# Questions tagged [gaussian]

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### Ideally Lowpass-filtered White Gaussian Noise: question about a derivation of variance and covariance

Consider white gaussian noise $\omega(t)$ that has passed through and ideal lowpass filter with bandwidth $B$. This filter has the impulse response $$h(t) = 2B\text{sinc}(2Bt)$$ Sampling the filter ...
0answers
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### Keysight ADS Gaussian noise + understand signal plan (BPSK-Mapping a. Demapping)

I have already created the circuit in the Schematic.I am concerned with the understanding of the diagram. In the diagram you can see the Gaussian noise before and after the addition and the question ...
0answers
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### How to add Rayleigh Fading Coefficient to a BPSK signal with AWGN?

I have a problem with my code. I saw many programs that add the coefficients of rayleigh like this: h=1/sqrt(2)*(randn(1,N)+1i*randn(1,N)), where N=number of bits. ...
0answers
15 views

### Choose the right Sigma for Gaussian filter

I have the following problem: I have a time series with counted data. I now want to smooth it using a Gaussian low-pass filter. Is there a method to determine the sigma value? The window should have a ...
2answers
73 views

### why GMSK use a gaussian filter instead of raised cosine filter?

I'm wondering why GMSK use a gaussian filter instead of raised cosine filter as a pulse shaping filter? Is there special reason?
0answers
21 views

### when exposure time is longer, the Poisson noise become Gaussian

Can we have an explanation of why exposure time is longer, the Poisson noise become Gaussian? Or any reference? Please provide a reference and I like to dig into more. Thanks in advance!!
1answer
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### Finding optimal decision threshold for binary comm system

I'm trying to solve the following exercise: Given a system that transmits bit $b$ with probability $p_b$ and $-b$ with $p_{-b}$ and the transmission is degraded by AWGN $N(0,\sigma^2)$. What is the ...
1answer
78 views

### Having problems with understanding the meaning of PSD for colored Gaussian noise

After reading two articles on signal processing stack exchange: On coloured Gaussian noise How the white and colored noise differ in time domain I do understand that variance do not change over ...
1answer
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### 1st and 2nd Gaussian derivatives for edge detection

I have a project about edge detection, I made research on internet about filters and read many articles but there is an article talked about using Sobel and Gaussian derivatives then it mentioned &...
0answers
25 views

### How do you derive the new mean and variance when two gaussian functions are multiplied together?

I'm trying to understand the contents of this web-page which suggest that multiplying two Gaussian functions together produce a new Gaussian function with a new mean and variance. Say I have the two ...
1answer
38 views

### Relation between Gaussian derivatives and Gausian-windowed Cosine function

I am doing some research on UWB radars which transmit a pulse given by: $$g(t) = p(t) cos(2\pi f_{c}t) = A e^{(-\frac{t^{2}}{2\tau ^{2}})} cos(2\pi f_{c}t)$$ In some other papers, the transmitted ...
1answer
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4answers
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### gaussian window for designing filters in DSP

I understand that we do not use rectangular window as a window in filter design because of the ringing/gibbs artifacts due to the sidelobes of the resulting sinc function in the time domain. ...
2answers
93 views

### Fractional Bandwidth of a Gaussian Amplitude Modulated Signal

a gaussian modulated sinusoidal signal may be expressed as $$x(t)=A\cdot e^{(j2\pi ft)}\cdot e^{\left[-\frac{1}{2\sigma^{2}}\cdot(t-t_{0})^{2}\right]}$$ Let's consider the case in which the gaussian ...
1answer
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### What is the frequency of the Gaussian white noise model in control systems?

The design of control systems, particularly for SISO systems, is made convenient by tools such as Bode plots and the corresponding Nyquist stability criterion. These concepts allow engineers to design ...
1answer
117 views

### Variance of Integral of a real white Gaussian Noise Process

In this question, is the answer not equal to infinity ? Answer is mentioned as 6. But my doubt is cant we think of it like a linear combination of many independent random variables each having ...
0answers
36 views

### Pulse Width and Duty cycle in Gaussian pulses

I have a pulse-based radar which transmits frequency-shifted Gaussian pulses. The Gaussian pulse ($p(t)$) is given by: $$p(t) = V_\text{TX} e^{\frac{-t^2}{2 \tau ^2}}.$$ The frequency shifted ...
0answers
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### What types of distributions (except the Gaussian) that follow for random jitter in a correlated signal?

For the simple case, let's consider the correlated signal $s$ with jitter (without noise) as follows: \begin{align} s(t, \theta_i) = \cos(2\pi f (t + \epsilon_t) + \phi + \theta_i), ~~ i=0,1, ... \end{...
1answer
42 views

### White gaussian noise analysis deduction

I´m stuck in a deduction analysis of the variance of a gaussian white noise signal in a "integrate-and-dump detector" of a baseband data transmission receiver, where $n(t)$ is white noise ...
1answer
155 views

### Why do we need to construct Gaussian pyramid using SIFT detector

I am learning about SIFT detection and descriptor. I am slightly unsure about why a Gaussian pyramid is built for the image. I do understand that within each octave, we are applying the Difference of ...
1answer
272 views

### The Effect of the Standard Deviation ($\sigma$) of a Gaussian Kernel when Smoothing a Gradients Image

I am trying to understand why smoothing an image with a gaussian kernel of different sigma values and then computing the gradients of the smoothed image leads to "thicker" trails. In the ...
2answers
302 views

### Derivation of the LMMSE (Linear Minimum Mean Squared Error) Estimate and the MMSE Under Gaussian Prior

I am learning estimation theory through Steven M. Kay - Fundamentals of Statistical Signal Processing, Volume 1: Estimation Theory. In the ...
0answers
42 views

### What could be the optimal filter given this situation?

I am using a camera and a Deep Neural Network to predict one angle. This network received as input the frame, and calculates the mean and the variance associated to the prediction (which is basically ...
3answers
547 views

### Is white noise WSS by nature or not?

I want to know what is the difference between white noise and WSS white noise. is there any difference between them or they're equal? and what about white Gaussian Noise?
0answers
87 views

### Generate skew-normal signal

Is there a simple way to generate a skew-normal shape? Shouldn't be perfect, I just need a rough approximation of it to test peak-detection algorithms. I tried generating the signal according to the ...
1answer
197 views

### Laplacian of Gaussian operator

This might be a silly question. I was reading about the Laplacian of Gaussian (LoG) operator and got confused about the alternative equivelant ways we can make use of it. Let's assume we have a 2D ...
1answer
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### Need assistance from MATLAB point of view [closed]

In my work there are three entities i.e, Tag , reader and RF source. In which for a single bit (0 or 1) from tag towards reader there are 40 consecutive complex gaussian signals at reader . How to ...
0answers
72 views

2answers
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### Formula to calculate/generate gaussian noise?

What is the formula to calculate gaussian noise, given we have variance and mean? I am trying to search google for formula but i am unable to find any much relevant result. If for example i have mean ...
1answer
134 views

### Meaning of AWGN complex and real noise under BPSK Decision Scheme

I'm currently studying error correcting codes and decided to replicate some common Bit Error Rate curves under BPSK modulation. I initially had trouble to convert SNR to a Gaussian $\sigma$ because I ...
0answers
25 views

### Channel Impulse Response is zero mean Gaussian random variable?

In the Paper "Key Generation From Wireless Channels" the channel estimation is given as: $\tilde{h}_{1,A} = \sigma_1^2 + \frac{\sigma^2}{||S_B||^2}$, \$\tilde{h}_{1,A} = \sigma_1^2 + \frac{\sigma^2}{||...
2answers
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### Channel noise - A misnomer?

I was discussing with a colleague with background in communication about white Gaussian (WG) channel noise. He said noise is not added by the channel and it's just a misnomer. Noise, which is thermal ...