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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
98 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
55 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
33 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
46 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
69 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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2answers
118 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
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
23 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
28 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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26 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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1answer
28 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
40 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
50 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
60 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 ...
2
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1answer
343 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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115 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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0answers
32 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
69 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
80 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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179 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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1answer
100 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
77 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
23 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
63 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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2answers
775 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 ...
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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
28 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
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1answer
74 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
631 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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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
696 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
50 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
167 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
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1answer
147 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
106 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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0answers
26 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
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
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1answer
370 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
275 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
2k 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
42 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
203 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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1answer
228 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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0answers
65 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
33 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
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0answers
163 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
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1answer
51 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
55 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 ...