# Questions tagged [optimization]

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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 ...
1k views

### Adaptive filtering: Optimum filter length and delay

I'm trying to find the optimum filter length for an Adaptive Filtering, using RLS Algorithm. I'm using this design: So the "error" signal is the signal without noise (and that's the signal that I ...
960 views

### Design ${L}_{2}$ Norm Optimal Infinite Impulse Response (IIR) Filters

It is widely known that matching a FIR filter of fixed length to a band model is an unconstrained QP-problem. The MATLAB function firls() implements a solution to ...
423 views

### Significance of $\lambda$ in Basis Pursuit

In basis Pursuit, L1 minimization is done to perform compressed sensing. In the literature there is a $\lambda$ parameter used as a regularizer. What is its significance?
264 views

### How to improve filter quality at low fs

This my 1st post here. I'm using this impulse invariant (MZT) based method to calculate coefficients for biquad digital filter (for RIAA and non-RIAA de-emph.): ...
157 views

### Implementation of Block Orthogonal Matching Pursuit (BOMP) Algorithm [closed]

How would one implement the Block Orthogonal Matching Pursuit (BOMP) Algorithm in MATLAB?
The Total Variation Denoising Problem is given by: $$\arg \min_{x} \frac{1}{2} {\left\| A x - y \right\|}_{2}^{2} + \lambda \operatorname{TV} \left( x \right)$$ Where $\operatorname{TV} \left( \... 1answer 101 views ### On the Measurement Matrix Used for Compressing Sensing Assume we have a matrix$x$of size$(8,8)$where each column is considered to be sparse with degree of sparsity equals to$4$. it means that every column can have$4$zeros and$4$non-zeros values ... 1answer 778 views ### How does parallel structure implementation of IIR speed up the process ? What happens in case of FIR? I was learning about digital filter structures and there I came to know that parallel implementation of IIR filters speeds up the process and I understand that.But what I am not convinced of is that ... 3answers 5k views ### Librosa stft + istft - Understanding my output (which always seems too perfect) at varying window lengths I've just started to use Python with Librosa for a DSP project I'll be working on. First thing I've been trying to do is determine my preferred parameters for the FFT window size, and hop-distance. ... 1answer 2k views ### Fitting an IIR filter to a complex transfer function anybody knows of better ways to fit an IIR filter to a complex transfer function than Matlab's invfreqz.m? I'm implementing a little transfer function fitting ... 1answer 50 views ### Resources on Solving Convex Optimization Problems in the Compress Sensing Field When I read papers of compressed sensing, sparse representation and whatever requiring optimization of a cost function, I just find the final results as an iterative equation or so which will converge ... 1answer 222 views ### How to Smooth Gradient Estimates for Steepest Descent Optimization In steepest descent methods of minimizing a function$f(x), x \in \mathbb{R}^d$, it's common to approximate the gradient by finite differences:$\qquad\qquad \nabla f(x) \approx gradest( x; h ) \...
There are two real signals in the form of $A_i sin(wt+p_i), i=1,2$. Suppose frequency $w$ of both the signals is the same and amplitude $A_i$ and phase $p_i$ are different. The first signal has ...