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Cross-talk filter with known source

Hello fellow Stackers, This question was also posted on StackOverflow, but perhaps this is a more suitable location for this question. I currently work in an experimental rock mechanics lab, and when ...
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How to solve this complex-valued exponential signal ? Help !!! [on hold]

Consider the complex-valued exponential signal $$x(t)=Ae^{αt+jωt}, α>0$$ Evaluate the real and imaginary components of $x(t)$.
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Minimum phase non-rational transfer function: Hilbert transform between log magnitude and phase

In Signal Processing literature, it is well known that a minimum phase sequence with rational transfer function ('zeros' and 'poles' in unit circle) has Hilbert transform relation between log ...
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2answers
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I want to know whether the following is periodic or not periodic

I have a question about system properties of the following function whether it is periodic or aperiodic. With an insight, I'd determine the function is aperiodic since the unit-step term looks ...
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1answer
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Convolution Case

The * denotes convolution and u[n] as the heaviside function. $x[n]= u[n]α^n$ Determine a sequence $h[n]$ such that-: $x[n]∗h[n]=α^n(u[n+2]−u[n−2])$ I am trying this problem for quite awhile now. ...
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show the AR process is non-stationary. [closed]

A first order auto-regressive (AR) process $u(n)$ satisfies the equation: $$ u(n) + a_1 u(n-1) = v(n) $$ where $a$ is a constant and $v(n)$ is a white-noise process with variance $\sigma^2_v$. Show ...
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1answer
26 views

Why does the discrete cosine transform compact the information at the “low frequencies”?

I've been investigating about the discrete cosine transform. I think I understand the practical applications it has and how it is used in image/audio compression. I also know it is related with the ...
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2answers
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A simple Fourier Transformation

I am a bit stuck with this small basic signal. I have this $$y(t)=\frac{\sin(200\pi\,t)}{\pi\,t}$$ and I want to take its Fourier Transformation. Obviously it looks like the sinc function. But that ...
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1answer
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choose appropriate sampling frequency for yahoo data

let us consider following data from finance.yahoo.com http://finance.yahoo.com/q/hp?a=&b=&c=&d=8&e=16&f=2014&g=d&s=MTLA.HM%2C+&ql=1 for MOTOROLA SOLTN (MTLA.HM), i ...
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“Energy” of a signal

If we have a signal $$x(t)=\begin{cases} t &0\leq t < 1 \\ 0.5+0.5\cos(2 \pi t) &1 \leq t < 2 \\ 3-t &2\leq t<3 \\ 0 &\text{elsewhere} \end{cases}$$ It's energy is ...
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Fourier Interpolation

I have this Equation, that I modeled from my measurements and simulations. $I^{exp}_{l,m} = (\mathbf{F}^{H}.\mathbf{A}.I^{true})_{l,m}$; $H$ is the Hermitian transpose and $\mathbf{F}^{H}$ is a block ...
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1answer
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Variance of amplitude and phase from sin and cos regressors in polar coordinates

On a data set, I estimated the sine and cosine weights at a specific frequency, $\beta_{\sin}$ and $\beta_{\cos}$. I can extract the amplitude and phase from these regressors as follows: ...
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1answer
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Convolution: $ f (-)*g = g(-)* f$ does this mean both $f$ and $g$ have to be even functions?

Assuming $f$ and $g$ are different functions, does $ f (-)*g = g(-)* f$ mean both $f$ and $g$ have to be even functions? In fact, this is equivalent to $f\star g = g \star f$ (i.e., cross-correlation ...
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1answer
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Fourier transform and Z transform question?

Lets suppose we have an exercise where I have to find the Z transform and its region of convergence.I find the Z transform and the region.How do I determine if the Fourier transform exists from this ? ...
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1answer
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operative priority with multiple signs

hi everyone I'm confused with the following problem. -+-(-5) how I can resolve this?. first change the value inside of parenthesis or I begin from left to right?.
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choose correct variant of signal/noise ratio calculation

let us consider following sinusoidal model ...
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1answer
31 views

Signal processing question explanation

We have the system : $$y(k)= |x(k)| +x(-k) + 2x(k-2)$$ In my book it says that this system is not causal and also not stable. I would like a detailed explanation. Edit : its y(k)
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understanding discrete-time convolution

I'm trying to understand the discrete-time convolution for LTIs and its graphical representation. standard explanations (like: this one) start with the idea of decomposing an input signal $x[t]$ into ...
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why use complex numbers when representing periodic signals?

a large class of periodic signals can be defined with sinusoidals. but many texts introduce these and then use a representation of periodic signals that has sinusoidals with real and imaginary parts - ...
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example of time invariant system and connection to memoryless

textbooks give abstract examples of time invariant and non-time invariant (time sensitive) systems. can you please give an intuitive example of a time invariant system and one which is not? obviously ...
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Problems filtering a signal

The signals I'm inspecting are taken from an accelerometer. Up until now I've been filtering noise by decomposing the signals using a Fourier series and getting rid of all modes greater than a certain ...
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1answer
13 views

Signal “representation” terminology

A paper I'm reading now defines invariant signal "representations" as those functions $\Phi$ of signals $x$ in a Hilbert space such that $\Phi(g\cdot x) = \Phi(x)$ where $g\cdot x$ is the action of ...
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1answer
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Frequency response of unit impulse function

Could someone throw some light on how to get the frequency response of unit impulse function. I am not from EE, but I need it for my wavelet study.
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The relation between non-Gaussianity and statistical independency

I have read in Wikipedia article which is talk about ICA , that the definition of statistical independence can be achieved by maximization of non-Gaussianity , my ...
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1answer
38 views

Fourier transform of a continuous non-periodic function in matlab

I would like to use matlab to find an Fourier transfom of a function which is known only on a grid. As an example I take the function f(x) = exp (-x^2), which Fourier transform is known and is equal ...
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1answer
37 views

How do component wavelengths *add* to wavelength of light color?

Say you have 3 leds at frequencies (or wavelengths) $u_1, u_2, u_3$ in Hz (or nm). Then how do you calculate the apparent or center of, or blah frequency (I don't know what I want really) of the ...
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48 views

Why would the discrete fourier transform “see” signals like this? What is the origin of spectral leakage?

The discrete fourier transform of $x = (x_{0},\dots,x_{N-1})$ is defined as $\displaystyle X_{k} = \sum_{n=0}^{N-1} x_{n}\omega^{kn}_{N}$ where $\omega^{kn}_{N} = e^{-2\pi ik/N}$ and ...
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How to draw the Bode diagram for a given transfer function?

With this transfer function: $$G(s)=\displaystyle\frac{10(s+1)}{s(0.1s+1)}$$ I need to do operations to draw the Bode diagram manually I have this: $G(jw)=\displaystyle\frac{10jw+10}{-0.1w^2+jw}$ ...
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1answer
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Definition of “uniformly regular” signals (as used in the book “Wavelet Tour of Signal Processing”)

The author uses the term "uniformly regular" and I get the idea of it's meaning through the context, yet the phrase is used as if could also have a precise mathematical meaning. Is there a definition ...
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How do I get around finding a digital filter which is a narrow bandpass with a small group delay?

I need to find a digital filter that meets the following criterion: Is a narrow bandpass (1/40 of normalized frequency width) As small as possible group delay (preferably less than 300 samples) ...
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1answer
26 views

Help for understanding Danielson-Lanczos lemma

The Danielson-Lanczos lemma is the basis for fast Fourier transform algorithms. Now, I do understand this step $\displaystyle X_{k} = \sum_{n=0}^{N-1} x_{n}\omega^{kn}_{N} = \sum_{n=0}^{(N/2)-1} ...
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60 views

Looking for a nice expression of these functions in terms of trig functions

I have come across three sinusoidal functions f1, f2, and f3 which, up to scaling and translation, are very close to each other. When normalized and plotted together, they are hard to tell apart. ...
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Discrete-time lowpass filter with rapid response to significative changes in the input

I have a signal that looks like this: To obtain an average, I apply this formula y[i] = α * x[i] + (1-α) * y[i-1] With a relatively small value of α the ...
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Example 8.10.1 from Van Trees' Optimum_Array_Processing

According to Example 8.10.1, the task is to construct a beamspace matrix of standart linear array which consists of 10 elements. The beamspace matrix should have 3 column-vectors of Taylor series ...
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3answers
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3 points on “horizontal” sinusoid, what is its period?

Imagine you have 3 points that are all a distance of 1 separated from each other. How do you find the sinusoid that goes through these 3 points if you also know that the sinusoid is not at a strange ...
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2answers
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Physical interpretation of L1 Norm and L2 Norm

In signal analysis, students have no qualms about associating the L2 norm of a square integrable function f(t) as the energy associated with that signal. A good understanding of whether a function ...
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Subject to in equation

I have the formula below: $$\hat x_2=\arg\min\lVert x\rVert_2\quad\text{subject to}\quad A{x}=y.$$ But I didn't understand what was meant by "subject to" ? does $x$ is replaced by $x_2$? please can ...
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Causal non-causal sequences

This answer says that $Y = zX$ is a simplest example of non-causal system because it corresponds to $y_n = x_{n+1}$ and current output depends on future input. Yet, it is causal because both $x_n$ and ...
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Decomposition of $a\sin(\varphi t)+b\sin(\vartheta t)$ into AM and carrier

I feel like this should not be so hard, but I am somehow stuck. I would like to decompose the signal $$a\sin(\varphi t)+b\sin(\vartheta t)$$ into an amplitude modulation and a periodic carrier ...
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How to derive the process noise co-variance matrix Q in this Kalman Filter example?

How to understand the process co-variance matrix Q in the example below ( I extracted it from Wikipedia http://en.wikipedia.org/wiki/Kalman_filter ) "Consider a truck on perfectly frictionless, ...
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1answer
55 views

Parseval's theorem.

We consider two signal $h(t)$ and $g(t)$ such that $$\int_{-\infty}^\infty |g(t)|^2dt<+\infty$$ $$\int_{-\infty}^\infty |f(t)|^2dt<+\infty$$ Parseval's theorem states that: ...
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The bandwidth of the signal $x(t)$.

The bandwidth (B) of the signal $x(t)$ is the range of frequencies (measured on the positive semi-axis) in which $X(\omega)$ takes values ​​different from $0$. Very often $X(\omega)$ is different from ...
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Using l1 magic toolbox for compressive sensing : Positive definite matricies.

I'm trying to use l1 magic to reconstruct an image from a single pixel camera I've developed. The test functions used are random binary patterns projected onto the object scene, so each pattern is ...
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1answer
25 views

Is there a way to modify the exponential smoothing function to account for varying sample rates?

I am using a simple exponential smoothing formula to smooth a signal. X(n) = a * S(n) + ( 1 - a ) * X(n-1) However on certain setups, the sample rate is much ...
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Top and bottom power spectral density of a height profile

Imagine I have a simple 1D height profile which is NOT symmetric. Now, what is truly important for me is to know what are the frequency content of the top profile (i.e. a cut profile above the ...
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Is there a standard way for modeling a Kalman filter where the measurements are obtained from differences?

Consider for simplicity a Kalman filter applied to the one-dimensional state space model $x_{n}=f_{n}x_{n-1}+q_{n}$ $y_{n}=h_{n}x_{n}+r_{n}$ with white noise errors. Assume that $r_n=e_n-e_{n-1}$ ...
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1answer
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find period of discrete cosine

let us consider following we should find period of this discrete signal,for periodicity we should have $x[n+kN]=x[n]$ or $10\cos(0.088\pi(n+kN) +\phi)=10\cos(0.088\pi n+\phi)$ or $0.088\pi ...
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Total change of a signal overtime

I have some signals whose analytic type I do not know. I can only sample them every 0.1 secs. I want to pick that signal that changes as little as possible. For example, between sin2t and sint I ...
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Covariance between real and imaginary parts of Fourier transform of a stationary time series

Since Fourier transform of a random stationary time series(in the case of existence) is not necessarily real, my question is what is the relation between the covariance of real and imaginary parts of ...