# Questions tagged [math]

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### 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 ...
751 views

### Design ${L}_{2}$ Norm Optimal Infinite Impulse Response (IIR) Filters

It is widely known that matching a FIR filter of fixed length to a band model is an unconstrained QP-problem. The MATLAB function firls() implements a solution to ...
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.
162 views

### Laplace Transform of $-e^{-at}u(-t)$

I have found a problem in applying Laplace Transform to $-e^{-at}u(-t)$ I am doing these steps: $$= - \int_{-\infty}^{+\infty} e^{-at}u(-t) e^{-st}dt$$ $$= - \int_{-\infty}^{0} e^{-at} e^{-st}dt$$...
772 views

### 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 ...
724 views

### 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 ...
This question is based on the application of the pdf which was an earlier question of mine asked here Confusion regarding pdf of circularly symmetric complex gaussian rv If $v \sim CN(0,2\sigma^2_v)$ ...
Probably a stupid question, but I'm slowly making my way through Julius Smiths' filter book. The maths is slightly defeating me at points. This function $H(e^{j\omega t})$, why is it a function of ...