# Questions tagged [math]

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### Mathematical question that comes out of using bilinear transform

So this is related to the Cookbook and I tried solving it maybe two decades ago, gave up, and was reminded of the unsolved problem. But it's pretty damn straight forward, but I still got slogged down ...
2k views

### Replacing “e” in Euler's formula with another number

Does Euler's formula remain valid if we use any real number other than the constant $e$? For example replacing $e$ with 5 would make the formula look like this: $5^{it}$. I tried this idea in ...
3k views

### What is the math behind median filter's noise reduction property?

I am interested in understanding the mathematical reason for why does applying a median filter on an image (or signal) result in reduction of noise.
1k views

### Books/resources for implementing various mathematical functions in fixed point arithmetic for DSP purposes

I'm looking for books or resources that cover the following in detail: implementing mathematical functions (e.g., logarithm, exponential, sine, cosine, inverse) in fixed point arithmetic for DSP ...
4k views

### Phase correlation vs. normalized cross-correlation

I asked this over at Mathematics Stack Exchange, but since this sort of lies on the border of the questions normally asked over there and the questions you see over here I'll ask it here as well. (As ...
4k views

### Looking for an arcsin algorithm

Does anyone have a simple algorithm for computing a reasonably accurate arcsine? By "simple" I mean some sort of polynomial that requires <= 5 multiplies per output sample. And by "reasonably ...
2k views

### Functional analysis for signal processing engineers

It seems that the most advanced pure mathematics course most EE engineers take is Fourier analysis, and after that it's basically 'applied' courses. There's probably a good reason for this, but I'm ...
464 views

### Derivation of fixed-point $\tt atan2$ with self-normalization

I'm trying to understand the maths behind this Fast fixed-point $\tt atan2$ calculation with self-normalization. In particular, equation $(2)$ for theta1 appears to ...
1k views

### State Estimation by steady state Kalman Filter

I am working with a discret Kalman filter on a System $x_{k+1}=A_k x_k+B_k u_k+\omega_k$ $y_k=C_k x_k+\upsilon_k$ $E[\omega_k\omega_k^T]=Q$ $E[\upsilon_k \upsilon_k^T]=R$ I have estimated the ...
864 views

### What is the meaning of this notation?

I have seen this notation in the book Schaums-Outline a couple of times now and I can't quite understand it. I'd very much appreciate if someone explained what it means. I am thinking that it means ...
269 views

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### How moving part pixel intensity values of video frames becomes dominant compared to stationary part intensities in reconstructed frames?

Hello everyone i want to do dynamic texture video sementation using the Fourier transform in MATLAB. I am applying 3-D fft on dynamic texture video frames (using matlab function 'fftn') and ...
344 views

### Mathematical relationship between highpass and lowpass filtering

Let $g, h_{HP}, h_{LP}: \mathbb{R} \rightarrow \mathbb{R}$ and $G, H_{HP}, H_{LP}$ denote their continuous Fourier transforms under the Fourier operator $\mathcal{F}$. Let $*$ denote the continuous ...
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### Independence of Noise at Each DFT Output

My math may be a little rusty, so I would like confirmation or correction or my calculations here. Given white noise samples, $x_i$, which are IID and zero-mean, and variance $\sigma^2_x$. I want to ...
115 views

### Weighted Sum of Auto Correlation - Lower Bound

Given a vector $v$ with elements ${\left\{ {v}_{n} \right\}}_{n = - \infty}^{\infty}$ and denoting ${v}_{n}^{\left( k \right)} = {v}_{n - k}$, namely, a shifted vector by $k$ elements (Mind ...
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### What is the difference between entropy and entropy rate and which one is important in information theory? [duplicate]

By entropy I understand the uncertainty or randomness. But if the uncertainty is high then what is its implication and advantage in transmitting information or as an information source or is high ...
257 views

### How to efficiently calculate points of intersection of a straight line and a contour?

Ex. I have an image, let's say 100x100 pixels with some shape on it. And a set of straight lines that are passing through origin located at some point of image, for example origin located at point (...
379 views

### How to understand energy function in thin plate splines?

guys! I have carried out some experiments using matlab warp tools from here. But the results are not good, so I decide to read its original paper Principal Warps: Thin-Plate Splines and the ...
345 views

I'm trying to create a simple NFC/RFID software simulator and am having a hard time understanding the math fully. I know that NFC tags respond by load modulating the 13.56 MHz wave that the reader is ...
Let $\Omega > 0$ and denote by $\mathcal{B}_\Omega$ the subspace of $L^2(\Bbb R)$ consisting of signals that are bandlimited to $(-\Omega, \Omega)$. Denote \$\mathcal{L}_{\Omega} : L^2(\Bbb R) \...