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36 views

Integrating two exponentials produces a cosine integral? Can somebody explain?

I discovered the following conversation that I do not understand. It reads: $$\int_{-U_1}^0 {(\frac {u_1} {U_1}+1)e^{-j\omega_1u_1}}~du_1+\int_0^{U_1} {(-\frac {u_1} {U_1}+1)e^{-j\omega_1u_1}}~du_1 = ...
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2answers
63 views

Fourier Transform: why do all segments generate the same magnitude response?!

I'm working on a DTMF program, and what I've done is to break the one long input signal I initially receive into a bunch of smaller components. I perform an FFT on each of the small components and ...
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1answer
245 views

Finding the period of complex exponential function

I am having some trouble finding the period of the following discrete signal: $x[n]=e^{jn2\pi/3}+e^{jn3\pi/4}$
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1answer
78 views

How do digital filters work in time domain?

I am trying to understand how do digital filters work and how to actually calculate the output numerically. I have read that they are characterised by a transfer function $H(z)$ which results in a ...
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0answers
65 views

understanding of discrete prolate spheroidal sequences

i would like to know some details about discrete prolate spheroidal sequences or Slepian sequences,because they have application in multitaper method used in DSP,as i undersood they are time varying ...
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2answers
95 views

What's the point of Dirac delta function?

I have heard that The main useful property of Dirac delta function is it's fundamental property that $$ \int_{-\infty}^{\infty}f(x)\delta(x-a)dx=f(a) $$ I don't understanding why this equation is ...
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1answer
50 views

Why divide by N (length of input sequence) during IDFT?

During DFT of a input sequence of length N, we find X(k). We find inner product with a basis vector to get the coefficient: X(k) = <x[n], e[k, n]>    |  k = 0, 1, 2, ... ...
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1answer
40 views

LTI system response question

if figure (b) is the output of signal in figure (a) in an LTI system, how can I get the output of another signal (one in figure c) in an LTI system?
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39 views

Question about the frequency domain and the fourier transform

if you have a signal say x(t) in continuous time and you transform it using the Fourier transform for continuous time you get X(w) which is the frequency domain representation of this signal x(t). ...
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13 views

equal-variance whitening transform

Out of all the whitening transformations, PCA gives us the one that maximizes the discrepancy in variances, i.e. the components in the PCA basis have the biggest and the smallest variances. How does ...
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35 views

analog BANDPASS filter difference equation

does anyone know what is the difference equation for band pass filters in terms of bandwidth,low frequency,high frequency.... I'm trying to design a band pass DISCRETE filter using Mat lab !
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0answers
23 views

recovering of time series in SSA

i am trying to reconstruct time series from SSA ,because according to this link http://en.wikipedia.org/wiki/Singular_spectrum_analysis there is procedure ...
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1answer
62 views

Amplitude Spectrum, Nyquist Frequency, mixed/min/max wavelets

The problem is here. Now I know the definition of mixed/max/min phase wavelets, whether the roots lie within the unit circle or not. Starting from n = 1, let $$ x_t = ( 5, 6) $$ $$ X(z) = 5 + 6z $$ ...
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1answer
218 views

Autocorrelation and spectral density in MATLAB

This question is threefold. We have an LTI system that is a first degree Butterworth LP filter with the power TF where fu = 110Hz and ...
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0answers
32 views

Phase vocoder equation

I know I can adjust the frequency of a waveform using a modified version of the sine wave equation amplitude*cos(2*pi*frequency*time+phase) this will allow me to adjust the frequency of a signal. ...
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0answers
15 views

Is the autocorrelation of a function the same if one term is flipped on the y axis?

I have some questions about autocorrelation. They are very related, so I thought that one single post was appropriate for the topic. The first question is already illustrated in the subject: if I ...
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2answers
130 views

Fourier transform of 1 cycle of sine wave

Consider the signal: $\begin{align*} f(t) &= \sin(\omega t) \tag{$0 \leq t \leq 2\pi/\omega$}\\ &= 0 \tag{elsewhere} \end{align*}$ How to compute the Fourier transform of $f(t)$? I ...
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20 views

use relevant wavelet basis for periodic components

i would like to understand how should i use following code for code for detection of uknown frequencies?let us consider following signal ...
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1answer
32 views

The fourier transformation of complicated function

What is the Fourier transformation of $\operatorname{sech}(at)\operatorname{exp}(bt^2)$, where $a$ and $b$ are some constant?
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29 views

is following model stationary?

I am interested if following model is stationary,model is represented by following formula $$ x(n) = \sum_{p=1}^{P} a_p \cos(2\pi f_pn + \phi_p) + \epsilon(n) $$ $n$ is changing from $1$ to $N$, I ...
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2answers
107 views

detect largest period in non-harmonic components

let us consider following sinusoidal components $\sin(2\pi 13.5t)+\sin(2\pi 13.99t)+\sin(2\pi 25.3t)+\sin(2\pi 26t)$, clearly this is not periodic in total,because frequencies or periods are not ...
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2answers
369 views

understanding the convolution in signals and systems

Hi : I've been reading introductions to signals and systems but my background is probability and statistics. In probability, the concept of convolution makes perfect sense to me. If $t$ is a random ...
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2answers
173 views

Curve Fitting a Cyclical Pattern of Data

I'm analyzing phonological characteristics of the 22 letters used in the Hebrew alphabet, and assigned each letter an enumeration to see if they are organized based on place of articulation: ...
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19 views

Transforms with $O(N \log N)$ Complexity

Beside the Discrete Fourier and Walsh-Hadamard operators, are there any non-trivial, bijective operators that admit an evaluation algorithm of $O(N \log N)$ time complexity or better, whose inverses ...
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0answers
28 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
37 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
123 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
45 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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9 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
41 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
20 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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34 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
44 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
61 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
46 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
198 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
15 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
158 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
29 views

use wavelet transform to analyze signal

let us suppose that we have following signal ...
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1answer
68 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
473 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
67 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
17 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 $$\|AH_1\|^2=\max \frac{\|Ax\|^2}{\|x\|^2}$$ ...
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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
54 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
56 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
61 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
42 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 ...