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Questions tagged [power-spectral-density]

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

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Why is “$1/\mathrm{Hz}$” unchanged while converting$\mathrm{V}^2/\mathrm{Hz}$ to $\mathrm{dB}/\mathrm{Hz}$?

When computing power spectral density via Fourier transform and Parseval's theorem, one gets units of $V^2/Hz$ (e.g. Wiki). As a popular next step, the following unit conversion is widely used: $V^2/...
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78 views

find power of the signal

I have this signal: $$x(t)=\sum \mathrm{rect}\left(\frac {t-kT_0} {20}\right)+\mathrm{rect}\left(\frac {t-kT_0} {40}\right)+\mathrm{rect}\left(\frac {t-kT_0} {80}\right)$$ with $T_0=140$, pass it ...
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385 views

Frequency magnitude distribution of noise

By the Wiener-Khinchin theorem, we have a straightforward way to calculate the power spectral density for stationary noise. If we know the bandwidth of a system, we can further calculate the variance ...
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207 views

Need of $\tt abs()$ method when plotting a power spectral density for a given dataset

I am a newbie in signal processing and would like to know the significance of using the abs() function and squaring the values received as an output of ...
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1answer
2k views

Why DFT-SPREAD OFDM has lower PAPR than OFDM?

I just read 4G LTE/LTE-Advanced for Mobile Broadband, and found the content as below, If the DFT size M equals the IDFT size N, the cascaded DFT/IDFT processing would obviously completely cancel ...
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960 views

Interpretation of Clarke's Doppler power spectral density

What I understand of Doppler spread is that the relative motion between Transmitter (TX) and Receiver (RX) change the exposing time of signal. In rapport to a constant-distance TX-RX, a moving toward ...
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1answer
121 views

Cepstrum analysis - Cut off frequencies displayed

My inquiry is regarding the so called cepstrum analysis. By conducting some experiments, i have real time data at my disposal. The acquisition rate is 1600Hz. I wanted to try cepstrum analysis just ...
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1answer
11k views

Calculate the signal's average power

We have this signal: $$x(t)= 2 + 2\cos(2\pi f_0 t) + \frac{2}{T_0} \operatorname{sinc}\left(\frac{2 t}{T_0}\right)e^{j2 \pi 4/ T_0} + \operatorname{sinc}\left(\frac{2 t}{T_0}\right)e^{-j2 \pi 4/ T_0}....
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54 views

Epoching Data with no Events in mne?

I am new to Python and signal processsing, and I'm trying to create a spectrogram of EEG data taken during a course of general anesthesia. I would like to use MNE's ...
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285 views

How to choose notch frequencies for filtering line noise?

I'm using the function to filter out line noise at 60 Hz (and 120, 180 Hz) caused by electrical noise: ecogNotch In the case below I can effectively filter out the line noise with a notch filter at ...
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1answer
2k views

Average value of power spectral density

I have a spectra of power spectral density (PSD) (vector (1:1e6)) from experimental data (blue color). However I want to plot only average value of PSD (red curve)....
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536 views

Relationship between Wavelet transform and Fourier Power Spectral Density

Is there anyway to obtain the Fourier Power Spectral Density from a wavelet transform of a time series? I am particularly interested in this problem because I was wondering if there is any ...
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1answer
210 views

Oversampling while maintaining noise PSD

I'm designing a digital PID for control and stabilization of laser amplitude. The noise PSD of the laser intensity is around -140dB/Hz, and I want to servo that between DC and 100kHz. I think I've ...
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23 views

Appropriate model for IIR filter to compare with spectral ratios

A quick, basic question. I have measured spectral ratios - comparing a measured signal to an 'ideal' signal. I am fitting a specific, simple IIR filter to that data for transfer functions. So, if I'...
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1answer
301 views

Power Spectral Density of Sigma-Delta modulator

I am simulating a 3rd order SDM and I want to plot the PSD of the output. As you may know, the output is a sequence of pulses ranging from -3 to +4. The number of samples is $N$. The way I ...
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1answer
185 views

Confidence Interval For Frequency of Peak in Averaged Periodogram?

I am averaging periodograms from sets of ~15-25 experimentally measured timeseries all of the same length. To do this I am just summing the power in each frequency bin over all periodograms and then ...
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2k views

Power spectrum of 2D image: result interpretation

Let's say I have an image, which is NxN pixels in size. If I calculate the fourier power spectrum of this image, I get NxN values, with the highest distinguishable frequency at +- N/2 in each ...
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1k views

When to use cross spectral density versus cross correlation?

All my life, I've used cross-correlation to analyze the strength of the relationship between an input signal and the output signal. I use this to determine which ...
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1answer
475 views

PIsarenko Harmonic Decomposition method for PSD estimation

i would like to present steps for estimation Power Spectrum density using Pisarneko Harmonic Decomposition i would like to present code for step 1 part ...
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2answers
1k views

VSD in rms voltage

I am looking at a datasheet where they show a graph: $V_{RMS}/\sqrt{Hz}$ as a function of frequency = VSD (voltage spectral density). The question is: how can a spectral density be in RMS? The root ...
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1answer
93 views

Is Spectral Coherence (MSC) dependent to the initial amplitude of the comparing signals?

Given the signals \begin{align} x(t) &= A_1\sin(\omega t)\\ y(t) &= A_2\sin(\omega t) \end{align} Do $A_1$ and $A_2$ play a role in the $C_{xy}$ coherence estimator? MATLAB's ...
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353 views

Best way to synthesize signal from Power Spectral Density (PSD)

I am looking for methods of synthesizing a random time history signal from a PSD. To me it seems that the simplest method is to take the square root, randomize the phase and then take inverse FFT. ...
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138 views

Applying periodogram-based PSD

For plotting a Power Spectral Density graph based on FFT results, I had used two different approaches, but they produced very different results, and it'd be great if anyone knows why. Note: From this ...
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2answers
375 views

Effects of averaged periodogram (Welch's Method) on resolution?

I'm trying to make an app(running on an android phone) that can detect the frequency of a guitar string being played. I know it'll be hard to detect that but that's a problem I'll deal with later. ...
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235 views

Interpreting dataset of a power spectrum

I am currently working with kaldi, and are trying to make spectrogram plots of different audio files. Kaldi is a speech recognition toolkit. Kaldi frames its input in frames of 25 ms with a ...
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3answers
362 views

How should this fft output be intepreted?

I am currently reading some code, so I can understand how this FFT output is actually been stored. I have a function which computes FFT of audio file, and stores is in the format. ...
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1answer
1k views

How to explain this BER vs SNR behaviour?

I wrote a script in MATLAB to simulate an LDPC created using an algorithm of a colleague of mine. The parity check-matrix is regular and has dimensions $1012 \times 1518$ and the code rate is $R=1/3$. ...
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248 views

Derivation of PSD of sampled bandlimited random process

When a bandlimited random process whose PSD \begin{equation} S(\omega) = \begin{cases} \frac{N_0}{2} & -10B<\omega<10B\\[2ex] 0 & \text{otherwise.} \end{cases} \end{equation} is ...
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2answers
2k views

RMS averaging in spectrum analyzers

While studying spectrum analyzers I ran into the concept of RMS averaging as a mean to reduce dispersion of data without affecting power spectral density (PSD). What is not really clear to me is how ...
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1answer
102 views

How to read off power at different frequencies

In MATLAB, consider a signal y and its Fourier transform Y: ...
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1answer
919 views

Estimate the wavelength of an oscillatory signal

I need to estimate the dominant wavelength of a signal that is looking like this: My first attempt was using scipy.signal.argrelmin in Python in order to detect the ...
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1answer
2k views

Scaling for a 2D Hanning Window

I am trying to find the PSD of a 2D set of data and representing it as a function of frequency in both these directions. I start with a 2D FFT and generate the 2D hanning window for a $M\times N$ ...
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207 views

How to fit Welch's window segments to a time series of variable length

I'm trying to write a small Welch's PSD method in R right now, but I've had trouble finding information on how exactly the window segments are fitted to a given time series. For instance, when the ...
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1answer
1k views

Comparing PSD two signals of different length

I have two time signals A and B which are of different length, length(A) < length(B). Now I calculated the cumulative PSD of both signals. What is the best way to compare this result? If I am ...
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1answer
515 views

PSD Magnitude with Welch's Method

I'm having some trouble getting consistent results with PSD calculations. If I just take a basic sine wave ...
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1answer
328 views

Occupied Bandwidth

I am pretty new in the field of Signal Processing. I am a structural engineering graduate student at the UT at Austin. I am currently working on a project that regards acoustic emission monitoring of ...
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798 views

Yule-Walker PSD Estimate of an AR Process

I am trying to implement a Yule-Walker PSD estimation in Python but my results are not up to the expectations. In MATLAB, I would normally implement my functionality as follows: ...
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1answer
146 views

Most appropriate spectral analysis method for a recording of a saxophone note?

I'm currently doing an investigation where I am attempting to resonant frequencies of an Alto Saxophone at various different notes. I have taken audio recordings of the notes with a sample rate of $...
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1answer
251 views

calculate SNR of two signals with power spectral density

You can see my system's diagram as shown below At output,two different input signals are sited in each ($\frac{H}{3}$) position $(w_2=w_1+ \frac{H}{3})$ and if output power spectral density equation ...
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1answer
602 views

SNR estimation in segmented speech signals

I was called to estimate the signal-to-noise ratio in a collection of recordings that were manually annotated, meaning that the speech and noise segments are known. The noise is uncorrelated with ...
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2answers
307 views

Find highest frequency of a very manky signal

I'm trying to compute the highest frequency (as can be sampled) in some pretty manky looking discrete time-dependent signals. My current method - a discrete fourier analysis - fails for some pretty ...
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1answer
149 views

Some subtleties in the PSD of digitally generated noise with $S_X(f) = A(f)$

I understand that the title is not the most descriptive, but I didn't know how to describe my problem in a more literal way. The situation is as follows: I wanted to digitally generate noise with an ...
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1answer
698 views

Classifying a time series with a Lorentzian power spectral density

I was wondering if there is a general classification for time-varying signal with a Lorentzian shaped power spectral density, specifically with some nonzero center frequency. In terms of equations, ...
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231 views

Can one generate a signal with an asymmetric power spectral density?

My question is as follows. I know that classically speaking, if you have some time varying signal $X(t)$ its power spectral density $S_X(f)$ will be symmetric around $f=0$ as the signal is real. This ...
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1answer
924 views

Power spectral density of a PAM signal

Say I have a PAM signal as $x(t) = \sum_n a_n h(t-nT)$ where $\{a_n\} \in \{\pm 1\}$ are equiprobable random binary bits and $h(t)$ is bandlimited to $[-1/(2T),1/(2T)]$. ($x(t)$ is random process and ...
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2answers
205 views

Power spectral density of $\left(x(t)\right)^2$?

The relation between $x(t)$ and output $y(t)$ of a non-linear device is expressed as $$y(t) = (x(t))^2$$ Let $x(t)$ be zero-mean stationary Gaussian random process with auto-correlation $$R_x(...
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65 views

How to preprocess such signals?

I am interested in denoising accerelation measurements, recorded in ambient vibration tests. Such tests consist in recording the vibrations of a mechanical structure, say a table for example. So say I ...
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1answer
664 views

What does PSD represent in the spatial domain?

People use FFT methods to analyze topographic features in the spatial domain, such that the signal varies over (x) rather than (t). If a PSD curve characterizes amplitude versus frequency of an ...
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99 views

Can white Gaussian noise improve signal level in non-linear device?

In the system shown below, can white Gaussian noise amplify or attenuate the input signal? Most of the time we check signal level proportional to noise level (such as noise figure) not singly. I ...