# Questions tagged [derivation]

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### Causal noise free 1st order derivation in discrete domain

I need to have causal noise-free first order derivation. Now I am using a simple (x(n)-x(n-1))/Ts. It is super-sensitive to noises. Do we have a noise-free or noise-reduced first order differentiation ...
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### What will the impulse response of a matched filter look like if the input is complex?

If $h(t)$ is the impulse response of a filter matched to a signal $s(t)$, I read that $h(t) = ks(t_o - t)$. But what if the signal is complex? I went through the derivation of the matched filter and ...
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### Bounds of the difference of a bounded band-limited function

For a continuous signal (function), we have Bernstein inequality : $$|{df(t)}/dt| \le 2AB\pi$$ where $A=\sup|f(t)|$ and $B$ is the bandwidth of $f(t)$. The question is: is there a relationship ...
394 views

### my Butterworth lowpass formulas do not agree with Fisher webpage

I want to implement Butterworth low-pass filter. Thanks to this question, I have found out that the filter coefficients can be generated using Tony Fisher web-site or using his code. But the problem ...
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### Butterworth filter approximation: derivation and output poles

I am having trouble understanding the exact derivation of the butterworth filter and how it results in the output of the poles. I have researched multiple lecture series and textbooks and this is my ...
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### Derivation of range migration algorithm

Problem: In Walter G.Carrara's book on synthetic aperture radar, the equation is presented: $\Phi(K_X, K_R) = -K_XX_t - R_B\sqrt(K_R^2 - K_X^2) +K_RR_S$ (10.30) And this is said to come from ...
175 views

### Doubts on LMS derivation

I have been trying to follow the Least Mean Square(LMS) algorithm derivation given by Wikipedia here and have the following questions. Here I expected $y(n)$ is to be computed by convolving $x(n)$ ...