Questions tagged [approximation]
The approximation tag has no usage guidance.
54
questions
1
vote
0
answers
79
views
Approximating fractional-octave Gaussian smoothing with non-causal variable-width IIR filters
I am trying to implement fractional-octave smoothing of amplitude response data with approximated Gaussian filters, as briefly discussed in this AES paper.
Unfortunately, no implementation details are ...
- 11
0
votes
1
answer
123
views
What is the sum $\sum_{m} e^{i (U_m k + \beta_m)} $ when $U$ and $\beta$ follow different distributions
I have the following function.
$$ x(k) = \sum_{m} e^{i (U_m k + \beta_m)} $$
$i = \sqrt{-1}$
Here, $U_m$ are samples drawn from a Gaussian random distribution.
$$ U_m \sim \mathcal{N}(\mu, \sigma) $$ ...
- 107
0
votes
0
answers
40
views
Approximate irregular signal to square signal
I'm trying to approximate this irregular signal to a square signal because I need to get the amplitude and pulse width of it. Is it possible to do an approximation for it?
- 1
2
votes
0
answers
83
views
calculate or decompose a Fourier transform signal amplitudes with unknown weights on sources
migrated from math-se...
I am trying to calculate , or approximate the solution of following Fourier-sine transform problem that can be expressed as a contributions of periodic sources $f_i(x)$ and ...
- 113
2
votes
1
answer
1k
views
Quantization error of SAR-ADCs
My question is related to the quantization error and the functionality of SAR-ADCs. In general, the quantization error of an ADC is defined as +-0.5LSB. If this concept is correct a voltage that ...
- 85
0
votes
1
answer
87
views
Performance bounds for low-pass filters
Precisely how does the performance of an FIR filter depend on its design criteria?
To illustrate, here is a specific question that probably does not have a convenient answer:
The Parks-McClellan ...
1
vote
1
answer
113
views
Optimally approximating the sign function by functions with compactly supported Fourier transform
I'm re-posting a question of mine from math.stackexchange in hopes that folks here might have the right kind of expertise.
I'm looking for a systematic way to approximate the sign function
$$\...
- 113
2
votes
1
answer
107
views
Approximation and IIR Filters
Consider the discrete-time time-invariant system with input $x[n]$ and
output $y[n]$ satisfying
$$y[n] = \sum_{k=1}^5{x[n-k]}$$
Consider approximating the desired system with a second-order IIR
system ...
0
votes
1
answer
260
views
How to save Fourier series approximated signal to a WAV file
I changed this Matlab/Octave code to approximate square wave by using combination of Fourier series and Fejér taper:
...
- 867
2
votes
1
answer
171
views
How to estimate the modulation transfer function of images?
I'd like some way to estimate the modulation transfer function in images. This is the observed drop in amplitude vs increase in frequency of spatial details - nice illustration here:
(from https://...
- 230
4
votes
4
answers
434
views
How to determine precision needed for sin approximation used for sound synthesis?
I am doing some procedural sound synthesis in Java. I want to have a sine wave as one of the possible basic sounds. When experimenting with that, I have found the default Java ...
- 141
0
votes
1
answer
324
views
Is there a way in MATLAB to approximate an FIR filter using an IIR Filter? [duplicate]
I am a student trying to understand how this is possible. I've done some research on the web with not many sources showing up with solutions to this problem that are usable. What techniques are used ...
- 11
-2
votes
1
answer
327
views
Confusing regarding triangular wave vs square wave?
I am reading signal processing first by Mcclellan. In chapter 3, I came across the term "discontinous" as shown underlined in attached photo.
Apparently "discontinuous" means having a gap/break but ...
- 1,850
1
vote
0
answers
155
views
"Improved" MZT/IIM type One pole LPF
Some time ago, while playing with all kind of approximation of common math functions, I came up to this idea to calculate a1 coefficient for a one pole low pass filter:
\begin{array}{l}a1=-(1+x+\...
- 867
0
votes
0
answers
49
views
Some difficult-to-approximate signals to test an signal extracting algorithm
I am searching for some strange signals in order to test an algorithm that I am developing. I've found an article by Donoho and Johnstone where they propose to test the algorithms using Blocks, Bumps, ...
- 143
2
votes
1
answer
234
views
Amount of exactly approximated samples with Padé approximation
I've already had some good discussion with Fat32 in this question yesterday.
Today I'm confused again. The author of Statistical digital signal processing and modeling M.h. Hayes and Fat32 both ...
- 328
0
votes
1
answer
140
views
Self study question about Padé Approximation and transfer functions
Given a signal $x[n] = [1, 2, 3, 4, 5]$. How many transfer functions can be found with Padé approximation which have a causal impulse response and start with those five samples. How many of them are ...
- 328
3
votes
1
answer
117
views
Ratio of expected values of squares of errors in power quantities, in dB
An amplitude quantity $a$ is estimated by two estimators $\hat a_1$ and $\hat a_2.$ The error of estimator $\hat a_2$ is compared to that of $\hat a_1$. One possible comparison is the ratio of ...
- 13.5k
0
votes
1
answer
2k
views
What's wrong with my implementation of the Matching Pursuit algorithm?
I have recently attempted to implement a simple version of the Matching Pursuit algorithm, following the description detailed on Wikipedia. Although the algorithm itself seems dead simple, my ...
- 111
2
votes
2
answers
5k
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 ...
1
vote
1
answer
246
views
Techniques to reject noisy neural network input
Suppose an artificial neural network is used to approximate a sine wave (shown in red in the graph below), given the linear input variable $x$ (scaled such that the ANN input is $x_{\rm nn}\in[-1;1]$)....
- 165
1
vote
1
answer
365
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/...
- 113
0
votes
1
answer
80
views
How to determine which Fouriers Series terms to use to approximate a signal?
I have a signal (a time-series of air temperature values) that I can approximate quite well with a Fourier series. However, the number of terms in the series grows rapidly, to the point that 30 - 40 ...
- 103
19
votes
5
answers
6k
views
Finding polynomial approximations of a sine wave
I want to approximate the sine wave given by $\sin\left(\pi x\right)$ by applying a polynomial waveshaper to a simple triangle wave, generated by the function
$$T\left(x\right)=1-4\left|\tfrac{1}{2}-...
- 390
3
votes
2
answers
806
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} = \...
- 135
2
votes
2
answers
2k
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 ...
- 35.2k
1
vote
0
answers
339
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 ...
- 11
0
votes
1
answer
766
views
How to approximate the sample rate?
I have a simple program that captures audio from an audio device. I have configured a nominal sample rate of 48000Hz and a buffer size of 1 millisecond. The audio sub system should execute my capture ...
- 239
2
votes
1
answer
153
views
Biorthogonal Wavelet Expansion
Consider a multiresolution analysis (MRA) $\{V_j\}$ in $L^2(\mathbb R)$ generated by the scaling function $\phi(x)$ and such that for each $j\in\mathbb Z$, $V_j\subset V_{j-1}$. For a given function $...
- 768
3
votes
4
answers
3k
views
Relation between curve fitting and filtering
Before I ask the question: I am from mechanical background and would appreciate a detailed answer.
Generally, for automobiles, I am trying to understand the following:
Given, say $1\;\mathrm{sec}$ ...
- 207
1
vote
1
answer
2k
views
Adaptive Piecewise Constant Approximation (APCA) with wavelets/DWT
I am trying to approximate a vector or a time series, in order to have as little changes as possible. To do so, I pretend to apply the Adaptive piecewise constant approximation (APCA) algorithm. ...
- 121
2
votes
1
answer
1k
views
Determinant of Hessian approximation (SURF)
I have a question regarding formula in SURF article by Bay et al.
Theory
Given a point $p=(x,y)$ in an image $I$, the Hessian matrix $\mathcal{H}$ in $x$ at scale $\sigma$ is defined as follows
$$
\...
- 21
2
votes
1
answer
696
views
Wavelet transform: How to compute the initial coefficients when only samples are available?
In standard MRA we have that the space of functions at scale J can be expressed as
$$V_j = V_0\oplus \left(\bigoplus_{j=0}^{J} W_j\right)$$
where $V_0$ is spanned by the orthonormal system of the ...
- 768
3
votes
1
answer
1k
views
Approximation of Hilbert Transform Using Very Short Hilbert Transform FIR / IIR Filter
Hilbert transform is a quite sensitive topic here, since Gabor's paper, Theory of Communication, J. Inst. Electr. Engineering, London, 1946. Perhaps even more important than the Fourier transform.
...
- 31.7k
0
votes
2
answers
110
views
How to choose basis functions that contribute most efficiently per term to an approximation of an image f(x,y)?
GOAL:
I would like to approximate some positive, scalar function, $f(x,y) > 0$, on a 2D field of finite size i.e. $x=[a,b],y=[c,d]$
OBSTACLE:
I am familiar with the set of basis functions used ...
5
votes
1
answer
283
views
Looking for a better algorithm for finding the slope of an input signal
I've got an input signal that while sloping up, approximately bounces off an imaginary line. I'm looking for the equation to that imaginary line. I have a method, but is very brute force and it ...
- 151
3
votes
1
answer
271
views
Wavelet decomposition
For the following code,
X=[2 2 3 100 4 0 98 100 90 2 3 67 98 0 6 6 89 9 21 78]
[C,L]=wavedec(X,N,'db1');
where N is the ...
0
votes
0
answers
70
views
Unexpected peak after up & down sampling
I am working on signals to check how approximation can change the results. I am testing on example that can change frequency from 22kHz to 20 KHz. I prepare this script in MatLab
...
- 5
0
votes
0
answers
179
views
Second-order sections from complex coefficients
I have an impulse response ir that I need to approximate with an iir because of realtime requirements. For stability I want to break down the 10th order IIR generated with Steiglitz-Mcbride to biquads ...
- 1,123
0
votes
1
answer
87
views
How to determine best fit from two?
I'm studying some variances ($\sigma^2$), that in my case, they must depend by velocity squared $v^2$.
So, in my experimental proofs, I have plotted a graph of $\sigma^2/v^2$, and I was hoping to ...
1
vote
0
answers
210
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 ...
- 11
0
votes
1
answer
275
views
Calculating Signal Approximation Error (Theoretical signal - Real hardware signal)?
I've got a FIR filter, which I developed in IC. Now, when I got my results, I ended up with two signals:
Theoretical signal calculated through MATLAB as a response to my input.
Real response given by ...
- 595
1
vote
1
answer
401
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 ...
- 11
0
votes
1
answer
963
views
How to use Expectation maximization to estimate poisson noise matlab [closed]
I delved into the state of the art of algorithms for Poisson noise estimation in order to estimate the variance, I found that the Expectation Maximization algorithm is very used and it is very ...
- 9
4
votes
3
answers
1k
views
The Mathematical Relationship Between Derivative and Convolution
What I'm looking for is the mathematical proof of why we can calculate derivatives as a simple convolution of a mask, and how do we get that mask?
I know it has something to do with how the derivative ...
- 141
1
vote
0
answers
105
views
How to Approximate / Fit a Function and a Lower Bound on It?
I am dealing with a complicated optimization problem with two parameters $N, K$. Setting $K =$ constant and finding the minimum for different $N$'s lead to a set of function values. I can do this for $...
- 288
-4
votes
1
answer
146
views
How to combine similar signals to generate another one?
Assume there are 11 signals. These signals are very similar to each other in both time and frequency domains. (And the similarity between them is not random; they are similar because they have somehow ...
- 99
1
vote
1
answer
830
views
Signal approximation using linear combination of functions
How I can approximate the signal $x(t)=0.001\,t^3 \exp(-0.1t)$ in the interval $[0,100]$ using a linear combination of the following functions:
$f_1(t)=A_1$
$f_2(t)=A_2\cos(0.05t)$
$f_3(t)=A_3\cos(...
- 481
18
votes
2
answers
18k
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 ...
- 1,122
1
vote
1
answer
138
views
Establishing the function of a decaying signal
I have a set of samples from a signal. The signal is erratic in behaviour at the beginning but then it settles down and oscillates around the value of 100 (the frequency of oscillation is not ...
- 275