Questions tagged [power-spectral-density]

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

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Is it possible to compute the PSD of s(t)^2 given the PSD of s(t)?

Given a well-behaved signal $s(t)$ given by, $s(t) = \sum_{i}^{N} \cos( \omega_it + \phi_i) $ with a large $N$ and a well-known power spectral density (PSD), $\tilde{S_1}(\omega)$. Is it possible to ...
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Kay Statistical Signal Processing Estimation Theory Example 7.14

Example 7.14 from Kay Estimation Theory A common WSS random process has the ACF $$r_{xx}[k]= \begin{cases} 1+b[1]^{2}+b[2]^{2} & \text{k = 0}\\ b[1] +b[1]b[2] & \text{k=1}\\ ...
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Units of a Fourier Transform (FFT) and Spectrogram [closed]

I am very interested in analyzing signals in the frequency domain. Units of a Fourier Transform (FFT) when doing Spectral Analysis of a Signal 1.In the previous question, answer the unit for the ...
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1answer
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Noise Power Spectrum from Log Video Amplifier

I know that if I use a square law detector on band limited noise - let's assume it's rectangular - the noise power spectrum becomes the convolution of the input power spectrum. After lowpass-...
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2answers
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Computable Time-Frequency Distribution without Cross-Terms

Context: I have a single receiver that is receiving multiple signals. Each signal has a few strong harmonics, but I don't know the fundamental frequency. I would like to display them on a spectrogram ...
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1answer
38 views

Having trouble working understanding a noise shaping filter

As context, I'm trying to understand and implement this Von Karman turbulence model in a simulation I'm working on. In order to generate turbulence velocities on the fly using the model, a ...
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1answer
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Infinity values in statistical analysis of minute frequency data

I'm trying to extract statistical features from power spectral density values in Python. My data is actigraphy data with sampling rate 1/60 Hz (once per minute). This is a sample from my data, "...
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1answer
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Is "Introduction to Statistical Signal Processing" by RM Gray good for starting?

I am working on noise processes in electronic devices for my studies, by now Ive been doing a fairly large amount of processing of time measurements, like calculate PSD, estimate thermal, flicker ...
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Extracting "frequency domain features" from signal for classification

I have a real signal with only nonnegative values (actigraph measurements). Many papers say they use "frequency domain features" for classification, such as mean, variance etc. But I'm ...
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Generate a time series from power spectral density

I have a model function for a power spectral density (PSD). I want to simulate a time series with a power PSD equal to my model function. After some browsing about how to do this, I came up with the ...
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How to compute the theoretical power spectrum of a first order autoregression (AR1) model

I'm trying to figure out how to compute the theoretical power spectrum of a first-order autoregression model (AR1). The AR1 model is given as $x_i = r_1 x_{i-1} + e_i$ where: $x_i$ is real-valued ...
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How to Normalize a Power Spectral density?

I have a spectroscopy data representing Periodogram of 1024 pts (Periodogram estimate a theoretical PSD), however it is not normalized. How do we normalize the PSD ? The normalization I am looking ...
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1answer
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Does pwelch function, in matlab, adopt already the correction factor due to the window?

Does pwelch function, in matlab, adopt already the correction factor due to the window? When we use a window, like hamming or hanning, a correction factor for the amplitude or energy is needed. In ...
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dB octave band spectrum

When I was at the University I did some courses about Acoustic. I always seen the dB octave band spectra, as the Fourier Transform of the dB in time. Now looking at some reference in Matlab, I noticed ...
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1answer
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Results do not match between manually computed PSD values and those from MATLAB pwelch function

The power spectral density (PSD) of the given input signal $x[n]$ is computed as follows: ...
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Average Power Spectral Density (1D and 2D) of multiple images of different sizes in python

I am trying to calculate avg 1D and 2D PSD of multiple image with different sizes. Any idea how can I do this? Current I'm calculating 1D psd using this function. The problem here is that each image ...
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3answers
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What does the intensity values on wavelet transform mean? Amplitude or power?

So when applying wavelet transform, we get a 2d plot. Each point in that 2d plot has a color, showing intensity of something. But I cannot understand if it is an amplitude or power?
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Frequency response terminology: $N(i\omega)$, $Q(i\omega)$

I am reading through an analysis of a system $$ Y(t) = \frac{d}{dt}X(t) + X(t) $$ and the frequency response $H(i\omega)$ is defined as $$ H(i\omega) = \frac{N(i\omega)}{Q(i\omega)} = \frac{1+i\omega}{...
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1answer
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Extracting EEG Bands from raw EEG signal to match with the Bands calculated on the sensor level

I have recently got my hands on a commercially available single channel EEG Sensor from Neurosky. This sensor acquire raw EEG signal at 512Hz from the frontal part of the human head and also process ...
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A scaling difference between MATLAB's pwelch and Python's SciPy welch

I'm having trouble in python with the scipy.signal method called welch (https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.welch.html), which ...
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40 views

Calculating power of brain signals

I have a dataset that contains EEG (or MEG) recordings of brain signals during some cognitive tasks. Each row, shows the source estimates of neurons in a particular region. source estimate contains ...
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Given a noise power spectral density, how long does it take for the underlying process to deviate by a given amount?

Assume we are given a noise power spectral density $S(f)$ for a stochastic process $x(t)$. What can be said about how long it takes for the underlying stochastic process to deviate by a given amount $...
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What is the meaning of magnitude of the noise power spectral density?

Say we have a noise power spectral density that has the following form (I think the question is the same for more general forms as well) $$ S(f) = Af^\alpha, $$ In experiments people usually discuss ...
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Low Pass Filtering, Welch's Method, ENBW

I am working on using Welch's method (https://www.osti.gov/servlets/purl/5688766/) to estimate a Power Spectral Density (PSD). This algorithm involves scaling a set of averaged FFTs by the equivalent ...
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1answer
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Estimating the SNR of respiration signal

I'm trying to evaluate the SNR of a respiration signal on Matlab environment, so the bandwidth considered is [0.04-1Hz]. The problem is that noise is overlapped on the signal, so I can't evaluate the ...
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1answer
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Why Bluetooth 2 use pi/4-DQPSK instead of OQPSK?

From the peak to average power ratio point of view OQPSK is better than pi/4-DQPSK. What is the advantage of pi/4-DQPSK compare to OQPSK? Why Bluetooth 2 use pi/4-DQPSK instead of OQPSK?
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Converting from PSD (V^2/Hz) to dBV (1 Volt RMS reference)

I'm having difficulty figuring out how to convert from PSD (V^2/Hz) to dBV (1 Volt RMS reference). The goal is to have a 1 Volt RMS input show as 0 dBV. Essentially I calculated the PSD of a signal ...
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1answer
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Spectrum in real life with Spectrum in theory

as you know it is possible to measure the power spectral density ($|X(f)|^2$) of a certain voltage signal $x(t)$ through a Spectrum Analyzer. As far as I'm concerned, the simplest spectrum analyzer ...
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Why are some Shannon's limit plots exponential rather than logarithmic?

This diagram again. This is clearly not the shape of $\log_2(1+SNR)$ but I very frequently see this instead of this: But this is also a stupid diagram because it doesn't cross at the origin. Also why ...
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1answer
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Why do we need to 'estimate' the PSD

I've read about the PSD of one OFDM symbol for instance being an estimate of the PSD, but how can it be an 'estimate', when it literally is the PSD of that OFDM symbol. What is actually being ...
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Estimating Average HR from PPG sensor

I am reading Smartphone based Blood Pressure Monitoring via the Oscillometric Finger Pressing Method, which is trying to estimate blood pressure from a PPG sensor and a small applied force finger ...
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Coherence of a signal with itself to assess the PSD increase due to device turning on

I have a sensor that acquires data in the form of a time series, which I can model as a (mostly Gaussian) stationary stochastic process. I can study it in the frequency domain through its Power ...
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1answer
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Obtaining real numbers from FFT with same length as original signal

In this article the real valued time domain signal is transformed to the frequency domain to extract some features like mean or variance. But after transform to the frequency domain I calculate ...
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1answer
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Calculating total power for the signal

In my previous question I asked about calculating a single number as "Spectral Density" feature from signal data. We concluded that it is really a total power and article (link) authors ...
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2answers
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Power Spectral Density as a single number confusion

I'm trying to recreate the results of a machine learning applied to the DSP classification in the article: link. I have a signal (activity measurements from a smartwatch) per patient, so about 30 ...
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Trying to implement matlab pwelch function in python using scipy welch

I am trying to port the statistics toolbox function pwelch from matlab into python, but when I am trying to implement it using scipy.signals.welch, it does not return the same results as it does in ...
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Why is Power spectral density of random walk noise defined despite it being non-stationary? [duplicate]

While reading up on oscillator stability, I noticed that authors characterize random walk noise (Brownian noise) as having a PSD of $S_y(f) = h_{-2} f^{-2} $ where $h_{-2}$ is some constant. This is ...
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1answer
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Allan Variance vs Autocorrelation - Advantages

I am currently studying oscillator stability and have come across the Allan variance. I gather that it was developed as an alternative to the standard variance as it doesn't necessarily converge for ...
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Relation between probability of a signal and its magnitude spectrum

I am a newbie. In these days I am searching if there are reference about properties that can relate the probability of the signal and the magnitude spectrum. I know what are both. But I was curious ...
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What are the kernels that are used in the Smooted Psuedo Wigner-Ville distribution?

Defined in Matlab's docs for WVD, SPWVD is given by: $\int_{-\infty}^\infty g(t) * H(f) x(t + \frac{\tau}{2}) x^*(t - \frac{\tau}{2}) e^{-j2\pi\tau\,f} \, d\tau$ H(f) and g(t) are the smoothing ...
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Given the Power Spectral Density of a random process determin if it is stationary in a wide sense

I am studying a Communication Systems course and have trouble figuring out how to tell and prove if a random process is stationary in a wide sense while only having it's power spectral density. some ...
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signal of $\frac{1}{f}$ Noise

I am working on kind of signals that can be classified as 1/f Noise. In this article is explained that the time history of 1/f noise follows a power law proportional to $t^{-\alpha}$. I am very ...
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1answer
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Does a power spectral density that follow a power law imply that the time hisory follows a power law?

This is a question related to this previous question "I cannot find reference (paper) of this relation $u(t)t^{α} ↔^{FT} f^{-(α+1)}$". The signal that I work with g(t), is the time history ...
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Periodogram/PSD from FFT amplitude

I have performed a STFT for signals and obtained the amplitude through ...
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1answer
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Power Spectral Density of a Filter

I need to calculate the output power spectral density of the following digital filter My calculations are as follows: $y\left(n\right)\:=\:x\left(n-1\right)+d\left[x\left(n-1\right)+x\left(n\right)\...
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1answer
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Calculate average from a power spectrum

I want to calculate the average of a power spectrum in the complete frequency range. I have done a stft and want to calculate power in dB and then the average. Please let me know from the code below ...
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1answer
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How to calculate mean and Variance of Gaussian-distributed random noise?

I have been given a Gaussian-distributed random noise n(t) which has an average power of 5 mW. How can I calculate the mean and variance of noise n(t)? Any suggestions? Thanks!
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1answer
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How to get velocity from PSD graph

Hello everyone! I have a graph, which is Spectra inside cavity. PSD vs. frequency. I need to get velocity [m/s] from PSD [dB/Hz]. Does anyone know how to do that?
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1answer
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The plot of instantaneous power of the Dirac function

I am very confused. I have tried researching this question for the last two weeks and I cannot get a conclusive answer. I was wondering how would I go about plotting the instantaneous power in the ...
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2answers
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Windowing of signal before FFT

I am facing an interesting problem: I have a signal in the time domain. In order to avoid discontinuities at the edges of the signal --- which would lead to artifacts when calculating the FFT --- I ...

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