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8
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0answers
151 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, ...
0
votes
0answers
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 ...
0
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1answer
54 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 ...
1
vote
1answer
41 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 ...
1
vote
0answers
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 ...
0
votes
1answer
55 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 ...
0
votes
1answer
258 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 ...
1
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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 ...
1
vote
1answer
36 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 ...
2
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0answers
26 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 ...
0
votes
1answer
31 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
votes
1answer
341 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 ...
1
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0answers
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 ...
3
votes
1answer
310 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; ...
0
votes
1answer
41 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 ...
0
votes
1answer
83 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 ...
0
votes
1answer
72 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. ...
0
votes
1answer
64 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 ...
1
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0answers
21 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 $M >> N$ $W$ ...
1
vote
1answer
45 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) ...
4
votes
1answer
167 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 ...
0
votes
1answer
52 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: ...
0
votes
3answers
640 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 ...
0
votes
1answer
41 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 ...
1
vote
2answers
85 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) = ...
0
votes
1answer
118 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} & ...
1
vote
0answers
54 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 & ...
1
vote
2answers
32 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 $$\vec{x}(k+1)=\textbf{A}\vec{x}(k)+\textbf{B}\vec{u}(k)$$ ...
2
votes
0answers
103 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 ...
3
votes
1answer
44 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 ...
1
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0answers
40 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
votes
1answer
98 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), ..., ...
1
vote
0answers
33 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 ...
0
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0answers
30 views

Analyzing Cyclic Behavior of the Temperature in an Office Building

let us consider following code ...
1
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1answer
58 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 ...
1
vote
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 ...
0
votes
1answer
28 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. ...
0
votes
1answer
72 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 ...
2
votes
2answers
52 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 ...
0
votes
1answer
31 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 ...
0
votes
2answers
53 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 ...
1
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0answers
57 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 ...
2
votes
1answer
74 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: ...
1
vote
1answer
78 views

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 ...
0
votes
1answer
41 views

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 ? ...
0
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1answer
24 views

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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0answers
35 views

choose correct variant of signal/noise ratio calculation

let us consider following sinusoidal model ...
0
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1answer
36 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)
1
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0answers
53 views

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 ...
2
votes
1answer
136 views

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 - ...