# Questions tagged [approximation]

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### What is the sum $\sum_{m} e^{i (U_m k + \beta_m)}$ when $U$ and $\beta$ follow different distributions

I have the following function. $$x(k) = \sum_{m} e^{i (U_m k + \beta_m)}$$ $i = \sqrt{-1}$ Here, $U_m$ are samples drawn from a Gaussian random distribution. $$U_m \sim \mathcal{N}(\mu, \sigma)$$ ...
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### Approximate irregular signal to square signal

I'm trying to approximate this irregular signal to a square signal because I need to get the amplitude and pulse width of it. Is it possible to do an approximation for it?
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### calculate or decompose a Fourier transform signal amplitudes with unknown weights on sources

migrated from math-se... I am trying to calculate , or approximate the solution of following Fourier-sine transform problem that can be expressed as a contributions of periodic sources $f_i(x)$ and ...
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1 vote
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My question is related to the quantization error and the functionality of SAR-ADCs. In general, the quantization error of an ADC is defined as +-0.5LSB. If this concept is correct a voltage that ...
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### Performance bounds for low-pass filters

Precisely how does the performance of an FIR filter depend on its design criteria? To illustrate, here is a specific question that probably does not have a convenient answer: The Parks-McClellan ...
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### Relation between curve fitting and filtering

Before I ask the question: I am from mechanical background and would appreciate a detailed answer. Generally, for automobiles, I am trying to understand the following: Given, say $1\;\mathrm{sec}$ ...
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1 vote
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### Adaptive Piecewise Constant Approximation (APCA) with wavelets/DWT

I am trying to approximate a vector or a time series, in order to have as little changes as possible. To do so, I pretend to apply the Adaptive piecewise constant approximation (APCA) algorithm. ...
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### Calculating Signal Approximation Error (Theoretical signal - Real hardware signal)?

I've got a FIR filter, which I developed in IC. Now, when I got my results, I ended up with two signals: Theoretical signal calculated through MATLAB as a response to my input. Real response given by ...
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1 vote
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### Standard deviation of Gaussian corresponding to perfect low pass filter [1,1]

For a time discrete signal, the rect-filter (for 1D signal [1,1]) is a perfect low pass filter. I was wondering, what is the best gaussian approximation of this filter? For a current problem, I ...
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### How to use Expectation maximization to estimate poisson noise matlab [closed]

I delved into the state of the art of algorithms for Poisson noise estimation in order to estimate the variance, I found that the Expectation Maximization algorithm is very used and it is very ...
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### The Mathematical Relationship Between Derivative and Convolution

What I'm looking for is the mathematical proof of why we can calculate derivatives as a simple convolution of a mask, and how do we get that mask? I know it has something to do with how the derivative ...
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### Using continuous verses discrete wavelet transform in digital applications

I am familiar with much of the mathematical background behind wavelets. However when implementing algorithms on a computer with wavelets I am less certain about whether I should be using continuous or ...
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1 vote
127 views

### Establishing the function of a decaying signal

I have a set of samples from a signal. The signal is erratic in behaviour at the beginning but then it settles down and oscillates around the value of 100 (the frequency of oscillation is not ...
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