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1answer
290 views

Absolute value in exponential, signal energy?

How can this give this result? Isn't the absolute of $(e^(-2*t))$ always 1?
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25 views

Detection theory - Sensitivity, Specificity - in Multi-Detection scenario

I am working in computer vision and have this scenario: For each frame of a video sequence I have the following: Image with a resolution of width * height discrete pixel locations. List of "...
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1answer
84 views

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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0answers
56 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
33 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
357 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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0answers
750 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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0answers
29 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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1answer
429 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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2answers
475 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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0answers
32 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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1answer
130 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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2answers
1k 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 http://...
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1answer
45 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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1answer
102 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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1answer
59 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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1answer
35 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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0answers
47 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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0answers
93 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. $$x(t)=A\Lambda\left(...
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2answers
162 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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1answer
37 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
26 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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1answer
29 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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0answers
32 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: $|F(u,v)|=\sqrt{...
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1answer
30 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
44 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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1answer
55 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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0answers
68 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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1answer
440 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. $y(t)=H(t)*...
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0answers
131 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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36 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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1answer
90 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
91 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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203 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, h\rangle_{L^2[...
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1answer
135 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
98 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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0answers
24 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 constant....
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1answer
65 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 x_0}...
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2answers
1k 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
22 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 modulus ...
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1answer
40 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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0answers
29 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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1answer
106 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 $x$ = ...
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1answer
824 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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0answers
31 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 ...
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1answer
881 views

Plotting discrete time signals involving sumations in matlab.

Many of the examples I've encountered while looking for an answer are simple functions that do not involve summations. Suppose I have the following function; ...
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1answer
55 views

Expectation of a powered complex circular gaussian process

Assuming a complex circular zero-mean gaussian random process (or vector) $\textbf{x}$ $\left(\textbf{x}\sim \mathcal{CN}\left(0,\sigma^2\right)\right)$. $\mathbb{E}\{\textbf{x}\}=0$. The question is:...
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1answer
245 views

The mean of a deterministic sequence

could someone explain to me why the expected value of $y(n)$ is the following: $\operatorname{E}(y(n)) = f(n)$ when $y(n) = x(n) + f(n)$ and $x(n)$ has zero mean. But why is the expected value of a ...
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1answer
203 views

sinc in 2d: how to interprete this in spatial domain?

The following two images are the ideal low pass filter in the frequency domain. As you can see, the origin (low frequency component), can pass through this filter while the high frequency are blocked. ...
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1answer
122 views

Writing a function in terms of the rect and delta functions.

Say I have a function that is equal to 1 at two unit area squares. One is centered at $(-3,0)$ and the other at $(3,0)$. I am trying to find a formula for this function using only the rect function ...