## Forums Search for: Gaussian Noise

## SNR of signal perturbed by WGN

inI am trying to analyze the variability of detection time by a threshold detector for input signal perturbed by a White Gaussian Noise (w[n])...

I am trying to analyze the variability of detection time by a threshold detector for input signal perturbed by a White Gaussian Noise (w[n]) N(0,sig^2). My input to the detector is a ramp-signal x[n] with added WGN w[n]. The input signal is supposed to have a fixed SNR. Now, I decide to use the input of duration/length L. Then compute the input signal power as sigPower = sum(x[n].*x[n])/...

## What does colored signal mean?

inHello, I would just like to clarify what people mean when they say a signal is colored? My assumption is it means white gaussian noise is...

Hello, I would just like to clarify what people mean when they say a signal is colored? My assumption is it means white gaussian noise is added to the signal, but I just want this to be clarified. Thank you.

## detection in coloured noise

inI have a signal detection problem. The observer is presented 2 waveforms r1 and r2 on every trial. One waveform contains the signal + noise, and...

I have a signal detection problem. The observer is presented 2 waveforms r1 and r2 on every trial. One waveform contains the signal + noise, and the other just noise. Eg r1 = s + n1 r2 = n2 The noise in the two waveforms is correlated Gaussian noise with covariance matrix R. Ie corr(n1,n2) is nonzero. If there were no correlation, the optimal way to make the decision would be to cross-corr...

## maximum likelihood sinusoidal signal detection with sinusoidal noise

inHi guys I'm trying to find a solution for detecting a sinusoidial signal under non-gaussian noise, for example sinusoidial noise, consider the...

Hi guys I'm trying to find a solution for detecting a sinusoidial signal under non-gaussian noise, for example sinusoidial noise, consider the following model: y1(t)=A*exp(j*w*t)+B*exp(j*w*t)+n(t) y2(t)=B*exp(j*w*t)+n(t) I want to detect if y1 or y2 is present, do you think that ML detection is applicable here (p(r/y1)/p(r/y2)>

## What is the optimal estimator?

inConsider an unknown DC level in a white Gaussian noise with zero mean and unknown variance. The value of the DC level is restricted to a range...

Consider an unknown DC level in a white Gaussian noise with zero mean and unknown variance. The value of the DC level is restricted to a range of [A0, A1], the observations, that is the DC level plus WGN are also restricted in this range. Then what is the optimal estimator for the DC level and the variance of the noise?

## Ensemble averaging for multiplicative noise

inIn my problem there exists a vector x = [x1,x2, ... x_N] of length N, and I have M measurements y_k = x .* e_k, 1

In my problem there exists a vector x = [x1,x2, ... x_N] of length N, and I have M measurements y_k = x .* e_k, 1

## How to do digital dithering in FPGA

inAll- I have 14-bit A/D samples in FPGA and I want to perform dithering to eliminate harmonics. How can I do it? I added the signal with...

All- I have 14-bit A/D samples in FPGA and I want to perform dithering to eliminate harmonics. How can I do it? I added the signal with Gaussian noise and did subtract dithering. And that didn't work. Any suggestion is very appreciated. Thank you. Billy

## Gardner Timing Error Detector - Loop Filter

inHi! I'm simulating a burst QPSK modulation and demodulation through a canal with distortion and additive white Gaussian noise. Thus far...

Hi! I'm simulating a burst QPSK modulation and demodulation through a canal with distortion and additive white Gaussian noise. Thus far everything is going as planned and I can retrieve the data. I've decided to implement a gardner timing error detector in order to compensate for some very small clock drift. So I've read some documentation and I now compute the Gardner TED error. But i...

## Correlated noise samples

inI always had this question in my mind: The autocorrelation function of the filtered white Gaussian noise is simply a sinc function (inverse...

I always had this question in my mind: The autocorrelation function of the filtered white Gaussian noise is simply a sinc function (inverse transform of the output of a brickwall filter with bandwidth 1/2T). Now if we sample the autocorrelation function with rate 1/T, the discrete-time noise samples are uncorrelated due to the sinc function passing through 0s at the T-spaced sampling instants. How...

## Question about a Bandlimited Process

inIs it possible to even simulate a true bandlimited process? That is we would like the spectrum to be zero at some frequency less that nyquist....

Is it possible to even simulate a true bandlimited process? That is we would like the spectrum to be zero at some frequency less that nyquist. Surely passing gaussian noise through some FIR filter would shape the noise to be 'small' in the band of non-interest but is not exactly zero. But seeting up a FIR is probably a quick and easy way out. Would a better means of simulating a bandlimit...

## CC and GCC for time delay estimation

inHi guys, I have to determine the time lag between two signals x and y for an acoustic distance measurement setup. The signal x is the test...

Hi guys, I have to determine the time lag between two signals x and y for an acoustic distance measurement setup. The signal x is the test input signal and y is the reflected signal from the acoustic path. This is modeled the following: y = h * y + N whereas N is additional gaussian noise and h is the impulse response of the acoustic path. (The operator * states for a con

## Max absolute value of colored Gaussian noise

inI need a number, and I'm feeling lazy; has anyone worked this out recently? I want to know the distribution of the maximum of the absolute...

I need a number, and I'm feeling lazy; has anyone worked this out recently? I want to know the distribution of the maximum of the absolute value of a vector of samples of a colored, zero-mean Gaussian process. Or, stated another way, I want to shove white noise into a filter, then examine a finite chunk of the filter output for it's maximum absolute value. Anyone know the answer? ...

## Convolution of same PSDs

inHi, I have a (for simplicity brickwall) bandlimited white Gaussian noise signal x[n]. Hence I know roughly its PSD. I would like to get an...

Hi, I have a (for simplicity brickwall) bandlimited white Gaussian noise signal x[n]. Hence I know roughly its PSD. I would like to get an estimate of ||x^3[n]||/||x[n]||^3 (||.|| l2-Norm of the discrete time signal x[n]). My idea was now to go to frequency domain (Parseval) and obtain the PSD of x^3[n] via 2-fold convolution of X[k]. If I would just approximate the PSD of x[n] as ...

## How to get likelihood of a bearing estimation?

Hi, I am reading a paper on particle filter on bearing estimation. The system model is: x_k = P*x_k-1 + w_k P is a 4X4 matrix. x_k is...

Hi, I am reading a paper on particle filter on bearing estimation. The system model is: x_k = P*x_k-1 + w_k P is a 4X4 matrix. x_k is the position and speed of a 2-D of the object position (a, a^, b, b^). The measurement z_k is: z_k=tan^-1(b_k/a_k) + v_k w_k and v_k are Gaussian noise. On particle filter, it needs likelihood to calculate posterior probability: p(z_k|x_k...

## FIR filter

inThe input signal is white Gaussian noise - 8000 sample (uniform power across all frequencies). If I represent it by the histogram, the limit of it...

The input signal is white Gaussian noise - 8000 sample (uniform power across all frequencies). If I represent it by the histogram, the limit of it is about [-3.5 3.9] also in a report I saw limit of it is [-8000 8000], Where am I wrong???

## error caused by Wien-Hammerstein system (Bussgang?)

Hi, I have the following setup: x ---> [ G(z) ]-----> [ (.)^3 ]-----> [ H(z) ]-----> y where x is a Gaussian input with E(x)=0 and...

Hi, I have the following setup: x ---> [ G(z) ]-----> [ (.)^3 ]-----> [ H(z) ]-----> y where x is a Gaussian input with E(x)=0 and autocorrelation Rxx. For simplicity, I can set Rxx=sigma^2*delta(tau) and G(z)=1, i.e. a pure Hammerstein system driven with white Gaussian noise (I would like to generalize afterwards if possible): x ---> [ (.)^3 ]-----> [ H(z) ]-----> y Now I would lik