# Questions tagged [power-spectral-density]

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

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### 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 ...
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### FFT Artifacts and their cause beyond frequency resolution

I am trying to work through an issue with an FFT for audio : I have no spectral leakage while playing back audio, but the moment I change or zero out a value in any of the FFT bins, artifacts are ...
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### Equivalence between two PSDs

I'm very very new to these topics, as I started last week my master thesis (mechanical engineering) on something related to vibration analysis. From an engine RPM distribution and the acceleration ...
1 vote
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### What is the best way to decide whether a periodic signal is present in a noisy environment with a limited number of samples?

Suppose I have few samples (e.g. 20) of a decaying sinusoidal function and I am heavily noise-dominated (SNR ~1, noise is Gaussian or Poissonian). Let's think of e.g. y(t) = A \, \sin(...
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### Power spectral density and scaling

I know that PSD is the FT of the auto-correlation function. Does this mean that if we multiply a signal with a real-valued coefficient (to alter its amplitude), the PSD of this new signal would be the ...
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### how to convert W^2/Hz to dB/Hz?

I have power spectral density data in W^2/Hz? I want power spectral density in dB/Hz. How to convert W^2/Hz to dB/Hz? I saw some answers. But I did't understand. Please explain
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### PSD to FFT for audio [duplicate]

I'm trying to convert a noisy input to fft and extract the signal using a local average. By the way, after the transformation of fft, it was found that the values of adjacent times of the same ...
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### What a SDR can (and cannot) tell about a received signal's power/energy

I'm rather new to SDR and I'm still wrapping my head around understanding how it functions. I greatly appreciate it if you guys can help me understand what's going on. From what I've gathered, an SDR ...
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### 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, ...
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### Power Spectral Density and Wiener–Khinchin theorem for 2 different stochastic processes

I know the famous Wiener-Khinchin theorem for stationary random processes: the Fourier transform of the autocorrelation function of a stationary random process is equal to the Power Spectral Density ...
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### why need de-correlated signal for measuring phase noise in laser

when measuring phase noise from a laser by using heterodyne method , we will get the output signal as de-correlated. why we using de-correlated output for phase noise mesurement. how it is related to ...
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### understanding a spectrum of a modulated signal

I plot a spectrum of a modulated signal. It is a GMSK modulated signal. My goal to find the best parameter for a realisation it. My first spectrum with oversampling ration M = 4 and BT (the product of ...
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### Power of signal in specific frequency in FM and AM modulation

My professor gave us the following problem: Given a sinusoidal signal with $f_m = 1KHz$ which is put into an AM and FM modulation find the modulation index of FM and AM if you know that (amongst ...
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### Power Spectral Density estimation method for a general signal

Starting form the following input parameters: samples = 3372 duration = 5.2404810335956297e-05 ...
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### What is best filter to get 1/f(^alpha) that is linear on a log(PSD) vs log(Frequency) plot

I have a white noise signal that I plot on a log(PSD) vs log(frequency) plot. Now I want to filter that signal with several different filters to to get different alphas (0.5 to 3.0) in the 1/f^alpha ...
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### Computing Peak Value of Tones FFT

I'm synthesizing a tone, computing the FFT, power and then normalizing by the sampling rate and FFT size to get the magnitude in dB/Hz. ...
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### Plot the Power Spectral Density for a signal in Matlab

I have an OFDM signal x, generated using QAM modulation, I first use the command in matlab y1 = ifft(x); to generate the time-...
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### Why there is a difference from amplitude calculated from PSD and the real one? [duplicate]

I make a script in python to extract amplitude from power spectral density. I try to verif it but I have a difference between the real amplitude and the amplitude extracted from PSD. To calculate the ...
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### How to take amplitude and frequency from the power spectral density?

I try to take the amplitude and the frequency from the power spectral density. So I make a time series with a 5 component waves, then I draw the PSD with the welch method. Now I need to take the ...
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### Combining multiple signal acquisitions to produce one big FFT

I found myself in working with an FFT that does not have sufficient frequency resolution and I would like to increase this sensitivity. Since I have to perform this FFT on multiple noise acquisitions (...
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### How to obtain the wave height "H" /wave period T from the spectral density S(f)

I have the equation of the power spectral density $S(f)$. I seek $(H,f)$ of each sinusoid which $H$ is the magnitude and $f$ is the frequency. How to calculate $H$ from $S(f)$? $S(f)$ is the spectral ...
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### 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.
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### How to draw the PSD from a time series

I try to draw the spectral density of a time series in order to compare it with the theoretical one. Please can any one help me to do this. This is the time series of all the data. Thanks Dan Boschen ...
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### Best way to get the bin amplitudes of an audio DFT "normalized" 0-1

I'm working on a spectral processing plugin that's predicated on allowing the user to manipulate per-bin values in an STFT algorithm. I normalize the bin amplitudes by diving them by $N$ (number of ...
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### For two signals having a common frequency, w, and differing by a fixed phase shift, why is the coherence even defined at frequencies other than w?

This question is related to one posted a couple years ago at (Why the spectral coherence is unity for all frequencies between single-frequency time series and itself). Suppose two signals have common ...
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### Questionable results of on-line butterworth bandpass filtering using scipy.signal.lfilter

I have a data_stream that I'm attempting to filter using two on-line butterworth bandpass filters to extract two frequency bands of interest. The original ...
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### For two sinusoidal waves, what does the magnitude of their coherence tell us, and why do the periodogram and csd commands yield incorrect results?

Suppose I have 2 seconds of data sampled at 1000 Hz., and two sinusoids differing only in amplitude and phase shift: ...
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### Calculating instantaneous power of a frequency band in a 1-d signal

I am trying to calculate the instantaneous power of a 1-d signal within a particular frequency band in an on-line, real-time, streaming application. I have tried using sliding window FFTs but these ...
1 vote
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### 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 ...
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### Why does the variance of the Empirical Transfer Function Estimate not decay with increased sample points?

Please refer to Ljung's Lemma 6.1. In short, this lemma tells us that for a given LTI system $y[n]=g[n]*u[n]+v[n]$ where $v[n]$ is a stationary stochastic process with a zero-mean and a finite power ...
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### Reduce PSD Computation without Time Information Loss

Every computation cycle I get a large array D that is X IQ samples long, sampled over several milliseconds. I am then taking the PSD via the scipy welch function each cycle to detect short bursts of ...
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### Effect of sampling a cont. stochastic process on the variance

I am trying to understand the estimation of the power spectral density of a continuous time stochastic process from it's samples. Consider a normal wide-sense stationary white noise process with ...
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### Understanding spectral leakage in a pink noise dominated signal

I've been reading about power spectral density estimation based on the DFT, about spectral leakage, windowing functions and the Welch method. I've recorded a signal that's supposed to be pretty much ...
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### Units of PSD converted from spatial to temporal frequency

I am putting together some simple ride comfort models that use road surface PSDs from ISO 8606 (road surface profiles) as inputs to a quarter car suspension model to produce body acceleration spectra. ...
1 vote
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### Trying to understand the nperseg effect of Welch method

I am new in DSP and I like to compute the correct PSD. I have a 2s signal sampled at 256Hz I compute the psd ...
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### how to improve the noise estimation in PSD for non-coherent sampled data?

I am testing an ADC and the signal generator's frequency cannot be programmed to be exact so I am always doing non-coherent sampling (the noise/phase noise is ok, but low in precision). When there is ...
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### How does the RMS value of noise varies with sampling frequency?

I have been trying explore the background rates due to thermal noise (instrumental) through a simulation (python). So, what I have been essentially doing is the following ...
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### Derivation of Clarke's Doppler power spectral density

I am reading Wireless Communications by Andrea Goldsmith. I have some issues in the derivation of Clarke's Doppler power spectral density given there. 1)For beginning the autocorrelation of the in ...
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### Predicting distribution of integral of random process from power spectral density?

Suppose I have a random process $X(t)$ and I know the power spectral density of $X(t)$, $S_{XX}(f)$. What can be said about the distribution of $Y(t) = \int_{t'=0}^T X(t') dt'$? Bear in mind I have a ...
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### PSD of Poissonian shot noise

I have a signal $R(t)$ that is DC with shot noise. It has units of events per second. I am trying to understand this signal in a continuous-time picture. In time-domain, I can model it as a series of ...
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### Deriving a simple relationship between the PSD of $x(t)$ and the PSD of its square $x^2(t)$, assuming $x(t)$ is a white noise

Let $x(t)$ be a discrete time random process exhibiting a Gaussian density and a white noise, and a zero mean value. I am interested in deriving $S_{x^2}(f)$, the Power Spectral Density of $x^2(t)$, ...
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### What is the magnitude and phase of the wave represents in the k-space or Fourier space?

#Code from https://stackoverflow.com/questions/70768384/right-method-for-finding-2-d-spatial-spectrum-from-cross-spectral-densities I've an array of seismic sensors (say, N=34). Every sensor collect ...
1 vote
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### Fourier transform from the PSD

I need to compute the Fourier transform o the time derivative of the autocorrelation function (ACF) of a discrete signal with sign changed. Lets call it $Y(\omega)$. I had some computations problems ...
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### Issues on EEG PSD feature extraction using signal.welch

I am new to EEG signal processing and I am having some issues on calculating PSD using scipy.signal.welch. I am trying to implement a function to extract PSD features. The input of this function is a ...
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### How to calculate the average power of each frequency band?

I have EEG data from 30 participants, each recording is about 3 mins, and I'm trying to calculate the average power of each frequency band. I tried using Welch's or multitaper functions, but my values ...
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### How to select parameters suitable parameters for a spectrogram

I have a limited background in DSP but I need to generate a spectrogram of an electrocardiography (ECG). I am using the scipy.signal.spectrogram and I need to set ...
Given a stationary process signal with PSD $$S_u = \Lambda(f)$$ How to find the mean, power, and variance of the signal? I know how to find power given PSD (integrating from -inf to inf over f). ...