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Questions tagged [finite-differences]

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Linear difference equation and method of Least Squares

I'm reading the book "Fault-Diagnosis Systems" by Isermann in the par. 9.2.1a. The author explains how to estimate the parameter of a linear difference equation using Least Squares. We start with a ...
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Frequency response of numerical differentiation by polynomial interpolation / finite difference

One can use polynomial interpolation (or finite difference) to do numerical differentiation. However, there seems to be a surprising lack of interest in obtaining frequency response of this numerical ...
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Using Parks-Mcclellan (or others) for FIR differentiator?

I have never seen the use of Parks-Mcclellan for differentiator - most uses tend to be lowpass filters. Is this because Parks-Mcclellan implementation of FIR differentiator has numerical problems and ...
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How far can numerical differentiation be accurate for sinusoids?

Suppose you have samples of uniform interval of a sinusoidal signal that is some sum of sinusoids. Forget about aliasing, as the signal is bandlimited. If we have infinite number of samples at ...
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51 views

Backward finite difference differentiation filter frequency response

As title says what would be frequency response of backward finite difference differential filter, or what would be error of this differential filter, analyzed upon frequency of a signal?
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46 views

The Gradient Operator of a Vectorized Image in Matrix Form

I have this optimization problem: $$ \arg \min_{ X \left( i, j \right) } \sum_{i, j} \left\| X \left( i, j \right) - 255 \right\|_{2}^{2} + \lambda \sum_{i, j} \left\| \nabla X \left( i, j \right) - \...