Questions tagged [power-spectral-density]

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

Filter by
Sorted by
Tagged with
0
votes
0answers
10 views

Spectral decomposition of the DC part of the signal

The title of the question might be misleading, but it shows how clueless I am about this problem. I have a time series of some quantity $X(t)$. I can calculate autocorrelation of this quantity $Y(\tau)...
1
vote
0answers
16 views

Noise removal where gains are >1

I am currently working on some noise removal algorithms and have come across what seems to be an oversight in the design of some of these algorithms. Two of the algorithms I am looking at use the PSD ...
2
votes
1answer
98 views

Is spectral density conserved after aliasing?

Will the integral of the PSD of a down-sampled signal still equal the variance in all cases
1
vote
1answer
32 views

Should we divide the power at 0Hz by two for Single-Sided Power Spectrum with FFT?

To make my question as clear as possible I will go through an example. I want to plot one sided power spectrum of a signal. As an example my signal is sum of "50Hz sine with and amplitude of 1V&...
0
votes
0answers
21 views

Constrained filter design

I have a desired filter magnitude response, i.e. $|H(j\omega)|$. How can I find the time-domain coefficients of a filter $h=[h_0, h_1, ..., h_{L-1}]$ that has a similar magnitude response such that $...
0
votes
1answer
24 views

What is the relation between input and output PSDs given system transfer function $H(s)$

If I have the system transfer function $H(s)$ in the complex frequency domain, how would I relate the input/output power spectral densities? I have come across the relation $P_{out}(f) = |H(f)|^2P_{in}...
0
votes
1answer
58 views

Male and female voice spectrum

I have a set of data which consists of male and female voices. They are pronunciation of a same sentence. What's the appropriate method for getting an average spectrum for the male and female voices ...
0
votes
0answers
15 views

translating 1 dB increase in thermal noise to interference to noise ratio (I/N)

I often see statements like "1 dB increase in the receiver thermal noise density results in an interference-to-noise density ratio of -6 dB". How can I obtain this result mathematically? ...
0
votes
1answer
43 views

Power Spectral Density Reconstruction

I am from an ML background and I am working on MP3 audio reconstruction and I have managed some amount of spectrogram reconstruction but I have noticed that the higher frequency end of the generated ...
3
votes
2answers
55 views

Help with denoising signal and periodogram analysis resources

This is a cross posting from the crossvalidated stack exchange as I thought this may be a better forum to ask. I have a dataset consisting of respiratory time series signals of different lengths ...
0
votes
1answer
32 views

Signal Spectrum Shaping

I am looking for methods/algorithms for signal spectrum shaping. Let's say we have a white Gaussian noise and want to have a desired power-spectral density. The first solution that comes to mind is ...
1
vote
1answer
39 views

Magnitude response of mirrored (with respect to unit circle) poles and zeros

I just want to check that my understanding about the following paragraph from Optical Filter Design and Analysis by Christi K. Madsen, Jian H. Zhao is correct: A filter’s magnitude response is equal ...
1
vote
1answer
54 views

Squared magnitude of the Z-transform

I am basically new to the $z$-transform and there are some points regarding its square magnitude that I do not understand. Basically I do not understand how in slide 4 of PDF, they arrive at the ...
0
votes
1answer
20 views

How to run Welch’s method on cross-spectral density

I have a multivariate time series and I’m trying to figure out the cross spectral density of all pairs of variables efficiently. I’m unsure of how to implement Welch’s method in this context. Do I ...
1
vote
1answer
33 views

Spectral estimation in Spectrum analyzer

I understand that there are various techniques for spectral estimation of the signals. Methods such as parameteric(AR,ARMA etc.), non-parameteric( periodogram , welch etc..). But I fail to understand ...
1
vote
0answers
36 views

How to efficiently apply spectrum sensing algorithm

Lets assume 1 signal (lets call it PPG) that is composed "mostly" of 3 different main frequencies components ($f_1, f_2, f_3$) and their harmonics. Now let's assume we have 16 copies of this ...
0
votes
0answers
30 views

Sequence design for a target PSD shape

I want to design a sequence of numbers, which must include only -1, +1 and 0, to have a specific PSD. What is the best way to do that?
0
votes
0answers
25 views

PSD of linearly modulated signal using autocorrelation?

Consider a signal $v(t)$ given by $$v(t)=\sum_{n=-\infty}^{\infty} b[n]p(t-nT).$$ Assume that $b[n]$ is uncorrelated with zero mean, i.e. $\mathbb{E}[b[n]b^*[m]]=\mathbb{E}[|b[n]|^2]\delta[n-m]$ and $\...
0
votes
1answer
36 views

Lower bound of weighted average of sequence

Can anyone prove that $$\mathrm{avg}\left(\frac {a_i}{\left(1+a_i\right)^2}\right) \ge \frac{\mathrm {avg}({a_i})}{\left(1+\mathrm{avg}{(a_i)}\right)^2}$$ for a sequence of positive valued elements $...
1
vote
1answer
164 views

Difference between double-sided and single-sided AWGN noise after bandpass filtering?

Consider a bandpass signal $s(t)$ with bandwidth $W$. After bandpass filtering, let the output signal be $r(t)=s(t)+n(t)$ I have read a paper that denotes $n(t)$ as Gaussian noise with one-sided power ...
1
vote
2answers
45 views

What's the number of FFTs in Welch-based PSD?

I've read from the book "Proakis, J. G., & Manolakis, D. G. (2004). Digital signal processing. PHI Publication: New Delhi, India." Chapter 12 that the number of FFTs required for ...
1
vote
2answers
85 views

What is unit of time average of product of two signals?

Consider the signals $e(t)$ and $h(t)$ with units $\left[\frac{V}{m}\right]$ and $\left[\frac{A}{m}\right]$ and their Fourier transforms $E(\omega)$ and $H(\omega)$ with units $\left[\frac{Vs}{m}\...
1
vote
1answer
63 views

Sum of two random noises

Let $u_1$ be a random noise in $\mathbb R$. The PSD of $u_1$ is constant in the interval $[f_{1,1}; f_{1,2}]$ and is noted $p_1$. Let $u_2$ be a random noise in $\mathbb R$. The PSD of $u_2$ is ...
1
vote
1answer
39 views

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 ...
4
votes
2answers
54 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 ...
1
vote
2answers
156 views

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)=...
0
votes
1answer
51 views

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 ...
1
vote
0answers
40 views

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 ...
1
vote
1answer
104 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 ...
0
votes
2answers
149 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 ...
0
votes
1answer
73 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 ...
3
votes
1answer
120 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 ...
0
votes
0answers
34 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 ...
0
votes
1answer
51 views

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 ...
0
votes
0answers
32 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 ...
0
votes
0answers
22 views

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.
0
votes
0answers
35 views

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 $...
0
votes
0answers
26 views

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'...
2
votes
3answers
179 views

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 ...
0
votes
0answers
9 views

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 ...
0
votes
1answer
32 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?
0
votes
1answer
56 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: ...
0
votes
1answer
107 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?
0
votes
0answers
25 views

“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....
0
votes
0answers
21 views

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/...
2
votes
2answers
263 views

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 ...
0
votes
0answers
13 views

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 ...
0
votes
1answer
32 views

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 ...
1
vote
2answers
49 views

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 ...
1
vote
1answer
32 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 ...

1
2 3 4 5
12