# Tag Info

### Why is Gaussian noise called so?

Noise is random, but like most random phenomena, it follows a certain pattern. Different patterns are given different names. Consider rolling a die. This is clearly random. Roll the die 1000 times, ...
Accepted

### What Does It Mean Exactly When Two Parts of a Signal Are Correlated?

Yeah, it can mess you up pretty badly if you don't get the fundamentals right off the get-go. This is how I interpret correlation, and it has worked for me for what I do for a living. Let's start ...
Accepted

### What is the connection between analog signal to noise ratio and signal to noise ratio in the IQ plane in a quadrature demodulation system?

Because each step in the processing chain is linear we consider a case with only noise and no coherent signal. Denote the noise $\xi(t)$. The $I$ and $Q$ signals are \begin{align}\ I(t) &= \xi(t) \...

### Is Allan variance still relevant?

I currently work in the design of atomic clocks and precision frequency sources and pleased to report that the Allan Variance is still quite relevant and useful. In fact it's utility extends to ...
Accepted

### Concept About Estimated Standard Deviation

Given data ${ \left\{ {x}_{i} \right\} }_{i = 1}^{N}$ the Empirical STD of the data is well defined: $$STD = \sqrt{ \frac{1}{N - 1} \sum_{i = 1}^{N} { \left( {x}_{i} - \bar{x} \right) }^{2} }$$ ...
Accepted

### Adding Variance \ Weights Information When Solving a Basis Pursuit Denoising Problem (BPDN)

Your formulation: $$\arg \min_{\boldsymbol{x}} \frac{1}{2} {\left\| A \boldsymbol{x} - \boldsymbol{y} \right\|}_{2}^{2} + \lambda {\left\| \boldsymbol{x} \right\|}_{1}$$ Has 2 elements: The ...
Accepted

### Subsample Time Delay Estimation

Even though the signals are sampled you can get accuracy which is well above the accuracy offered by the samples as long as you sample using Nyquist. Actually, Using the Matched Filter you can achieve ...

### What Does It Mean Exactly When Two Parts of a Signal Are Correlated?

Correlation between 2 signals means you can say something about one of them by observing the other. If you mean the standard correlation, $E \left[ x y \right]$, it means you knowledge second moment ...
Accepted

### Capacity of cascade binary symmetric channels

A binary symmetric channel (BSC) can be characterized by its complemented probability $p$. Its well-known capacity is $$C = 1 - H(p) = 1 - (-p\log(p) - (1-p)\log(1-p))$$ where $H(p)$ is binary ...
Accepted

### How is cross-correlation related with orthogonality?

I suppose you mean the cross-correlation at lag zero. Well take an Hilbert space $H$ (i.e. a metric space in which you can define a scalar product $\langle\cdot ,\cdot\rangle$). Then $x,y\in H$ are ...
Accepted