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Which topics in maths should I know before I dive into programming for image processing?

I am a student who wants to start out with programming for Image processing but as I do not have a good mathematical background(I haven't studied A-level Maths) I would like to know what are the ...
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42 views

a window slides over a sinusoid, which calculation on window of length p/4 always returns a maximum value compared to other window lengths?

We have a set of discretely sampled points that are on a sinusoid, in this case its period is 40: If we have windows of different lengths that slide over this time series, like this little ...
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1answer
31 views

Show that for a real impulse response function the response to a sine input is …

Working on this problem on linear invariant systems in signal processing, but unsure if I've got the right answer: Show that for a real impulse response function of $H(\omega)$, the response to a ...
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2answers
78 views

Changing a sigmoid curve to have an adjustable point of inflection

I am trying to an implement an adjustable Sigmoid curve such as in the YouTube video here. I found a potentially good candidate: $$f_k(x) = \frac{\left(x-x\cdot k\right)}{k-\left|x\right|\cdot 2\cdot ...
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205 views

How to calculate wavelet energy?

Part of my assignment about signal processing says the following: Compute the Discrete Wavelet Transform for the input signals Group the wavelet coefficients in trees growing across scales ...
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20 views

How to reconstruct a sparsely sampled multiperiodic function?

I have $m$ oscillators, where $m$ is unknown, with periods $\vec p = p_1, p_2, \ldots, p_{m}$. Each of the oscillators $j$ has associated with it a vector of sine coefficients $\vec A_j$ and angle ...
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154 views

Implementing 1D Discrete Wavelet Transform in Matlab

I'm trying to write my own version of the Discrete Wavelet Transform using the bior4.4 filters. I think my implementation is not properly working yet, because whenever I input a signal and a number ...
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37 views

Why is the maximum value of cross-correlation achieved at similar section?

I'm a bit confused and probably need some sleep. When trying to find a short signal inside a long one (or the delay), it's almost a trivial fact that we should look for the maximal valued coefficient ...
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29 views

The probability that a process signals (simple conditional probability)

I have this problem (from Montgomery's Applied Probability and Statistics, 5th Edition, problem 2-145, if anyone wants to see the original problem) but it's long, so for the sake of brevity I'll give ...
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44 views

Is this signal band-limited?

I'm self-learning signal processing now, and I've run into this question about band-limited signals: Consider the signal $x(t) = 1$ for $0 \leq t \leq T$ and $0$ otherwise. I've found that its ...
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83 views

Laplace transform of $f(t)=te^{-t}\sin(2t)$

I was asked to find the Laplace transform of the function $\displaystyle f(t)=te^{-t}\sin(2t)$ using only the properties of Laplace transform, meaning, use clever tricks and the table shown at ...
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184 views

Improvement of Minimum description length (MDL) estimate.

I earnestly request apology if this question is inappropriate for the forum. The question has two parts one technical and the other is not technical. I would appreciate any response. Let me consider ...
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39 views

Why is a wave with high FM aperiodic?

I was playing with sound synthesis in a program I wrote and I had a wave of the form $\sin(2\cdot\pi\cdot(f_c+\sin(2\cdot\pi\cdot f_m \cdot t)) \cdot t) $ So, just simple frequency modulation. When ...
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89 views

From Orthogonal vectors to Useful Bivector

If we have set of orthogonal vectors (X) can we form a set of orthogonal bivectors from that set? I am trying to find if there is a way to get 'more information' from an orthogonal matrix by some ...
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32 views

Finding the coefficients of an MA(1) process given the expectation and variance.

The following is preparation of an exam I have coming up, any help would be appreciated. An MA(1) process is selected to model a stationary time series $\{ X_t \}$. We are given the lag one ...
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28 views

Minimum Phase Filter

Suppose we want to find the minimum phase filter of a causal system with system function $H(z)=z^{-1}−0.3$. The minimum phase filter is $H_1(z)=1−0.3z^{−1}$ (by taking the zero to its conjugate ...
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41 views

Sine wave from fos + simple signal

I have a first order system $\frac {1}{(s+c)}$ and a signal of the form $\sum_{k=0}^\infty (-1)^{k}e^{-2ks}a(\frac{1-e^{-2s}}{s}- be^{-s}(\frac{1-e^{-s}}{s^2})) $ i.e a periodic signal of a square ...
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50 views

Fourier transform on trig wave

Find the fourier transform for signal in this picture (sorry for the bad quality) Could it be done like this? The signal is a sum of two triangular waves that are each delayed. ...
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67 views

Sufficiently rich signals

I know that a signal is sufficiently rich of order $n$ when it "includes" at least $\dfrac{n}{2}$ different frequencies. This is intuitive when we are talking about a sine but what about other kind of ...
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36 views

exponential term evaluation doesn't make sense in this example

I am studying for my final and doing some practice questions, but I am confused by something: Here the solution says k at 0 we get N/2, but there is no way that answer is correct. If k is at 0 the ...
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1answer
19 views

Verifying by Signal Energy Method?

There's a question in my signal processing textbook that says: Verify that $\int_{-\infty}^{\infty} sinc^2 (kx)dx = \frac{\pi}{k}$ by signal energy method. I'm unsure what "signal energy method" ...
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27 views

Peak absolute variation of a Band-Limited Process around its current sample for a given horizon T

Is it straightforward to find a bound on the maximum possible absolute variation around the mean or the last sample of a band-limited process for a given time horizon like $T$? More specifically, how ...
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22 views

How to use trigonometric Fourier series to verify this result

I'm studying signal processing. I've found the associated Fourier Series for a message $m(t)$ = $t^2$ over the interval $[-1, 1]$ with period $T = 2$. However, I'm then asked to verify that ...
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21 views

Why does one compute the power spectrum of an image from the Fourier transform of its autocorrelation and from the square of its spectrum?

image: f(x,y) fourier transform of f is F(u,v) my Goal is to compute its power spectrum. [denoted by P(u,v)] the first way to compute is by using the magnitude of fourier transform: ...
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25 views

What happens to fourier transform of the sampled output of pure sinusoidal input of 26kHz if sampled with 44.1kHz sample frequency?

Because pure sinusoidal signal only contains impulses, I was wondering what happens to the fourier transform of the sample output from the sinusoidal input of $26$kHz if the sampling is done with ...
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1answer
24 views

hamming window eqation formula problem

can anybody know when to take hamming window equation $$w(n) = 0.54-0.46\cos(2\pi n/M)$$ or $$w(n) = 0.54+0.46\cos(2\pi n/M)$$ i am confused between $+$ and $-$ sign.. which sign wil be considered ...
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34 views

Solving convolution $f(t)*g(t)$ where $f(t) = u(t) - u(t-2)$ and $g(t) = e^{-2t}u(t)$ where $u(t)$ is heaviside step function

How does one solve convolution $f(t)*g(t)$ where $f(t) = u(t) - u(t-2)$ and $g(t) = e^{-2t}u(t)$ where $u(t)$ is heaviside (unit) step function? I tried using Fourier transform of both functions to ...
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13 views

Determine the filter order required for a checvshev filter design.

A highpass IIR digital filter is required to meet the following specifications....... I am not sure what the values of A-passband and A-stopband are.
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19 views

Can a rectangular pulse be understood as a normal distributed pulse?

Can a rectangular pulse be understood as a pulse with a normal distribution, like a gaussian pulse? In signal-processing there are some specific properties for gaussian pulses. I wondered if you can ...
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16 views

Do you know any f(x) formulas for quasi-random signal generation?

I wonder, if there are any f(x) formulas for quasi-random XY signal generation, which shows no signs of periodicity, or is similar to such electrophysiological signal as EEG (example below). ...
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43 views

Why are there so many different symbols to represent the Heaviside (unit step) function

In signal processing, the unit step function is typically written as $u(t)$. In other references though I have seen it represented as $H(t)$ and even $\theta(t)$. The unit impulse is fairly ...
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7 views

higher order derivatives of input than output

I am being asked in a problem to consider an input f(t) being sent through a system defined as: y(t) = (D^2 + a*D + b)f(t) (1) and then to use this as input to a system of the form: (c1*D^2 ...
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1answer
154 views

Convolution of sine and unit step function

I started studying signal convolution recently and the first sample problem I got is to find convolution of sine and unit step function (Heaviside function). Here is what I have right now. ...
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65 views

How can I mathematically proof an incoherent superposition of waves?

Let $\psi = A(t)\cos(\theta_1(t))$ and $\phi = B(t)\cos(\theta_2(t))$ two independent waves which phases and amplitudes depend on the time. Then it follows that the intensity of the superposition of ...
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23 views

Signal-extraction knowing both the sum and the sum of the absolute values of normally distributed variables

I have two normally distributed variables $X∼N(μ_{x},σ_{x}²)$ and $Y∼N(μ_{y},σ_{y}²)$. I can observe both the sum of their values and the sum of their absolute values, i.e. $Z₁=X+Y$ and $Z₂=|X|+|Y|$. ...
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32 views

Difference between the Rectangular “Window” Function and the Rectangle Function

I'm getting ahead in my differential equations textbook (Fundamentals of Differential Equations by Nagle et. al) and in the chapter of Laplace Transforms it states that the rectangular window function ...
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1answer
50 views

Marginal probability density function of Stochastic process

I was solving the following question and I derived the Auto correlation function and proved that it is a WSS process. However, I am not sure how to go about finding the Marginal probability density ...
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139 views

Sampling theorem.

Let us consider \begin{equation} \hat{f}(x)=\sum_{n\in \mathbb Z}\left\langle\hat{f},e^{i n x}\right\rangle_{L^2[-\pi,\pi]} e^{i n x} \ \ \ \ \ \ \ \ (1) \end{equation} where $\langle g, ...
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14 views

Evaluating Welch bounds for k > 1

I am getting an incorrect result when I try to evaluate the Welch lower bound $c_{max}\;$ for $k \gt 1.\;$ This bound is defined as: $\qquad\qquad$If $\{x_1,\ldots,x_m\}$ are unit vectors in ...
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32 views

Why is the Welch bound for max cross-correlation not 1?

I am trying to self-educate about m-sequences, which led me to the topic of the Welch lower bounds on the maximum cross-correlation of sets of vectors in $\mathbb{C}^n$. The Wikipedia page "Welch ...
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1answer
33 views

Magnitude of $H(\Omega)$

Could someone nudge me in the right direction on how to get the magnitude of $H(\omega) = (1-\sqrt(2)e^{-j\omega}+e^{-2j\omega}) / (1-.5\sqrt(2)e^{-j\omega}+.25e^{-2j\omega})$ If it was just a two ...
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22 views

recovering bits from distorted signal

I have a signal: $r(t) = \sum_k a_k g( lT/2 -k(T+\Delta T) )$ where $a_k \in \lbrace\pm 1\rbrace$, $g(t)=\frac {\sin(2\pi t/T)}{2\pi t/T}$, $T/2$ is the sampling period, and $\Delta T$ is a ...
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51 views

Shifted Fourier transform

Please can some one help and give me a direction to evaluate the following shifted Fourier transform: \begin{alignat}{2} s(x_c) =&\frac{1}{\Delta x_0} \int_{x_c-\Delta x_0}^{x_c+\Delta ...
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169 views

Matlab: Impulse response of linear time invariable (LTI) sine-signal

I'm preparing for a lab in a Signals and Systems course in my university, 5th semester. I've found old exercise material from the class and since I know some Matlab and have dealt with LTI systems ...
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1answer
21 views

How did they get this result through parseval's theroem?

How did they get this result. It does not make sense, can anybody show me how they derived this result. My question is how did they totally remove e^(jkwot), by what identity and I know it is ...
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1answer
35 views

Manipulating an expression into alternate form

I'm trying to get $1-1.4e^{-j\theta}+.81e^{-2j\theta}$ into the form $(1-d_ke^{-j\theta})$. I'm not sure which rules I could apply to get it into that form. May I have a hint at it or even if it is ...
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24 views

Reconstructing a signal at twice the bit-rate

I have a discrete-time signal as: $\alpha_l = \sum_k a_k g(lT/2 -k(T+\Delta T))$ where $a_k \in \lbrace\pm 1\rbrace$, $g(t)=\frac {sin(2\pi t/T)}{2\pi t/T}$, $T$ is the bit period, and $\Delta T$ is ...
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25 views

Inverse SNR: find the first point with a specified SNR ratio where noise and signal are simple normal distributions

I have a pair of 2 simple normal distributions for noise and signal , specified by $\mu1,\sigma1$ and $\mu2,\sigma2$, so I know how to calculate CDF1, CDF2 for every point. I would like to find $x$ = ...
2
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1answer
245 views

Fast fourier transform and nyquist frequency

Trying to figure out how to use Matlab to calculate the nyquist frequency of a signal. Given a function, lets say $y = 5\sin (2t + \pi /3) + \sin (t + \pi /2)$ for $t > 0$. How do we use a fft in ...
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30 views

Averaging and approximation

I read a paper reference at http://arxiv.org/pdf/1101.1764.pdf that if we average a set $V=\{V(t_0,\nu_0), V({t_1,\nu_1),..., V(t_n,\nu_n)}\}$; with $V(t_i,\nu_i)=e^{i\sigma(t_i,\nu_i)}$ then we can ...