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-2
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0answers
23 views

Power spectral density of the sum of two time-domain sinusoidal signals

Given $x(t) = \cos(2\pi f_{1}t + \theta) + 2\cos(2\pi f_{2}t + \theta)$, how can I find the power spectral density $S_{x}(f)$ of $x(t)$. I already tried to find the the $\mathcal{F}\left[\mathcal{R_{...
0
votes
0answers
19 views

can I compensate for hann-window preceding fft? [duplicate]

To reduce spectral leakage, I have created a hann window going from almost 0 to 1 to almost 0 across 128 time points. I multiply that with my 128-point time series data, then feed the result to FFT. ...
1
vote
2answers
62 views

What should be the correct scaling for PSD calculation using $\tt fft$

I would to calculate the PSD of a signal using FFT however the result do not match with periodogram command. What did was as follow : ...
4
votes
2answers
76 views

Zero-padding the middle of a signal

I sample a signal at a certain frequency for a finite amount of time to get a sequence $$(x_n)_{n=1}^N = (x_1, x_2, ... , x_N)$$ with the intention of analyzing its power spectral density by ...
0
votes
1answer
13 views

RTL-SDR units, $\textrm{dBm}$

I am using the Python rtlsdr library to get complex samples from my RTL-SDR USB stick. I am getting power by squaring the real and imaginary components of these ...
1
vote
1answer
10 views

Should I filter before calculating power, if I'm looking for relative changes in power?

I am building a "scanner" sort of program, which reads IQ samples from an rtl-sdr stick, and keeps track of the power on certain frequencies, in certain bands. I am interested in detecting activity ...
0
votes
1answer
40 views

PSD of a sum of two stationary real signals

I have 4 signals ($w_1(t),w_2(t),u_1(t),u_2(t)$ of which I know the power spectral densities (PSDs) $S_{w_1,w_1}(\omega),S_{w_2,w_2}(\omega),S_{u_1,u_1}(\omega),S_{u_2,u_2}(\omega)$ and the cross PSD $...
1
vote
1answer
25 views

Finding the deterministic autocorrelation function (ACF) from its power spectrum

The power spectrum of a stationary discrete-time random signal is $$\Phi_{xx}(e^{j\omega})=\begin{cases} 1 & |\omega|<\pi/2 \\ 0 & \pi/2 <|\omega| \le\pi \end{cases} $$ (a) ...
0
votes
0answers
28 views

Flattening out a power spectral density

The situation is as follows. I am generating a white noise voltage signal with a certain power spectral density amplitude of choice, from 0 to some cutoff frequency, for example 200 MHz. This proceeds ...
1
vote
1answer
28 views

Difference between PSD estimate and variance of DFT

In Bartlett's PSD estimate one averages over L segments of the squared DFT coefficients. From wikipedia I found this formula $$ \textrm{PSD}(k) = \frac{1}{L}\sum_{l=1}^{L} \frac{1}{M} \lvert X^{[l]}(...
1
vote
1answer
39 views

PSD looks to clean/continuous

I generated an signal with a base frequency of $50\textrm{ Hz}$ and its harmonics and quantization noise in it (as an array in MATLAB). It's sampled fast enough to make sure there is no aliasing etc. ...
2
votes
2answers
95 views

If noise is your signal, what is your noise?

Consider the following contrived situation. Imagine a Gaussian white noise process $x[t]$, with bandwidth $Δf$, with PSD equal to some quantity $A$ which you would like to measure. So the way to ...
0
votes
0answers
56 views

Epilepsy seizure detection in EEG

I want to develop a method to detect the occurrence of epilepsy seizure in an EEG signal. I am using a large data set for number of patients so the algorithm has to detect the seizure in any of the ...
0
votes
0answers
42 views

Why the SNR is very high?

In a cellular network, let us say that I have these parameters: Transmit power = 30dBm Noise spectral density = -174dBm/Hz (AWGN) Bandwidth = 10MHz Let us say ...
0
votes
0answers
31 views

Power autocorrelation function calculation

Calculate the power autocorrelation function $\phi^p_{ff} (\tau)$ and power spectral density $\Phi^p_{ff} (\nu)$ for the signal$$f(t)=A \cos(2 \pi \nu_m t) \cos(2\pi v_c t).$$ Attempt: According to ...
0
votes
0answers
27 views

Autocorrelation function and energy spectral density

Find the energy autocorrelation function $\phi^e_{ff}(\tau)$ and the energy spectral density $\Phi^e_{ff}(\nu)$ of the signal $f(t) = e^{-\gamma |t|},$ where $\gamma>0$ is a real constant. ...
0
votes
0answers
60 views

How to calculate Power spectral density of windowed signal

To compute the (absolute) spectral powers in the above eight frequency bands, PSD of the input signal needs to be estimated. The PSD of a signal describes the distribution of the signal’s total ...
0
votes
0answers
37 views

How do we find the Power Spectrum Density (PSD) and which data type is valid for that?

I want a simple explanation on how to find PSD and which type of data (in which units, I mean) can be used for doing so. If found similar interesting questions 1 & 2 and some on Mathworks, like ...
1
vote
1answer
22 views

Decorrelating Stationary Colored Gaussian Noise — Effect On The Desired Signal

So given stationary colored gaussian noise $\mathbf{n}$, I know that I can decorrelate it by first finding it's autocorrelation $R_{nn}$ and performing $R^{-\frac{1}{2}}_{nn} \mathbf{n}$. In ...
0
votes
1answer
100 views

Plotting Power Spectrum (Matlab)

I want to make a plot of the power spectrum for a .wav sound file, over the frequency range from -2000 to 2000 Hz. Attempt: I used the following code, but the resulting plot is one sided. It doesn't ...
0
votes
1answer
18 views

Evaluating the spectral density of generated noise through the autocovariance

I'm working on generating noise signals $X(t)$ (with $t \in \left[0,T\right]$ with step size $\delta t$) with a prescribed power spectral density $S_{XX}(f)$ and I'm figuring out how well I am ...
0
votes
1answer
32 views

Periodogram frequencies not matching with signals

I am new to signal processing world. I am working on a project where we have to find change points using spectral densities. I am running some simulations where in I created a wave which is a linear ...
2
votes
4answers
89 views

Finding the Amplitude of a Sinusoid in Noise

I'm trying to solve for the amplitude and frequency of a sinusoid embedded in zero-mean gaussian white noise. I am supplied a sample file of a 40000 element array. I first took the autocorrelation ...
0
votes
0answers
17 views

Derivation of Doppler Power Spectral Density

I'm looking for an intuitive explanation for the U-shared Doppler PSD and also it's mathematical derivation starting from the definition of auto-correlation function for the doppler scenario.
0
votes
1answer
27 views

Evaluation of Autocorrelation and Power Spectral Density of white noise through a filter

So say there's a filter with an impulse response of $h(t) = (0.8)^t u(t)$. I'd like to pass white noise through this and figure out the autocorrelation and power spectral density of the output. I'm ...
1
vote
0answers
78 views

1/f noise parameter characterization

I would like to characterize 1/f noise in some time series data. I would like to estimate the 1/f noise corner, and the standard deviation of the 1/f noise component and white noise component. The ...
1
vote
0answers
19 views

Generating 3-dimension $1/f^\alpha$ noise

I'm stumped trying to find a way to generate a 3-dimensional $1/f^\alpha$ noise time series. Basically I want simulate a forcing that is $1/f^\alpha$ in the 2 space dimensions and $1/f^\beta$ in time, ...
1
vote
1answer
91 views

Calculating energy spectral density function of half-cosine function

I have the following function: $$ g(t) = A\cdot \textrm{rect}\left(\frac{t}{T}\right)\cos\left(\frac{\pi t}{T}\right)$$ How do I find the energy spectral density function? I think? it is defined as ...
1
vote
0answers
41 views

How do I perform a spectral averaging? Amplitude spectral density

I haven't been doing much signal processing over the years and I'm wondering if my logic is sound. I'd appreciate any input. So, I have a data set with independent variable ($A$) in Frequency ($1\...
1
vote
0answers
38 views

Quantifying how good I'm producing a spectral density

I recently asked a question here on how to create noise with a specific spectral density $S_{xx}(f)$. The helpful people of this stack exchange told me one way to do it was filtering white noise with ...
1
vote
2answers
78 views

Numerically generating noise time series from spectral density

I'm trying to figure out a way to construct (numerically) time series of random variables given some spectral density $S_{xx}(f)$. I'm interested in various types of spectral densities (flat, ...
3
votes
3answers
129 views

How to interpret spectrogram correctly?

I have a pressure transducer signal from a reacting mixture available here, which has a sampling frequency of 50kHZ. I have also obtained the spectrogram of the signal with NFFT=256, noverlap=4 as ...
0
votes
0answers
17 views

Unit of the area between two power spectra

I calculated the area between two Power Spectral Density curves that are z-score normalized (frequency x normalized Power). What would the units be of the area calculations?
0
votes
0answers
16 views

Predict the maximum power of a signal in the presence of noise

My question relates to predicting the power of a signal in the presence of noise. The signals I am analysing are discrete quasi-periodic signals (jittered sine waves basically). If I do a spectral ...
1
vote
0answers
42 views

Why is it better to sample white noise in frequency domain here?

We have a channel $c(t)$ that we want to sample. It can be expressed as $ c(t)= g\ast x(t)$ where $x(t)$ is white complex Gaussian noise and $g(t)$ is a function that we know the PSD of, let's call it ...
0
votes
0answers
33 views

Error in summation of spectral components

The error associated with a given estimated spectral component $f(w)$ ($w$ is the frequency) of a Gaussian signal follows a Chi-squared distribution with $\nu=2$ degrees of freedom. For instance the ...
0
votes
0answers
29 views

Autoregressive Model for EEG frequency analysis?

I want to do EEG frequency analysis in matlab using autoregressive models (e.g. Burg's method). How do I do this correctly? I just treated each channel individually (loop over channels), so I go ...
0
votes
1answer
102 views

Keeping track of units for spectral energy of discrete signals

The energy of a continuous signal $x(t)$ recorded between $t=0$ and $t=T$ (namely $x(t \notin [0, T]) = 0$) is defined as $$E = \int_0^T |x(t)|^2\, dt.$$ In most signal processing texts I met, the ...
0
votes
1answer
56 views

How to calculate the discrete power of a discrete signal?

If I have a time series defined by a series like $$ x = [a_1, a_2, a_3, ..., a_n] $$ for time from $t = 1$ to $t = n$ How can I get to the power of the signal in this form: $$ P_x = [p_1, p_2, p_3, ...
1
vote
1answer
93 views

Apply band pass filter (BPF) before calculating the power of a signal (PSD)?

From my understanding PSD tries to give a good estimation on the power each frequency attributes to the overall signal power. If I am only interested in a frequency range $(\omega_0 \leq \omega \leq ...
0
votes
0answers
73 views

FFT and Power Spectrum from Time series using MATLAB

I'm trying to better understand some things about FFT so I've asked for a small assignment, in MATLAB, in which I'll make some signal analysis on existing data. All I have is a time series which is a ...
0
votes
0answers
64 views

Multiplication of two noise

I have a question on the multiplication of two noise. Suppose I have two noise $n_1[n]$ and $n_2[n]$. I only know their power spectral density $N_1[k]$ and $N_2[k]$. How can I get $N_3[k]$, where $...
0
votes
0answers
31 views

Sign of DC Component obtained from FFT differs with the sign of Mean of the signal, Does the sign really matter?

I've been working on 3-axis accelerometer data to predict the gesture of an user. Lot of literature pointed me to consider Frequency domain features for my problem and i'm using Mean of the ...
0
votes
1answer
124 views

Finding the right measure to compare sound signals in the frequency domain

I am comparing the spectral contents of some sound signals with Matlab. I have quite a few measures but wanted one that represents the centre of gravity of the spectrum. I used SpecCentroid() found ...
0
votes
1answer
117 views

How to find SNR of received DSB:AM signal with white noise after demodulation & LPF'ed?

This is a homework problem so please do not give a full solution. I intend to keep this at discussion-level. Problem Statement I am given the Power Spectral Density (PSD) of a DSB-Amplitude ...
0
votes
0answers
18 views

Understanding spectral diagram in Log-Log scale

I have a hard time understanding the signal composition via log-log representation of signal power spectral. For example, in the figure attached On the right is the Spectral Density of signal X and ...
0
votes
1answer
121 views

Power spectrum estimate from FFT

I'm plotting the FFT power-spectrum of a signal in MATLAB. I uploaded the 8000 samples time-series signal in a text file here: http://wikisend.com/download/896484/signal.txt I'm using the following ...
0
votes
0answers
26 views

how to apply x and y in cpsd matlab code?

i would like to ask question related to Cross Power Spectral Density function , which in matlab can be estimated using function : cpsd(x,y,[],[],1024,fs) but there is a main question that x and y ...
0
votes
0answers
23 views

Power estimation using eigenvalues

There are many different method to estimate power of a signal at a particular frequency or direction of arrival. As an example root music(Matlab rootmusic.m). The question is: do we have a bias when ...
0
votes
2answers
125 views

Increase power of signal in Matlab

I have a scenario where I have two OQPSK modulated signals and I need to increase the power of one signal by 3 dBm while keeping the other signal at the same power level. Could someone guide me on how ...