Questions tagged [approximation]

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23
votes
5answers
14k views

What Is the Best First Order IIR (AR Filter) Approximation to a Moving Average Filter (FIR Filter)?

Assume the following first order IIR Filter: $$ y[n] = \alpha x[n] + (1 - \alpha) y[n - 1] $$ How can I choose the parameter $ \alpha $ s.t. the IIR approximates as good as possible the FIR which is ...
11
votes
2answers
10k views

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 ...
0
votes
2answers
536 views

Kaiser window approximation

Are there any "good" low-computational-cost approximations for parameterized Kaiser window generation suitable for small systems/languages that do not include Bessel functions in their standard ...
0
votes
2answers
221 views

z-Transform Methods: Definition vs. Integration Rule

The definition of the z-transform is defined as $z = e^{sT}$ where "s" is complex frequency for continuous-time systems and "T" is the sample period. Why are rules such as the forward rectangular ...
3
votes
2answers
534 views

Pade Approximation of dead time

For the time delay $e^{-sT}$ I shall find the Pade Approximation for $M = 0$ and $N = 1$. $f(s) = \sum_i^{\infty} a_is^i \approx \dfrac{\sum_{n=0}^{N} b_is^i}{\sum_{m=0}^{M} c_is^i}$ $e^{-sT} = \...