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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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14 views

Estimator for a pointfunction depending on a random variable

PROBLEM STATEMENT: Let $X$ be random variable in $m$ dimensional space. The distance between each pair of vectors $x_i^m,x_j^m$ is $D_{i,j}^m =d(x_i^m,x_j^m)$. Correlation Sum, $C(r)$ represents the ...
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6 views

Wavelet on sinewave

I take a simple sine wave with any frequency and amplitude. I want to perform fft and Slantlet transform on it. What difference can i found when comparing these two fft and slantlet transform? I see ...
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1answer
9 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
23 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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30 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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7 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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1answer
12 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
25 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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17 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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1answer
47 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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1answer
12 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
20 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
28 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
21 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
20 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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11 views

How can one express the DTFT of the signal y[n] = x[n] - x[n-1] in terms of X(e^jw) ???

x[n] can be an arbitrary signal, not necessarily real valued, and its DTFT is X(e^jw). How can one express the DTFT of the signal y[n] = x[n] - x[n-1] in terms of X(e^jw) ??? Looking at DTFT tables: ...
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1answer
40 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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27 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
38 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
29 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 ...
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1answer
28 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
35 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
41 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 ...
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19 views

Estimation of Linear Projection

Given a linear system: $Y=AX+W$ Where: $X$ is the input signal of size $N \times K$ $Y$ is the output signal of size $M \times K$ $A$ is a projection of size $M\times N$; with $M >> N$ $W$ ...
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1answer
40 views

Is it always the case that lower frequencies contribute the most in a Fourier series?

Is it always the case that lower frequencies contribute the most in a Fourier series? Or to put it in other words, in the equation: $$f(t)=a_0+\sum^\infty_{m=1} a_m\cos \left(\frac{2\pi mt}{T}\right) ...
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1answer
51 views

Is there a way to relate prime numbers and the fourier transform

According to what I know about Fourier transforms, any continuous periodic signal can be represented as a combination of sine and cosine functions. To me, this looks analogous to the "Fundamental ...
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1answer
22 views

Find convolution of u[n]-u[n-2] and u[n]-u[n-2]

Question: Find convolution of $u[n]-u[n-2]$ and $u[n]-u[n-2]$ I have found that $u[n]\cdot u[n]=n$, $u[n]\cdot u[n-2]=n-2$, $u[n-2]\cdot u[n-2]=n-4$ Use linear property, my answer is: ...
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3answers
65 views

How to find the impulse response with input and output given?

The Question: A CT signal x(t), which is non-zero only over the time interval, t = [-2,3] is applied to an LTIC system with impulse response h(t). The output y(t) is observed to be non-zero only over ...
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1answer
36 views

Entropy of noisy signal

We have input signal $X$, the output signal Y and random noise $Z$, then: $$Y=X+Z$$ Of course, the mutual entropy: $$I(Y,X)=H(X)-H(X\mid Y)=H(X)-H(X-Y\mid Y) \geq H(X)-H(X-Y)$$ Could we say that ...
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2answers
26 views

What does conjugation in the time-domain of a signal mean?

I've never been explicitly told what the conjugation of a signal in the time-domain means. I'm mainly asking because in my signals class, my professor stated that for a signal x(t) to be real: x(t) = ...
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41 views

Why does the discrete cosine transform as matrix multiplication work this way?

I have read that the DCT can be computed as a matrix multiplication. The 8x8 DCT matrix is: $D=\frac{1}{2}\left[\matrix{ \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & ...
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38 views

Discrete Fourier Transform by hand

I have an assignment where I'm given the DFT of a sequence $x[n]$ as $X[k]=\{4,3,2,1,0,1,2,3\}$ and also $$y[n] = \left\{ \begin{array}[cc] xx[n/2] & \text{if n is even} \\ 0 & ...
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2answers
28 views

How to periodically estimate states of a LTI if the output is measured irregularly?

How can I periodically estimate the states of a discrete linear time-invariant system in the form $$\vec{x}(k+1)=\textbf{A}\vec{x}(k)+\textbf{B}\vec{u}(k)$$ ...
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0answers
36 views

Inverse Fast Fourier Transform to find the voltage across a capacitor of a RC circut

Fourier transform of a RC circuit The following example of a RC circuit describes the use of the fourier transform in order to receive the output voltage across the capacitor. My questions ...
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1answer
34 views

Detecting sinus with unknown period

I have some signal source, that can be in one of two states -- it is either emitting constant value 1.0 or oscillating in the way very close to sinus function from ...
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0answers
20 views

Bound on Signal Amplitude for subspace methods (MUSIC, ESPRIT)

MUSIC and ESPRIT are methods that use subspace decomposition to identify signal Parameters. Subspace decomposition is achieved either by SVD or Eigen Value Decomposition. Subspace decomposition ...
2
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1answer
83 views

A question about integral-squared error.

We consider the problem of representing a time function, or signal, $x(t)$ on a $T$-s interval $(t_0, t_0+T)$, as an expansion. Thus we consider a set of time functions $\phi_1 (t), \phi_2(t), ..., ...
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0answers
22 views

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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24 views

Analyzing Cyclic Behavior of the Temperature in an Office Building

let us consider following code ...
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1answer
26 views

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
34 views

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
26 views

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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1answer
41 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
45 views

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
22 views

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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2answers
48 views

“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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35 views

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
33 views

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: ...