Questions tagged [power-spectral-density]
The Power Spectral Density (PSD) is the distribution of signal power over frequencies.
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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 ...
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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 ...
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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 $...
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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 ...
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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 ...
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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 &...
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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 ...
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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] ...
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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.
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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
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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 ...
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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 ...
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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).
...
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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 ...
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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}=\...
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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 ...
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How do you average the power spectra across multiple samples to compare 2 conditions?
I have physiological signals from samples under 2 conditions and want to compare the difference in frequency content between the conditions. Specifically,I'd like to compare the average power spectrum ...
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Generating time-domain noise from PSD
I have a question regarding generating a time-domain noise from the power spectral density (PSD), this was addressed in this question (How to generate time-series from a given one-sided PSD?) but I ...
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Noise spectral density and windowing
I am wondering about the definition of Power Spectral Density, in the context of measuring noise, i.e., Johnson-Nyquist (thermal) noise.
Usually a windowing method, like Welch's method, is used to ...
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How to do FFT on I and Q DATA in Python
I am Working on a Satellite data, where information is stored in a Raw data exchange format .prd file, i have extracted the information in csv file where i got the I and Q data in decimal, now i ...
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DSSS spectrum not flat
Why is the PSD of the simulated BPSK/DSSS in AWGN not flat? Here are the simulation parameters:
BPSK symbols are randomly generated and are {+1,-1}
Spreading factor = 128
Spreading code is a randomly ...
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Measuring thermal noise of RLC circuit
I am confused about Johnson-Nyquist noise. Specifically, where does bandwidth come in?
Thermal noise voltage is usually defined as something like: V^2=4kT∫R(f)df, integrated over a bandwidth.
I am ...
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Weiner Filter - why does this computation explain that the necessary filter is a weiner filter?
$X_1(t), X_2(t)$ are random WSS processes with expectation 0, and correlation functions $R_{X_1}(\tau), R_{X_2}(\tau), R_{X_1,X_2}(\tau)$ $n(t)$ is a white noise with SPD $S_n(f) = \frac{N_0}{2}$ ...
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Power spectral density convergence for finite samples
Suppose a sequence $\{a_k\}_{k=0}^{\infty}$ has power spectral density
$$
S_{\mathbf{a}}(f) := \lim_{n\to \infty}\mathbb{E}\left[\frac{1}{f_0 n}\left| \sum_{k=0}^{n-1} 2\pi f_0 a_k \exp(-2\pi ikf/f_0) ...
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Power spectrum, Power spectrum density and windowing functions
At the moment I have some trouble understanding the different methods. I would like to calculate both the Power Spectrum and the Power Spectrum Density.
As the name suggests I thought that $PSD = PS / ...
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How can I convert a 1/3rd octave spectrum into a linear spectrum for use as a frequency response?
I have a one-third octave spectrum with 23 frequencies, and I want to use it as a frequency response to filter another spectrum, however that spectrum is specified linear with 2049 points.
I know I ...
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Average time-domain signal power from correlated Fourier transforms
Suppose I have real-valued continuous-time sequences $x_1(t), x_2(t), x_3(t)$ with Fourier transforms $X_1(\omega), X_2(\omega), X_3(\omega)$. I know that $X_3(\omega)=H(\omega)( aX_1(\omega)+bX_2(\...
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Confusion with Complex Gaussian process with Auto-covariance
I have a complex sequence $z(t)$ in time which I know to be a Gaussian process. I read that the complex Gaussian process is not only characterized by the covariance, but also the pseudo-covariance ...
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Relative loss of power and length of signal
I have EEG signal data from a single channel for 150 similar events (epochs), each spanning 11s which might be accessed from here.
I ran the following code block in MATLAB to remove line noise at 60 ...
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noise synthesis arbitrary PSD
I have noise measurements for a circuit, in units of noise power (measured in Watts against a known load), per frequency bin.
For simulation purposes, I wish to synthesize noise with the same spectral ...
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Three dimensional Wiener-Khinchin formula for incompressible isotropic random field
When I am reading Uriel Frisch's book "Turbulence", on page 55 he claimed that the Wiener-Khinchin formula for an incompressible isotropic random field, such as the velocity field of ...
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Lowpass filter to downsample data
I have some data that is sampled at a certain rate (16384Hz). I am only interested in the 10-30Hz region, so I want to downsample the data. My idea to do this goes as follows:
I apply some kind of ...
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How does downsampling decrease the noise power?
I read one equation from a technical document, i.e., assuming the time-domain white Gaussian noise samples with variance $\sigma_{TD}^{2}$ in dB are sampled using ADC with sampling rate $f_{s}^{ADC}$, ...
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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 ...
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Noise variance of DT samples from CT track-and-hold signal
(I will be referring to info from these slides in this post, for your reference.)
Consider first for comparison a typical CT low-pass filter, without any sampling, for example implemented by the RC ...
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Abnormal Y-axis value after performing FFT
I have an UFF file which consists of Vibration data. The objective is to convert the timewaveform signal to frequency domain.
I have written a python script to convert the timewave form signal to ...
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What is the jitter effect on the spectrum of impulse train?
How to derive the sepctrum of $$x(t)=\sum_{n=-\infty}^{\infty}\delta\left(t-nT-\tau_n\right)$$
where $\tau_n\sim N\left(0, \sigma^2\right)$
I assume that the randomness effect should behave as a low ...
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Check whether signal is periodic
I have a signal with multiple frequencies. The frequency changes depending on the amount of air flowing through the fuel snap. The signal resembles a square wave ranging from $0.4$ to $4.5$ Volts and ...
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MUltiple SIgnal Classification (MUSIC) for Frequency Estimation
I am trying to use MUSIC algorithm to detect individual frequencies of an incident signal. I read the original paper and some interesting books that explain the algorithm. I used the following ...
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Selecting Sampling Frequency for Welch Power Spectral Density plot for a daily frequency financial time series data on Python
I have obtained daily close price stock data ( and transformed them to logarithmic returns series data) from a Stock Exchange between 2 financial years, and I wish to generate a power spectral density ...
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Identifying frequency components only
I have a real world system of a rotating back and forth motion and the time domain data suggests that the data is a random signal (not a deterministic signal). I recorded discrete data points at a ...
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MUSIC Algorithm for 2D Power Spectrum
I am trying to use Frequency-wavenumber analysis for estimating speed of sound using two-dimensional data obtained via channel of arrays. The traditional technique is to use FFT to transform the data ...
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How is the PSD the Fourier Transform of the Autocorrelation function?
I am getting very confused with the textbook I am reading through: Modern Digital and Analogue Communication Systems:
3.8.1 Parseval's Theorem says that:
The total power in a power signal is its time ...
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Proof of the Wiener-Khintchine theorem in time domain
In a proof for the Wiener-Khintchine theorem (See p. 572-573)
I have seen the following operation being done:
\begin{align*}
S_{xx}(f) &= \lim_{T \rightarrow \infty} \int_{-2T}^{2T} Rxx(\tau) e^{-...
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Bispectrum vs cyclic spectrum
One of the definitions of the cyclic spectrum is
$$S^\alpha_x\left(f\right)=\lim_{\Delta f \rightarrow 0}\lim_{\Delta t \rightarrow \infty}\frac{1}{\Delta t}\int_{-\Delta t/2}^{\Delta t/2}\Delta f ...
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Power spectral density plot in terms of non dimensional frequency
I analyzed a voltage signal and plotted the PSD. However, I need to produce a power-spectral-density plot from the data in terms of non-dimensional frequency. How do I calculate the Strouhal number ...
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confusion understanding/interpreting power spectrum of audio in MATLAB?
Please find attached snapshot. I am confused regarding power spectrum in MATLAB as according to google definition in attached snapshot"the distribution of the energy of a waveform among its ...
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How can I plot the power spectra of a ST (Stratosphere Troposphere) Radar in MATLAB to estimate the doppler shift
Respected all,
I am trying to plot the power spectra of a ST (Stratosphere Troposphere) Radar to estimate the doppler shift. I am able to obtain a 3D plot between range, FFT point and Power density ...
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Power Spectral Density and Energy Spectral Density are both Fourier transform of autocorrelation?
I've been looking into both of these quantities and feel like I have a good understanding intuitively of what they each represent but according to Wikipedia both the PSD and the ESD can be computed as ...
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Computing Power Spectral Density from FFT vs Welch's method vs Periodogram [duplicate]
I'm looking into different ways to get the Power Spectral Density (PSD) (while toying around with python) of a discrete signal/time series, and I'm struggling to understand why I get (very) different ...
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