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3
votes
0answers
38 views

Amplitude/phase recovery on noisy signal

I have a noisy signal that has an ac component of fixed frequency but variable amplitude and phase. I'd like to recover the ac component. The signal (blue trace) is mostly smooth, but has a few ...
1
vote
0answers
114 views

Biquad Filter Optimization

I would like to try optimize a bit more the biquad filters indended for RIAA/non-RIAA equalization at low samplerates (44.1/48kHz). Best fit I get now is little below ±0.3dB for 44.1kHz and below ±0....
0
votes
2answers
127 views

How to improve filter quality at low fs

This my 1st post here. I'm using this impulse invariant (IIM) based method to calculate coefficients for biquad digital filter (for RIAA and non-RIAA de-emph.): ...
0
votes
0answers
21 views

Retrive texture / data from photos of sphere object

I've built a photo box for taking photos of spherical objects (balls etc). I take photos cubical from six different angles. Now I want to extract the bitmap texture from the object with most ...
1
vote
1answer
158 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 ...
3
votes
1answer
92 views

Lagrange Multipliers Optimization - Complex Functions

I want to optimize a sum of complex frequency responses (complex sum is SPL, sound pressure level as a complex function of distance) of a number of loudspeakers, say 10. There is a reference, desired ...
1
vote
1answer
110 views

Multiple parallel IIR bandpass filters with different centre frequencies combined into one filter for optimisation… possible?

Before I begin, I have read these already: IIR filter parallelization Concept of combining multiple FIR Filters into 1 FIR filter I am processing audio using Csound in a high performance real time ...
0
votes
0answers
33 views

Quantization threshold selection

I have the 256-bin histogram representing a distribution of the values taken by a certain descriptor element. This descriptor element takes the values in 0-255 range, hence 256 bins. I want to ...
6
votes
0answers
177 views

Will an unscented Kalman filter be “as good” as other optimisation algorithms for this problem?

I want to calibrate a tri-axis magnetometer when a tri-axis gyroscope is also available. I am fairly certain I can solve this problem using various optimisation algorithms, but I would prefer to use ...
1
vote
1answer
101 views

Optimized 2D wavelet transform using FFT

I'm currenty aiming to optimize my fast wavelet transform (FWT) algorithm for 2D signals (images). It works as follows: one iteration of 1D FWT does convolution of 1D input data with a selected 1D ...
0
votes
1answer
33 views

Optimized resource allocation problem

I am from ECE background and trying to solve channel allocation problem. Let's assume I have three users and three available channels. I would like to allocate channel among them in such a way that ...
0
votes
0answers
10 views

Subgradient method for k-means like problem

I want to solve k-means-like problem. But at first, I wonder that we can apply subgradient method to k-means problem. We want to find the optimal clustering $S = (S_1,S_2,...,S_k)$ such that $$ {\...
3
votes
0answers
83 views

Signal reconstruction in compressed sensing with a simple vector signal as an example

While going through the different types of reconstruction algorithm as mentioned in lecture notes in Compressed Sensing by Richard G. Baraniuk, I came to know that minimum $l_1$ norm reconstruction is ...
1
vote
1answer
63 views

find cross correlation lag by optimization

I have data from many closely located sensors (geophones). These are often contaminated with coherent noise which I need to remove. Some of the most effective de-noising methodologies work if the ...
1
vote
1answer
53 views

Filtering performance on Poisson noise with quadratic data-fidelity

We recently performed a work on signal filtering/component separation (sparse signal/trend/noise). The cost function contains: A quadratic data fidelity term, Some smoothed $\ell_1$ terms for ...
0
votes
1answer
54 views

Best way to approximate a curve?

I have a curve like this one: I need a function to approximate this curve, but I need that the function be a low order function (less than 5). What is a good way to obtain what I expect? Thanks!
3
votes
2answers
100 views

Convex optimization in signal processing

In signal processing, convex optimization plays a useful role in problems such as sparse signal recovery and filter design. What other places does convex optimization appear? For example, in ...
1
vote
3answers
73 views

Decomposing a DFT into multiple FFT calls

I'm using a good fast FFT implementation (vDSP) that will only work on power of 2 blocks of audio data. Now I have a problem where I would like to be able to apply the calculations to non powers of 2 ...
3
votes
0answers
161 views

Weighted Nuclear Norm Minimization for Image Denoising

Recently, I saw new published papers like this paper about denoising images using Weighted Nuclear Norm Minimization (WNNM) approach and I am wondering what is the physical intuition behind it. The ...
0
votes
0answers
20 views

Is it possible to auto compute for the optimal value of Lagrangian multiplier?

Consider the cost function $f(X,\lambda) = \|AX-b\|_2^2 + \alpha \|LX\|_2^2$ $A:$Measurement matrix($R_{m\times n}$,$m \ll n$), $b:$observation vector($R_m$), $L:$Laplacian operator($R_{n \times n}$)...
0
votes
1answer
36 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 regulizer. What is its significance?
0
votes
1answer
81 views

Finding the gradient of a norm in a minimization problem

I have to find the gradient of the following term with respect to $X_{1}$: $\|\Phi\circ(X_{1}-X_{2})-u\|_F^2$ , where $u\in\mathbb{R}^{n}$; $X_{1}, X_{2}\in\mathbb{R}^{N\times J}$ and $\Phi\in\...
2
votes
0answers
48 views

When does l1 regularisation give a sparse solution?

I was maximising a likelihood function, which is convex. I know that the system has a K-sparse solution. I wanted to know the conditions (or some sufficient conditions) on the likelihood function ...
1
vote
1answer
779 views

$l_0$ norm minimization in compressive sensing

I have recently taken up studying compressive sensing related papers. Some things are not very clear to me or may be I am not able to visualize the scenario as is said. Like how $l_0$ norm ...
0
votes
1answer
56 views

Iterative blind sinus signal suppression

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 ...
0
votes
0answers
48 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 ) \...
1
vote
1answer
164 views

L2-optimal 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 this problem. Basically, one ...
1
vote
0answers
92 views

Optimal filter bank from SVD/PCA

Given a million data points in say 100d, is there a way to generate an optimal filter bank of say 20 filters from an SVD of the data ? Call the 100d space $F$ (as in Frequency), with coordinates $[f_1,...
2
votes
0answers
102 views

Any idea how can I optimize morlet wavelet parameters by Heisenberg uncertainty principal and Shannon entropy?

Based on a paper in here, they have proposed a method to optimize morlet function parameter. I have tried to implement their technique, but I can't get rational results. any idea? In here you can see ...
0
votes
0answers
512 views

Digital Image Processing - Contemporary Research Topics

I need to propose a masters degree topic, and I'd like it to be in digital image processing. What are currently relevant topics in this area? I suppose that I'm looking for some kind of optimization,...
3
votes
0answers
62 views

Ideas on matrix factorizations and/or transformations for $\ell_1$ minimization

I am starting with a typical $\ell_1$ basis pursuit problem: $$ \min_{\mathbf{x}} \Vert \mathbf{x} \Vert_1 \quad \mathrm{s.t.} \quad \Vert \mathbf{ERx} - \mathbf{y} \Vert_2 \leq \epsilon, $$ where $\...
2
votes
1answer
186 views

Ideal geometric arrangement of microphone array

I'm going to have to give a bit of context for this question to make sense. I am working on a project which includes audio source localisation in 3-D space through TDoA (Time Difference of Arrival - ...
4
votes
0answers
360 views

fit theoretical spectrum to simulated one

I have a bunch of simulated time series, for which I can compute the power spectrum. Generally, the simulated power spectrum can be sketched as follows: I now aim to calculate the features of the ...
1
vote
1answer
2k views

Determine the optimum receiver and the corresponding $P_{eM}$ for an AWGN channel

I have a source that emits $M$ equiprobable messages, which are assigned signals $s_1, \dots,s_M,$ that are equidistant by $a$. That is, if we plot the $s_k$ signals in a horizontal axis they are dots ...
2
votes
1answer
109 views

How to calculate signal which is not changed by a filter?

Suppose that there is a FIR filter F and a signal S. The filtered signal is the convolution of F and S, F * S. The problem: how to calculate a signal S' such that F * S' = S' (the filtered version ...
2
votes
0answers
81 views

Phong Reflection Model Parameters

Question: Can anyone refer me the Phong reflection model parameters for a face image taken for web-cam? Details: I am doing 3D reconstruction of 2D images using 3D Morphable Model as in this paper ...
4
votes
1answer
123 views

Finding length of period in time domain data

I have a series of measurements of a signal source, which emits a periodic signal at an unknown interval time of p seconds. Detecting the signal is not easy so I am ...
15
votes
1answer
662 views

How to tell if an error surface is convex? (Is it determined by the Covarinace matrix or the Hessian)?

I am currently learning about least-squares (and other) estimations for regression, and from what I am also reading in some adaptive algorithm literatures, often times the phrase "... and since the ...