Questions tagged [power-spectral-density]

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

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How to reprocess SDR data to be equal to that captured with a higher RBW

I have a data set that consists of max hold frequency vs intensity data from an SDR at a specific RBW. I want to reprocess the data as if I sampled it with the larger resolution bandwidth so I can ...
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42 views

Moving from deterministic signals to stochastic signals in s-domain (Power Spectral Density)

Assume we have the following system (coming from control systems theory, hence in s-domain) $ Y(s) = H_A (s) \cdot A(s) - H_B (s) \cdot B(s) $ I now wish to consider $a(t)$ and $b(t)$ as white noise ...
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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)=...
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spectrogram of a leak in a water pipe

I'm doing a work on the acoustic emission of a leak. I am using a 1.80 m cylindrical tube with water, and the leak is simulated by means of a tap that opens after I have applied negative pressure ...
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How the power spectral density changes under frequency scaling?

Let the power spectral density PSD of a random process be $$\phi(w) = \sum_{k = \infty}^\infty r(k)e^{-i\omega k}$$ where $\omega \in [-\pi,\pi]$ and $r(k)$ is the correlation function. I have to show ...
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1answer
93 views

Finding Minimum SNR or Minimum Detectable Signal Based on Noise Spectral Density

Imagine I have an $n$-bit sensor, whose noise spectral density is $V/\sqrt{Hz}$. $V$ is an exemplary measurement unit. The desired measurement bandwidth is also known. Is there a mathematical way to ...
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105 views

What is the point of smoothing an FFT or spectral density plot, and how does that affect the noise floor?

It appears that smoothing the FFT or spectral density plots of a noisy signal is a common practice. I see that common tools like MATLAB and Python have functions built in to their FFT tools to do just ...
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57 views

How many bins to include when calculating SNR from FFT?

I'm a scientist conducting an experiment that requires some signal processing. My expertise is not in signal processing, thus here I am. We've basically re-created an experiment conducted by other ...
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1answer
100 views

Is spectral density sometimes normalized by sampling rate rather than bin size?

I'm a scientist conducting an experiment that requires some signal processing. My expertise is not in signal processing, thus here I am. We've basically re-created an experiment conducted by other ...
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0answers
33 views

Power spectrum of modified process

Suppose there is a process $x(t)$ with power spectrum $$S_x(\omega)=\lim_{T\to\infty}\frac{1}{T}\left|\int_{-T/2}^{T/2}\mathrm{d}t\,e^{j\omega t}x(t)\right|^2,$$ ignoring the expectation value for ...
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How to calculate PSD if i have power vs freq spectrum?

i have a signal something like this how to calculate PSD? i have freq from 191000200 to 196500000 time gap or delta t = 1 or 2 sec, (what i mean is [tn] - [tn-1]) i will be computing in python any ...
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25 views

Why is the Periodogram Used as an Estimate of PSD?

Why is the periodogram method as given by Schuster (1898) - which is not a consistent estimate of the PSD - still used, as opposed to consistent non-parametric methods for estimating the PSD like ...
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Energy or power signal for continuous signal

I have solved $w(t) = 1dt$ and determined it as power but when $w(t) =\Pi\left(\frac{t}{T_0}\right)$ it is energy.
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Estimating Signal-To-Noise ratio from discrete time series

A hidden variable $x(t)$ (in my case, neuronal signal averaged over a brain area) exhibits dynamics on multiple timescales from milliseconds to seconds. An observable $y(t)$ is produced by convolving $...
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Why is it used the Power Density Spectrum (PSD) over an anylisis with the Fast Fourier Transform (FFT)? [duplicate]

I'm currently working with physiological signals (PPG and GSR) for emotion recognition but, from my research, I've found out that almost everyone in that area use a PSD analysis over a FFT analysis. I'...
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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 ...
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Is it interesting to look at two conditions and compare their power spectral density at frequencies?

so I am doing my thesis in Neuroscience and trying to prove the alpha blockade, i.e. the reduction in power of the alpha frequency band when the eyes are open compared to when they are closed. I used ...
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30 views

BW of a modulated signal

I come across different types of bandwidth. In digital modulation should it be null to null always? when do we use 3 db bandwidth?
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50 views

Produce PSD from a FFT output

I am using an FFT function in PHP language (https://gist.github.com/mbijon/1332348) which works very well, but cant produce PSD from its output: ...
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76 views

noise floor of attenuator

NF of attenuator is same as the attenuation value as the noise floor remains same but signal level gets attenuated? But NF of amplifier depends on the device as it increases both signal and noise?
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“How is the noise floor of RF section is mapped to ADC noise floor for a 10MHz BW?”

My interpretation is if a gain of 40 is used before AGC -40 dBm become 0 dBm and -121dBm (noise level) becomes -81dBm SNR remain same (assuming NF =0 for theretical purposes). Noise floor of ADC is (6....
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Why is mean-square summation of the area under the curve?

Would someone please kindly help me to nail this "simple" issue? My input is a matrix of power PSD and frequency. I need to get RMS and I read this http://vibrationresearch.com/wp-content/...
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Autocorrelation and Spectrum Density

Wiener–Khinchin theorem states that autocorrelation function and power spectral density are a Fourier-transform pair - see Wikipidia (and lots of other resources). That means autocorrelation should be ...
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Permutation test on two simultaneously recorded EEG signals

I have two EEG signals that are simultaneously recorded (and has been further synced) using two EEG devices, namely device 1 (ground truth) and device 2 (investigational device). Imagine one device ...
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1answer
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Find signal power in a band by integrating the PSD in a frequency band (and zeroing the out-of-band DFT bins)

I know that directly zero DFT bins outside a frequency band has the side effect of introducing ringing, as this post says Why is it a bad idea to filter by zeroing out FFT bins?. But what about ...
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Comparing similarity of two simultaneously recorded EEGs in freq domain

I have two EEG signals that are simultaneously recorded during the night (sleep). Imagine one device recorded from channel F4 and the other from Fp2. Now I would like to check the similarity of these ...
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1answer
31 views

Power Spectrum analysis arbitrary length signals

I have signals belonging to diseased and healthy samples recorded from multiple electrodes. These signals are taken monthly and are of arbitrary length (say 4-5 mins). I am planning to do a power ...
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152 views

Power Spectral Density from Probability Density Function

The samples of a signal $x[n]$ are i.i.d. and follow a triangular pdf with $a = 0,\ b = 2,\ c = 1$: The DC-power of the signal is $$\mu_x^2 = \big(\mathbb{E}(X)\big)^2 = \left(\int_{-\infty}^{\infty} ...
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Power in a frequency band: Spectral estimation versus time domain

I wish to find total power in a given frequency band within different time windows of a signal. I see two methods of doing so, first in the frequency domain. One could estimate the power spectral ...
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28 views

Changing Coherence function from float to fixed point

I want to calculate the coherence between two audio signals. After referring a few websites, I found that the coherence is calculated by using the equation $(1)$ which is as follows $$\rm Coherence = \...
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56 views

Filter a negative SNR signal whose frequency spectrum lies inside the noise frequency spectrum

I am a newbie in Signal Processing and need your suggestion in the following problem. My signal amplitude is 10 times weaker than the noise. Furthermore, the frequency spectrum of the noise and the ...
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1answer
38 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 ...
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59 views

Practical implementation of Expected Value?

If i compute the average power of my input signal random variable $X(t)$ as $$R = E[X^2(t)]$$ i.e. as the expected value of a random process, is this really just an estimate of average power? More ...
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RMS of signal vs average amplitude

I am trying to estimate the average amplitude of some signal with frequency 6 Hz, sampled at ~300 Hz. See figures for a part of the signal and its dft calculated using matlab. I estimate the average ...
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1answer
65 views

Definition of “Power” in “Power Spectrum” (for translator)

I'm a technical translator who recently undertook translation of documents related to signal processing. Being a novice in the field, I'm searching the web for terminology and concepts. It appears ...
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1answer
56 views

Why use PSD to analyze a signal instead of its Fourier Transform?

Let's imagine I have a perfectly known signal $s(t)$ and I want to analyze its frequency components. I noticed that mostly everyone would use the PSD of $s(t)$ to do that, instead of simply use the ...
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1answer
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Normalised APSD

How you compute the Normalised APSD of a signal using python's scipy.signal libary. Do you compute only the APSD of the signal and divide it by (PSD * df) or there is something else?
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Perceptual Based Adversarial Audio Attacks

I am reading this paper Perceptual Based Adversarial Audio Attacks I have a doubt what is meant by weighting in the frequency domain and what does Section 3.4-equation-4 wants to convey .Please refer ...
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How to perform a permutation analysis of PSD?

I am new to Python & MNE Python. I want to perform a permutation analysis between the PSD of two conditions (1 & 2), across all subjects. I've written the following code for data that I have ...
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1answer
28 views

Fourier Transform of a PSD and response of a PSD input

Does a Fourier Transform of a white noise exist? If so, what is its general form? It is possible to compute the fourier transform of a Power Spectral Density? My problem in detail. I have to compute ...
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1answer
49 views

How to determine SNR required for adding AWGN noise to clean IQ samples?

I'm doing an experiment w.r.t PSD output. I have generated some 11a IQ samples and checking its PSD output in MATLAB using pwelch and comparing with the PSD output obtained using hardware. Here are ...
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1answer
27 views

Oversample or undersample correlated noise?

I wish to measure nontrivial (non-Gaussian) broadband current noise for its distribution and power spectral density. The noise is amplified (with transimpedance amplifier) with some characteristic ...
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PSD Accelerometer and Gyroscope

I used Xsens IMU and collected 1 Hour static data for accelerometer and gyroscope. I used the pwelch analysis in matlab to calculate the onsided PSD. The plots looks the following: How do I ...
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1answer
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How to extract the Freezing Index from Accelerometer data?

I'm working on a project to detect Freezing of Gait episodes for Parkinson's Disease patients, and according to this paper and other ones, extracting the freezing index which is "The power in the “...
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2answers
41 views

Welch’s Algorithm of Averaging Modified Periodograms

I am second year Undergrad student in computer engineering . I have a homework problem where I needed to compute Power Spectral Density . I'm using MATLAB as I noticed that it has good documentation ...
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1answer
97 views

Wiener Khinchin theorem : struggle in the derivation

I am reading Introduction to quantum noise, measurement and amplification, and I need to understand the Wiener Khinchin theorem: how to derive it. I also need to understand some context around this ...
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1answer
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Sinusoid amplitude loss in power spectrum estimation using Pwelch method

I am trying to estimate the amplitude or power spectrum of a sinusoidal signal using Pwelch method. The following is the matlab code I use. ...
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1answer
53 views

Evaluating discrete spectral density at only a few frequencies

I'm trying to obtain the spectral density at three particular frequencies for a computational chemistry problem that I'm working on (if you are curious, it has to do with the estimation of Nuclear ...
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1answer
54 views

Smoothing PSD plot

I am currently working with a signal, and I am interested in plotting its spectra. I have used python, I have computed the signal values, and I have an array that has the time-series values of the ...
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How to determine number of observations based on measurement frequency?

So I'm working on a problem where I'm measuring a signal with two different instruments -- one is a low frequency measurement system (1 Hz), and the other is a high frequency measurement system (200 ...

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