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5
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2answers
5k views

How do I - exactly - project a vector, onto a subspace?…

I am trying to understand how - exactly - I go about projecting a vector onto a subspace. Now, I know enough about linear algebra to know about projections, dot products, spans, etc etc, so I am not ...
0
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1answer
102 views

Signal Analysis/Processing Textbook

Can anybody recommend me a decent Signal Analysis/Processing textbook. If possible one that deals a little with MATLAB. I have an little knowledge of Real Analysis and fourier transforms. Wavelets i ...
1
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0answers
302 views

Fast Walsh–Hadamard transform generalization for non-power-of-two orders?

I have to process vectors through a Hadamard matrix of order N. If N is a power of 2, I can use the Fast Walsh–Hadamard transform; but if N is not a power of two (for instance, N=12), it is not ...
18
votes
8answers
2k views

Rapid approximation of $\tanh(x)$

This is kind of a signal processing/programming/mathematics crossover question. At the moment it seems more math-related to me, but if the moderators feel it belongs elsewhere please feel free to ...
0
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1answer
333 views

How to extract module and phase from this transfer function?

I have this transfer function: $$H(x)= \frac{1}{x+i(1+x)}$$ How can I extract module and phase and represent them?
1
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0answers
299 views

How to Find Phase Lead/Lag

I have the transfer function $$ H(s) = \frac{s+1}{0.1s+1} $$ I apply the Bilinear Rule with a sampling time T =.25 sec to the transfer function and get a z-domain representation of $$H(z) = ...
11
votes
3answers
11k views

What does the Fourier Transform mean in the context of images?

This is clearly a very important equation with tonnes of properties that I see come up a lot in image processing literature, but I don't understand why this equation is important, and what it is ...
5
votes
3answers
487 views

Period of a product of $\sin$ and $\cos$

I want to find the period of $\sin(t) \cos(\pi t)$. I started off by transforming that into $\frac{1}{2}\left [ \sin((\pi +1)t) - \sin((\pi - 1)t\right ]$, but then I get stuck. How do I find the ...
0
votes
1answer
572 views

Explanation of sinusoidal function: $f(x,y) = A\cos(2\pi(ux + vy) + \phi)$

I never got to take a signals and systems course and this has come up in the math of my image processing review. Can this be explained? The equation for a sinusoidal signal is $f(x,y) = ...
1
vote
1answer
311 views

Fourier transform of Kronecker deltas

I have a binary 2D image that consists of 95% black pixels with a few white pixels scattered about, and I want to convolve it with a 2D gaussian kernel. I'm hoping to exploit its sparsity to improve ...
1
vote
1answer
767 views

Inverse Z-transform of $\frac{1}{(1-z^{-1})^2}$?

What is the inverse Z-transform of $\frac{1}{(1-z^{-1})^2}$? Title says it all. I have a one line solution but can't work out how to get there from tables or first principals. Thanks!
0
votes
1answer
211 views

How to apply the solution of $y(n) = (0.85)y(n-1) + x(n)$ to data

I learned how to solve difference equation $y(n) = (0.85)y(n-1) + x(n)$ using z Transform, and inverse z Transform, I get $h(n) = 0.85^n u(n)$ where $u(n)$ is unit step sequence. Now my ...
2
votes
0answers
416 views

How can I use the time-frequency uncertainty principle?

I have a signal composed of the summation of a set of sine waves of different frequencies. The amplitude of these sub-signals can change so many times a second. I have been told that, if I want to ...
1
vote
1answer
531 views

Finding the poles of a system from a difference equation in MATLAB

I have a system tha is described by the following difference equation: $y(n) + 0.3y(n-1) - 0.3y(n-2) = 0.5x(n) - x(n-1)$ How can i compute, using MATLAB (e.g. with ...
2
votes
0answers
150 views

Singular Value Decomposition

I want to decompose an image $A$ using the Discrete Wavelet Transform and then find the singular values, $S$, such that $A=USV$. I will then do the same to another image such that $B=USV$. I will ...
1
vote
0answers
105 views

Signal filtering and moving averages

Background Given a signal $x_n$ for $n=1,2,\dots$ we can consider its filtered values: $$y_n = \frac{b(L)}{a(L)}x_n$$ where $a(L)=a_0 + a_1L + a_2L^2 + \cdots + a_nL^n$ (similarly for $b$) and $L$ ...
2
votes
1answer
113 views

How can one classify (match within a certain confidence interval) gestures based on accelerometer readings?

I am using an accelerometer-enabled device (mobile phone, to be specific) that enables sampling acceleration at a rate of about 20 samples per second. The samples contain three values, each ...
1
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0answers
30 views

Name this concept: Comparing equal sized vectors vs. comparing features

If you obtain a vector by taking $n$ discrete samples over some underlying function, then it's easy to compare that vector with another of the same size. With a bunch of $n$-dimensional vectors, you ...
0
votes
1answer
83 views

Haar Basis in Signal processing

I want to help one of my friends who studies engineering. He has a homework at the signal processing course. I think I realize what I have to do, but since I don't have their course, I do not fully ...
1
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0answers
97 views

Solving multiple phase angles for multiple equations

I have several equations and each have their own individual frequencies and amplitudes. I would like to sum the equations together and adjust the individual phases, ...
0
votes
0answers
290 views

Moving Average System?

Can someone elaborate on what a moving average system is? I know that the system is defined as: y[n] = (1/3) [x[n] + x[n-1] + x[n-2]] How would we draw y[n] given that we have a graph with ...
2
votes
1answer
371 views

What is a cardinal basis spline?

Wikipedia says: the normalized cardinal B-splines tend to the Gaussian function and writes them as "Bk". Meanwhile, cnx.org Signal Reconstruction says: The basis splines Bn are shown ... ...
1
vote
1answer
54 views

Calculating Basis Functions for DFTs (64 Samples)

I am attempting to graph some 64 sample'd basis functions in MatLab, and getting inconsistent results -- which is to say, I'm getting results that are still sinusoidal, but don't have the frequency ...
6
votes
3answers
534 views

Describing a Wave

I have this wave in front of me, and I am to describe this into a math description such as its function that is equivalent to representing this wave. I have no idea how to start and could use some ...
1
vote
1answer
41 views

Function to take discrete sample of a continuous sinusoid function?

Say I have continuous sinusoid function such as: $$x(t) = \cos(2\pi f_0 t)$$ where $f_0$ is the frequency and $t$ is some time in the function. I want to take samples of this function at some sample ...
2
votes
1answer
685 views

Hilbert transform of white noise

What is the Hilbert transform of a white noise $\xi(t)$? By the Hilbert transform I mean: http://mathworld.wolfram.com/HilbertTransform.html Thank you.
1
vote
1answer
241 views

Signal extraction from multivariate normal

Define: $y= \theta + \varepsilon + a,$ where $a$ is a choice variable in a behavioral economic model, with equilibrium solution $a^e$, and $\theta$ and $\varepsilon$ are independently distributed ...
1
vote
1answer
884 views

Combining Sine Waves on Chart

I would like to combine multiple sine waves with differing amplitudes, frequencies and phases into a single curve that I can display as a graph. What formula will I need to create the points for the ...
2
votes
0answers
68 views

Means to classify data streams or compare similarity

Last year I converted some Matlab code into c to run on embedded Linux. I'm an engineer and normally shy away from maths, but this got me thinking about different ways to classify data or compare the ...
2
votes
2answers
229 views

Can it be proven that such functions don't exist?

We are given $x_1,x_2 \in \mathbb{R}$ and we want to find two functions $v_1(t),v_2(t)$ such that: $$x_1x_2 = \int_{-\infty}^{\infty} v_1(t)-v_2(t) dt$$ A very interesting restriction that we have ...
0
votes
0answers
2k views

When comparing different signals, how can I normalize their amplitude?

I am comparing two sound signals in the frequency domain. As they can have been recorded in different volumes I need to normalize them. My initial approach was to divide each sample by the mean ...
1
vote
2answers
82 views

Should I combine the negative part of the spectrum with the positive one?

When filtering sound I currently analyse only the positive part of the spectrum. From the mathematical point of view, will discarding the negative half of the spectrum impact significantly on my ...
2
votes
2answers
402 views

normalization of a linear combination

I'm a newbie at this forum, so I hope, that this question is not so silly. Let's have some filter $F$, which is a linear combination, thus $F = \sum_{i=0}^{i=N}\alpha_ib_i$, where $\alpha_i$ are ...
1
vote
1answer
254 views

Short question to a pole-zero plot

I worked out this output of a sequence: $$Y(z) = \frac{(z-1)(z+\frac{3}{2})}{z^2 (z-\frac{j}{2})(z+\frac{j}{2})(z-\frac{1}{2})}$$ My problem is the $z^2$. $$z^2 = z * z = (z - 0)(z-0)$$ So I think ...
1
vote
1answer
312 views

How to take the inverse of this signal?

I have a little problem computing the inverse of this signal: $$X(z) = \frac{(z-1)(z+\frac{3}{2})}{(z+\frac{j}{2})(z-\frac{j}{2})(z-\frac{1}{2})}$$ $$X(z^{-1}) = ?$$ I know how to take the inverse, ...
6
votes
1answer
348 views

Qualitative interpretation of Hilbert transform

the well-known Kramers-Kronig relations state that for a function satisfying certain conditions, its imaginary part is the Hilbert transform of its real part. This often comes up in physics, where ...
2
votes
1answer
2k views

Speech processing pre-emphasis: how does it work?

In speech processing, the original signal usually has too much lower frequency energy, and processing the signal to emphasize higher frequency energy is necessary. To perform pre-emphasis, we choose ...
2
votes
3answers
13k views

Matlab Speech Recognition - Mel-Frequency Cepstrum Coefficient (MFCC)

I'm following this Matlab Speech recognition tutorial. I'm stuck on page 5 on the term/concept of MFCC feature vectors. I'm unable to grasp the concept of what an MFCC is.. a matlab function, ...
12
votes
3answers
439 views

Fast computation/estimation of the nuclear norm of a matrix

The nuclear norm of a matrix is defined as the sum of its singular values, as given by the Singular Value Decomposition of the matrix itself. It is of central importance in Signal Processing and ...
0
votes
1answer
78 views

Can u tell me something about these signals?

I have a problem with these signals: $x[n]$ is given: $ x[n] = 3 \delta [n] - 2 \delta [n-1] + \delta [n-1] \text{, } n = 0,...,N \text{, N=8 }$ I computed the DFT and afterwards the 5 IDFT's of the ...
5
votes
2answers
7k views

FFT bins from exact frequencies

I'm trying to understand a few concepts about Fourier Transforms (mainly in the context of signal processing). Let's suppose a signal is sampled at 10kHz and that the FFT size is 1000. If 1000 ...
0
votes
1answer
131 views

Trouble finding the right DTFT pair

i have a periodic signal $x[n] = \cos (\frac{2 \pi}{10}n)$. I found this DTFT pair: That's the only pair for a cosine function i found. But what is $\delta _{2\pi}$ ? Is it just a Dirac $\delta$ ...
1
vote
1answer
112 views

Express a signal by another signal?

I am having trouble understanding and getting the solution to this question: Let $x : \mathbb Z \to \mathbb C$ denote a discrete-time sequence and for $N \in \mathbb N$ let $x |_N$ be the ...
0
votes
1answer
112 views

Derive the function for a given symmetric impulse response

i have a symmetric impulse response: $h[n]=-h[M-n]$ , $0\leq n \leq M$ Frequency response is: $H(e^{j\omega})=je^{-j\omega N}R(e^{-j\omega})$ $R(e^{-j\omega})$ is a real-valued function. I want ...
2
votes
0answers
242 views

FFT signal post processing

This is more a "post a suggestion" topic rather than a question. And thank you if you are willing to read this whole. I've been studing the code in the Nvidia Cuda SDK regarding how to operate a ...
1
vote
1answer
458 views

Is this a square wave signal?

i have a decomposition of a square wave signal: $$ y = \frac{4h}{\pi}(\sin(x) + \frac{1}{3}\sin(3x) + \frac{1}{5}\sin(5x) + ...) $$ I computed the fundamental wave and 2 harmonic waves: $$ U_{r0} = ...
1
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1answer
230 views

When has this sequence a triangular shape?

Can someone explain to me why y[n] has a triangular shape? From what I have found, there is a specific range $n_0$ where y[n] is triangular. But right now I have no clue where to start. $^2$ Search ...
1
vote
1answer
3k views

What is boxcar averaging?

This is an application in signal processing but what I don't understand is how it's done algorithmically. I've seen some stuff online but most of it is just pictures. I would like an example on some ...
5
votes
2answers
6k views

How to fit a curve to a sinusoidal wave

I am wondering how to fit a sinusoidal wave (approximation). I would like to fit it in the form: $y = A\sin(Bx + C) + D$ where $A,\,B,\,C$ and $D$ are constants. The only constants I really care about ...
1
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0answers
649 views

Partial differentiation of vector to find Jacobian (extended Kalman filter)

I am working through some coursework on self-tuning control and part of one of the questions requires the use of the extended Kalman filter for joint parameter and state estimation. For completeness, ...