I have written this function in R to compute the power spectrum density (PSD) of a signal: ...
lafinur's user avatar
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computing the averge power spectral density with python

In order to compute the power spectral density of a signal, we can use np.fft.ftt in python in the following formula: ...
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Losing my mind over simple conversion of common Acceleration PSD-Units: g²/Hz to (m/s²)²/Hz

Because it causes confusion within my team I wanted to create a simple overview on how to convert from one PSD Unit to another. I know it is really simple but I've obsessed over it for a few hours. I ...
SpillTheFFTea's user avatar
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1 answer
45 views

Need help understanding FFT for timeseries analysis?

I am studying the seismo-ionospheric anomalies associated with the Japan earthquake using total electron content derived from a GPS signal. I am trying to detect acoustic-gravity waves in the signal ...
Imtiaz Nabi's user avatar
1 vote
1 answer
92 views

Blackman-Tukey PSD in Python

I am trying to calculate the Blackman-Tuckey (BT) PSD in Python to check my understanding (getting started with signal processing). I have tried making the calculation myself and compare it with Scipy'...
opengisapprendice's user avatar
3 votes
1 answer
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Does oversampling lead to colored noise?

Suppose we receive $R(t)=X(t)+W(t)$, where $X(t)$ is band-limited to $[-B/2, B/2]$ and $W(t)$ is white Gaussian noise with autocorrelation $R_W(\tau)=\frac{N_0}2\delta(\tau)$. If we filter $R(t)$ ...
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Filter coefficients hamming window for low-complexity Welch PSD computation

I am trying to implement the proposed method from this paper 1, to eventually have a more efficient PSD computation for feature extraction on a microcontroller. The method is suitable since I am using ...
michael's user avatar
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How to produce a noise spectrum from an rms velocity specification?

For a dynamic model I am looking at the appropriate input to analyse the performance under the influence of floor vibrations. The norm is an ISO VC-C floor spectrum as displayed in the image. However, ...
Jan's user avatar
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1 vote
2 answers
124 views

arithmetic mean vs geometric mean of Power Spectral Densities (PSD)

Sometimes I see papers that average the log of PSDs (i.e., in dB space), instead of the PSDs themselves. So they are doing a geometric averages. I found a paper that shows that geometric mean has some ...
Chachni's user avatar
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name for the product of oscillation amplitude and frequency over spectral bandwidth

In the field of signal processing, when a spectral peak is fitted with a Gaussian, is there a name for the quantity obtained by multiplying amplitude with frequency and dividing by the standard ...
fbaroni's user avatar
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1 answer
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NBFM and WBFM power spectral density

The power density of a general FM modulated signal(with modulation index close to 1) looks like this: By picking out the carrier frequency we can make the FM signal narrowband or wideband.Now ...
Root Groves's user avatar
1 vote
1 answer
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How to feed multi-channel spectrograms to Deep Neural Network?

I am using a 14 channel EEG device. To do away with the need for any handcrafted features, I wish to implement an ML classification task with the EEG data collected using deep neural networks (such as ...
Anantha Krishnan's user avatar
1 vote
1 answer
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Window Type Effect on Pwelch vs ShortTimeFFT PSD Result?

I am trying to make sure I understand the output scaling of pwelch. I am using the PWelch function to compute the PSD of a signal and I have manually computed the PSD from an STFT output. The results ...
Michael's user avatar
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Finding the Power Spectral Density of $x(t)$

Consider a binary signal $x(t) = \sum_{n=-\infty}^{\infty}a_ns(t-nT_b)$ where, $$ s(t) = \left\{\begin{matrix} 1& t\in[0, T_b) \\ 0& o.w. \end{matrix}\right. $$ and $$ a_n = \left\{\begin{...
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How to accurately estimate the quality factor of a noisy signal

I'm currently interested in measuring the quality factor of a noisy signal. For the purposes of example, consider a single degree of freedom mechanical system excited by white noise: \begin{equation} \...
AnonymousPlatypus's user avatar
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Power spectral density of a optical modulated signal intensity [duplicate]

If $E(t)$ is a carrier modulated by a complex baseband signal, what is the PSD of $|E(t)|^2$?
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What are the spikes here in the spectral analyser?

I'm learning to use the spectral analyser in Simulink, and tested it with a 500kHz square wave (sampled at 1MHz). When I set the Resolution Bandwidth (RBW) to 700Hz, the plot was beautiful and shows ...
George guo's user avatar
1 vote
1 answer
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$i^{\text{th}}$-dimensional autocorrelation function

I am referring to the work of Stephen A. Billings on "Identification of a class of nonlinear systems using correlation analysis" from the year 1978, where it is mentioned that the $i^{\text{...
Neuling's user avatar
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Implementing a non-causal Wiener filter

I'm attempting to implement a non-causal Wiener filter for removing additive white noise from a measured signal. I've had some trouble and I have reduced my problem to a demonstration on simulated ...
Marc's user avatar
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2 answers
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Fundamental question about Autocorrelation

I need help! I'm trying to calculate the Power Spectral Density of a quantum operator ($\delta \hat{n}(t)$) given by: $$ \delta \hat{n}(t) = A(t)\delta\hat{a}(t)+A^{*}(t)\delta\hat{a}^{\dagger}(t) $$ ...
Pedro Pinho's user avatar
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PSD of real and imaginary parts of complex envelope of a bandpass signal

I know that we can write a real bandpass signal x(t) as: $x(t)=x_c(t)\cos\omega_ct + x_s(t)\sin\omega_ct$ $x_c(t) = 2x(t)\cos\omega_ct$ for $|f|<W$ $x_s(t) = 2x(t)\sin\omega_ct$ for ...
Ang's user avatar
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1 vote
1 answer
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Find the spectral density of the square of white noise with a limited bandwidth

I tried the following order of operations: Let's consider the spectral density of the square of white noise with with a limited frequency band. If $S_{x} \! \left( f \right)$ is the spectral density ...
Raist Majere's user avatar
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1 answer
52 views

Derive PSD of an MA(1) process

Suppose there is a moving average process of order 1 that also includes a zeroth term thus: \begin{equation} Y_t=\theta\left(B\right)X_t = \left(\theta_0+\theta_1B\right)X_t \end{equation} where $X_t$ ...
hydrologist's user avatar
5 votes
2 answers
238 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
3 votes
1 answer
89 views

The power of a sinusoidal component in noisy PSD

I am very new to signal processing and I have been doing a lot of reading on it but I don't seem to understand everything. I'm hoping you can help my confusion a little. I am simulating a lidar signal ...
IhmeKyselijä's user avatar
1 vote
0 answers
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Calculation of the discrete cosine transform

I am wanting to use the discrete cosine transform to relate the autocovariance function of a process to its periodogram. Following Chris Chatfield's book (Time Series Analysis, p129), I am wanting to ...
hydrologist's user avatar
6 votes
2 answers
462 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
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0 answers
33 views

Periodogram Formula for sampling noise

The formula I know for the periodogram is $$I\left(f\right)=\frac{1}{NT}\sum_{n=0}^{N-1}\left|x\left[n\right]\exp\left(-2\pi fjnT\right)\right|^2$$ but for this one question I have which states that $...
namo's user avatar
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Allan deviation correct with one-side noise but wrog with two-side noise. Why?

I'm developing a Simulink model for noise according to the description of the algorithm of Accelerometer in this page: IMU simulation model. My system takes the RandomWalk (defined in [unit], being ...
Xwang's user avatar
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How to get Power Spectral Density of file using this research paper method?

I came across this research paper. In this they have mentioned power spectral density calculation of various file. I have read the paper and try to calculate and plot the graph, don't know it correct ...
i_am_learning's user avatar
2 votes
1 answer
101 views

Smoothening Noisy FFT

I've got the following FFT with a sampling frequency of 192 kHz that has around 17.000.000 samples. The signal is a hiss of escaping gas. This looks noisy and i want to determine the characteristic &...
Tom's user avatar
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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 ...
Tom's user avatar
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Finding mean, autocorrelation, and power spectrum of $y[n]=(x∗h)[n]$ where $x[n]$ is zero mean white gaussian noise

If given $x[n]$ is zero mean white Gaussian noise with variance $\sigma_x^2$, and a filter with a known impulse response $h[n]$, how would I find the mean, autocorrelation, and power spectrum of $y[n] ...
Mark Boccelli's user avatar
1 vote
1 answer
63 views

Deriving Power Spectral Density of $a \cdot x(t)+b$ if PSD of $x(t)$ is known

I want to derive the PSD of $a \cdot x(t)+b$ if the PSD of $x(t)$ is known. Here $a$ and $b$ are constant. The signal $x(t)$ is a zero mean stationary random variable. Thanks in advance.
Janmejay's user avatar
1 vote
1 answer
71 views

Why is the FFT of an even real valued vector not real?

I am trying to find the PSD of a signal by taking the DFT of its auto-covariance sequence. My code is as follows ...
Asmodeus's user avatar
3 votes
1 answer
249 views

What's the exact definition of the power spectral density function?

I learned from my signal processing course that PSD is the Fourier transform of the autocorrelation function. $$\mathscr{F}\Big\{\mathrm{E}\big[x(t)x(t+\tau)\big]\Big\}$$ Today I took my statistic ...
Xiangyu Cui's user avatar
1 vote
1 answer
71 views

PSD of the sum of two zero-mean white noise signals

I am trying to solve the following exercise, where $y(t)$ is the sum of two signals $x_1(t)$ and $x_2(t)$ with each of them being the product of the convolution of $e_i(t)$ with $h_i(t)$. So far I ...
Asmodeus's user avatar
0 votes
1 answer
277 views

How to calculate The Signal-to-Noise Ratio (SNR) in dB (different units)?

Recently, I've ventured into a new domain that I intend to incorporate into my work. After thorough research and consultation, I've found this model to calculate the data transmission rate (Capacity). ...
user4594525's user avatar
2 votes
1 answer
83 views

Why a windowed signal is considered to evaluate the Power Spectral Density?

Let's consider a real function of time $x(t)$ being a Fourier-transformable signal. The synthesis equation states that: $$x(t)=∫_{-∞}^{+∞}X(f)⋅e^{2πjft} df $$ Meaning: $x(t)$ can be seen as the sum of ...
Kinka-Byo's user avatar
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1 answer
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Time-varying shot noise generation

I'd like to model the behavior of photodiodes, the input is like data bits (0 & 1) where each bit is represented maybe with 100 samples / bit and the bit rate is $B$ bits/sec with period $T_{bit}=\...
Mohamed Osama's user avatar
0 votes
1 answer
169 views

How to get the total power of the signal from sound pressure levels?

I have the Sound Pressure Levels (SPL(f)) of noise signals in the frequency domain. I need to get the total acoustic power of the signal between a range of frequencies. Initially, I compute the Power ...
Student's user avatar

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