# Questions tagged [approximation]

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### 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 ...
566 views

### What approximation techniques exist for the square super-root function?

I need to implement an approximation to the inverse of $x^x$, i.e. the square super-root (ssrt) function. For example, $\mathrm{ssrt}(2) \approx 1.56$ means that $1.56^{1.56} \approx 2$. I'm not as ...
2k views

339 views

### Wavelet transform: How to compute the initial coefficients when only samples are available?

In standard MRA we have that the space of functions at scale J can be expressed as $$V_j = V_0\oplus \left(\bigoplus_{j=0}^{J} W_j\right)$$ where $V_0$ is spanned by the orthonormal system of the ...
235 views

### 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 ...
92 views

### Dimensional reduction from DWT with threshold

I have been trying to find out how can the discrete wavelet transform (DWT) be possible to reduce dimension of data. Then I saw the question which is seemingly related to my work: Feature extraction/...
197 views

### What approximations are involved in STFT of a convolution?

I have two equations in time domain: $$x_k(t)=\sum_{i=1}^N s_i(t)\star h_{ki}(t)+n^a_k(t)$$ and $$x_k(t)=\sum_{i=1}^N s_i(t)\star h_{ki}(t)\star n^c_k(t)$$ which explain the additive and convolutive ...
197 views

### MATLAB implementation Spline Fitting

Let $s(t)$ be a signal that can be approximated by a uniform spline function of order $K$ (say $K=2$): $$s(t)\approx\sum_{n\in \mathbb{Z}}c_n\beta_+^{(K)}(t-n)$$ Suppose that we know the ...