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29 views

Fourier transform, what is the signal we're analyzing?

I studied Fourier Transform at university (very basic) and I know that it is a mathematical tool to get the frequencies out of a time signal (of some kind). There's something I have always wondered: ...
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1answer
40 views

What is the relationship between periodicity in a time domain signal and periodicity in the frequency domain representation of the same signal?

Is it true that the frequency domain representations of signals are always periodic? If so, is there intuition as to why? I'm having some trouble understanding what periodicity in the frequency ...
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1answer
134 views

Multiplication with the derivative of the dirac delta

I have a function $x(t)$ that I'm multiplying with $\frac{d}{dt}\delta(t-kT)$ I know the property that $\frac{d}{dt}\delta(t-kT) = -\frac{\delta(t-kT)}{t-kT}$, and if I use that: ...
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1answer
29 views

Average power of a signal

What is the average power of the signal below?
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1answer
51 views

Should mean be subtracted before conducting singular spectrum analysis (SSA)?

I have read that for the multivariate form you need to subtract the mean and divide by the standard deviation. Is this necessary before performing basic SSA on one signal? Thanks
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0answers
10 views

How can I calculate distribution of minima of sections of a continuous path (from a stochastic process)?

I have a long slab whose width is defined by a stochastic process, whose complete statistics I am aware of, say. I now cut it into smaller sections of uniform length, and calculate the minimum width ...
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2answers
53 views

Finding transfer function with Fast Fourier Fransform.

I have two signals with input = a(t) and output = b(t) that have been sampled every 0.01s and as such the fast Fourier transform has been used on both and utilised to produce a transfer function. The ...
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0answers
21 views

Features of continuous-time sinusoidal signal

How I can find features of sinusoidal signals such as; amplitude, cyclic frequency, radian frequency, period ($T◦$), phase in degrees, phase in radians of an $x(t) = A \cos(2\pi f◦t + \phi)$. I ...
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0answers
35 views

Determining valid frequency domain DTFT's

This question may or not be off-topic but it concerns Fourier Transforms so I'm assuming it's of some relevance here. One of my problem set questions is... Are the following frequency domain ...
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1answer
48 views

The signal $\cos(2 \pi t )$ is an eigenfunction of every LTI system?

for $\sin(2 \pi t)$: Apparently that it's not an eigenfunction real-valued impulse response $h(t)$ but it's a eigenfunction for real-valued and even impulse response $h(t)$ What gives?
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0answers
62 views

what does the sine function tell you about an input

Intuitively, I'm trying to understand the significance of the input in a sine function. I'm currently, trying to develop intuition behind sinusoids and what the input tells you about the output and ...
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1answer
52 views

What is the meaning of a continuous curve in the frequency domain?

I am sorry for how rudimentary this question will sound. I approach the frequency domain thinking in discrete terms. The plane is frequency on the x axis and amplitude on they y (ignoring phases). ...
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1answer
1k views

Getting wiener filter coefficients in Matlab

I need to find two coefficients (w1,w2) for a wiener predictor filter of the signal x(n)=0.65x(n-1)-0.7x(n-2)+v(n) where: ...
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1answer
219 views

Plot recursive signal in Matlab

I need to create and plot this signal in matlab with 2000 points: x(n) = 0.6530 x(n-1) - 0.7001 x(n-2) + v(n) Where $x(-1)=x(-2)=0$ and $v(n) =$ white noise I ...
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1answer
16 views

Expressing array response $A(Z) = \sum_{-N}^{N} w_n Z^n$ as sine-function

The array-response of an antenna can be defined as: $$A(Z) = \sum_{-N}^{N} w_n Z^n$$ where $Z = \exp(-i \omega \Delta t) = \exp(-ik\Delta x \sin \alpha)$ According to my textbook, if we let $w_n = ...
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3answers
170 views

period vs time period of sine wave

It's weird I'm still confused about this, but usually when we figure out the period of a sine wave from its graph, it's in radians. But the true period should be in time, like how fast we are ...
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0answers
30 views

use wavelet transform to analyze signal

let us suppose that we have following signal ...
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1answer
73 views

Continuous time signal and Discrete time signal

I know that all periodic continuous time signal have discrete spectral representations, but are all discrete spectral representations periodic in continuous time? Also, can all periodic signals be ...
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2answers
520 views

Approximate a polynomial function using a sum of sine waves

I have a polynomial function which I need to approximate by a sum of sine waves with constant amplitude along a given domain. From what I hear, this might be a good time to make use of Fourier ...
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0answers
70 views

Harmonic F statistic

i am interested what does mean Harmonic F statistic in mathematical language?i have search about $F$ statistic and found a lot of explanation,for example like this "**F Statistic The F statistic ...
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0answers
18 views

Maximizing orthonormal subspace, Signal Processing

Let A any matrix. If we eigen-decompose $A^TA=HDH^T$, where $H$ is unitary and $D$ diagonal, then the columns $H_i$ of $H$ satisfy $$\|AH_1\|^2=\max \frac{\|Ax\|^2}{\|x\|^2}$$ ...
2
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0answers
22 views

How do I estimate the derivative of the current position, when I have only values from past to present?

If I have a discrete real-time signal $x[n]$, with its latest value $x[i]$ and all its past values $x[i-t]$, how can I estimate the derivative at $x[i]$?
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1answer
55 views

How does this phase shift in x-space affect the position of a spectrum in k-space?

I'm working on a new form of signal detection with which I hope to recover both the amplitude and phase of a very small signal. However, doing this requires the use of some Fourier maths that I don't ...
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1answer
57 views

Kronecker delta

$D=C\cdot V$ ; C and V are both matrices and C is a square by square matrix $C_{ij}=1$ if i=j and $C_{ij}=0$ for $i\neq j$ (Kronecker delta). $\mathcal{F}^{-1} D = \mathcal{F}^{-1} C$ $ * ...
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1answer
63 views

Can any piecewise function be represented as a traditional equation?

In "Fundamentals of Electrical Engineering" we learned about piecewise functions for the "unit-step" and "ramp" which are represented by $f(x)= \begin{cases}0, & \text{if }x< 0 \\ 1, & ...
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0answers
44 views

Asymptotic result on quadratic variation of a semi-martingale linear functional estimator

In the same context of this previous question. Consider $$ \mathcal E^{(n)}_t := \sqrt{n}(\widehat\Lambda_n(\phi)_t - \Lambda(\phi)_t )$$ I desire to prove that $$ \left \langle \mathcal ...
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1answer
39 views

Find if the system $(x(t-1))^2 + x(t) +(x(t+1))^2 = y(t)$ is invertible

If there wasn't the $x(t)$ term, I could use $x(t) = x$ and $x(t) = -x$ to disprove invertibility, but I can't think of two functions that give the same $y(t)$ in this case. When I tried proving ...
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0answers
101 views

Symbolic math engines barf on this ostensibly tractable integral.

$$\frac14 \int_{-M\pi}^{N\pi - s} \cos(tu/M) \cos((t+s)u/M)(1-\cos(t/M))(1-\cos((t+s)/N))\space \mathrm d t$$ with integer $u$. Alpha runs out of time. Maxima gives a tremendous result that can ...
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1answer
42 views

Arcsine for a value

I want to exactly determine the arcsine (sine inverse) for a value. Say I take $\sin$ for $60000$, which is approximately $-0.866$. I want to get back $60000$ from this. Taking a sine inverse will not ...
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2answers
51 views

Very short theory question signals?

My teacher asked us this question yesterday in the lecture but it didn't make any sense to me. He asked: What do the coefficients of the exponential Fourier series represent? Also, what's the ...
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2answers
70 views

What calculation remains constant for discretely sampled points of a sinusoid on a window of 1/4th its period?

I have a univariate time series that consists of discretely sampled (equally spaced) points of a sinusoid. If you have a window that slides over these points (like this animation) with a length of ...
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1answer
76 views

2-D Fourier Transform of complex exponential with 2-D quadratic phase

I've been looking around to see if there is either an exact transform pair or an approximation to either of the following but have not been able to find anything: $$ \mathcal{F}_{xy}\left( ...
4
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0answers
62 views

Detecting the respiratory rate of a breating lung.

I am currently working with some data-sets that represents the movements of a beating heart and breathing lungs. The data-sets are represented as a collection of floats that range from 47 to 51. We ...
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1answer
27 views

Prove that the function in the domain of Z is a high pass filter

I need prove that the function \begin{equation} L(z) = 1-z^{-1} \end{equation} is a high pass filter, but I have not much understanding of the $z$ transform and what really the $z$ domain is. So how ...
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0answers
49 views

How does SVD work?

Trying to find information, and, no-one seems to know the answers. I have a time-series, represented by $T = [0, 1, 1, 0, \ldots, n]$ the time series is then transformed into the Spectral results: ...
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2answers
67 views

Reducing a two term signal to one term

I am trying to solve a phasor addition problem, reducing from its original form to $$X(t) = A \cos(\omega_0 * t + \phi)$$ The original equation is : $$X(t) = 2 \sin(\omega_0 * t + 45) + ...
2
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1answer
132 views

Need to learn wavelet, suggest steps and resources

I am looking for a good introduction to wavelets and wavelet transforms. that covers the following: Basics Vector Spaces – Properties– Dot Product – Basis – Dimension, Orthogonality and ...
2
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1answer
220 views

Kalman Filter Process Noise Covariance

I want to model the movement of a car on a straight 300m road in order to apply Kalman filter on some noisy discrete data and get an estimate of the position of the car. In a Kalman filter the matrix ...
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0answers
79 views

Fourier Transform of a Gaussian Signal?

As far as I know this is the formula for FT : On this question on part b) I fint on the answer the part with e^-jwt is changed with cos(wt) I have no idea how cos(wt) came in ... would you please ...
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1answer
49 views

Frequency response of Continous-time system

Not sure where to start on this one: $$H(s)={(s-j\omega_0)(s+j\omega_0)\over(s+\omega_0\cos\theta+j\omega_0\sin\theta)\left(s+\omega_0\cos\theta-j\omega_0\sin\theta\right)}$$ Sketch the frequency ...
3
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0answers
105 views

Artifacts and low frequencies FFT.

I am working on analyzing a time signal and want to preform a FFT. However I run in to some artifacts at low frequencies. I have managed to reproduce the behavior in a test signal. Given by $S(t) = ...
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1answer
60 views

what is the period of this sinusoidal function funtion

How can we find the fundamental period of this sinusoidal discrete function $x(n) = 10\cos{(\frac{4n\pi}{31}+\frac{\pi}{5}})$ I tried using the formulae $\frac{2π}{\omega}$ and got the answer 31/2, ...
2
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2answers
167 views

Z-Transform, Transfer Function, Poles & Zeros

I've been working on a question that I'm now stuck on. I need to: Determine the transfer function and poles-zeros of: $y[n]=0.5y[n-1]-0.25y[n-2]+x[n]$ So far I've carried out a z-transform in ...
2
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1answer
755 views

Bandpass filter with Fourier and inverse.

My understanding of signals is limited. I did a signal processing subject in engineering, but I can't say I got much from it. For me, the subject wasn't taught with enough 'real world' explanation - ...
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1answer
59 views

Z-transform: Convolution <=> Multiplication giving strange results

I try two slightly different routes to an answer, and get two different answers. (This is from a past exam paper.) Find h[n] if $ H(z) = \frac{1}{(1-az^{-1})^2} $ First try: $ H(z) = H_1(z)\cdot ...
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0answers
41 views

Error bounds in representing a vector using a truncated Moore-Penrose biorthogonal basis

I was reading and trying to reproduce the results in the arXiv preprint of Periodic Gabor Functions with Biorthogonal Exchange: A Highly Accurate and Efficient Method for Signal Compression by Asaf ...
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1answer
116 views

Given a Poisson-noisy signal, what is the noise distribution of its Fourier transform?

Disclaimer: I'm not a mathematician, but here's my attempt at a mathy version of my question Start with a noiseless, discretely sampled expected signal $I(x_n)$. Construct a Poisson-noisy measurement ...
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1answer
58 views

Fourier analysis of an exponential function review

I am working through and reviewing some of the examples presented on Fourier analysis from a Modern Digital and Analog Communication Systems book. In one of the examples, the author goes through the ...
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1answer
141 views

calculating an incoherence property

With respect to Matrix Completion and Compressive Sampling (CS) I'm trying to understand how to calculate an incoherence property μ between two bases Φ and Ψ. Getting this incoherence is important ...
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2answers
114 views

Applying a Kalman filter to a WiFi power signal

I have created an app that uses the power of a WiFi signal to determine distance to the WiFi access point. Problem with that power reading is that it is not very stable. I have been looking into ...