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Is it possible to reconstruct signal using phase/magnitude only?

I am studying Fourier Transform and it's inverse. We get phase and magnitude from Fourier transform and reconstruct it back from both together My question is that is it possible to reconstruct given ...
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1answer
13 views

Meaning of co-ordinate system of Covariance matrix

Can we think that any matrix representation has an underlying co-ordinate system? Now consider a positive definite sample covariance matrix. If so what is the meaning of the co-ordinate system of the ...
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2answers
36 views

Discrete Fourier Transform of generalised Hamming Window

The generalised Hamming Window is defined as: $$ w(n) = \begin{cases} \alpha - (1 - \alpha)\cos(2 \pi n /N), & \text{if $ 0 \leq n \leq N$} \\ 0, & \text{otherwise} \end{cases} $$ with $ 0 ...
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0answers
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Does exise a,b,c make the same input lead to same output?

The first function is y[n]=x[n]+0.5*x[n-1]+0.25*x[n-2] the other is y[n]=a*x[n+1]+b*x[n]+c*x[n-1] Does exist some ...
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0answers
24 views

Fourier transform of a 3sinc^2(100πt)

I'm currently studying for an exam, and I'm not sure the textbook's answer for the fourier transform of 3sinc^2(60πt) is correct. For this question, I incorporated the duality property. Below is my ...
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0answers
12 views

How to express a signal in terms of Riesz bases?

Fast discrete wavelet transform allows us to express any discrete signal in terms of wavelet bases by convolution with filter coefficients. How can one express a digital signal in terms of ...
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0answers
13 views

What is Phase congruency?

I am beginer in signal processing. I am studying the importance of phase in signal.I want to know about Phase Congruency but there is very little information available on internet . So can anybody ...
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1answer
41 views

Proof of the discrete Fourier transform of a discrete convolution

Let the discrete Fourier transform be $$ \mathcal{F}_N\mathbf{a}=\hat{\mathbf{a}},\quad \hat{a}_m=\sum_{n=0}^{N-1}e^{-2\pi i m n/N}a_n $$ and let the discrete convolution be $$ ...
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0answers
9 views

Errors of approximating continuous Fourier transform by discrete Fourier transform

In http://planetmath.org/approximatingfourierintegralswithdiscretefouriertransforms some error analysis of using DFT to approximate continuous Fourier transform is indeed done, but there are things I ...
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1answer
27 views

Show if signal is time variant or not

I know that I have to show that \begin{align*} y[n-n_0] &= f \Big( \{x[n - n_0]\} \Big) \end{align*} in order to tell if a signal is time-varying of not. Having a signal $y[n] = ...
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0answers
28 views

Exact formula for alias of Discrete Fourier transform for periodic sigals

Suppose that $f(t): \mathbb{R} \to \mathbb{C}$ is a $T$-periodic signal, with highest frequency $f_h$. Now suppose that our sampling rate frequency is lower than $f_h$, and is not any multiples of ...
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0answers
37 views

Real and imaginary part of an Eigenvector.

Apology if my question not clear or appropriate. Consider a complex positive definite sample covariance matrix (SCM) generated by a band limited signal on a set of sensors. Is there a relation ...
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0answers
32 views

Savitzky-Golay Coefficients for end points

I've been looking for solution to clean up SG Filter end points and I discovered a shifted set of coefficients in Numerical Recipes that might do the trick. Nr = 0; Nl = 4; 0.086, -0.143, -0.086, ...
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1answer
49 views

Is there a relation between half space and Eigenvectors?

I request earnestly apology if the question is not well defined. I think I understand half space and Eigenvectors to an extent, but could not connect both of them under the same geometry or ...
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0answers
17 views

Spectral Analysis: How to interpret a periodogram.

I'm reading a paper that has to do with financial volatility. The author uses a periodogram to estimate the power spectrum density of the volatility time-series. Evidently, the plot (below) is ...
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0answers
21 views

Condition Butterworth polynomial

My course states that a polynomial is a Butterworth polynomial when it satisfies the following condition: $|B(j\Omega)|=\sqrt {1+{\Omega}^{2\,n}}=\sqrt {1+{(\omega/\omega_p)}^{2\,n}}$ I'm really ...
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0answers
84 views

Properties of eigenvectors of a sample covariance matrix?

My apology if the question is not appropriate. For me Eigenvectors are quite a mystery. Does it have any property that we can relate to the matrix it came from? By property I mean something like the ...
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1answer
16 views

how can I plot the infinite sum in matlab [closed]

I'm lookin for a way to plot $$\hat x= \sum_{n=-\infty}^\infty 0.5cos(1.3\pi n)sinc(t-n)$$ in matlab, and I can't find out how
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0answers
22 views

A “Fourier Phase” for (stationary) random processes?

Let $X_t$ be a real w.s.s. random process. Its spectrum is given by $S(f)=\mathcal{F}R_X(\tau)(f)$ where $R_X$ is the process autocorrelation. As $X_t$ is real, the spectrum will be real and ...
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0answers
23 views

How can I make the mean of samples be approximately equal to the mean of actual continuous signal?

Suppose there is signal f(t) that is continuous and periodic. It is known that this f is T-periodic. (but it's not necessarily a single cosine f(t).( I'd like to make the mean of samples be ...
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1answer
16 views

Frequency scaling property for Fourier series

For Fourier transform, there is an equation connecting time-scaling with frequency-scaling. (By scaling, I mean multiplying by constant for time or frequency) Is there such a relation for Fourier ...
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1answer
32 views

Help in understanding step function calculation

Dear community I would appreciate if you can help me understand these equations. I mean how did he jump from line 1 to line 2? How do u[n] get cancel? Then in the last line where did the "8" come ...
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0answers
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How to check periodicity of $f(t)$ using samples

Suppose that we know that signal $f(t)$ is $T_1$-periodic. Let $f_1 = 1/T_1$. But we want to know whether signal is $T_2$-periodic also. Let $f_2 = 1/T_2$, and $f_2$ is positive integer multiples of ...
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0answers
23 views

If $f(t)$ is periodic, is there any $t$ that would equal to DC components?

Suppose $f(t)$ is periodic with period $T$. Would there be $t$ that would necessarily equal to DC component (it can be scaled)? By DC component, I mean $F(0)$ where $F$ is fourier coefficient of $f$. ...
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0answers
20 views

Is there anything similar to DTFT for Fourier series?

So if sampling condition is met well, with aperiodic signals we have discrete-time Fourier transform (DTFT) that allows us to get frequency-domain data that resemble continuous-time fourier transform. ...
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1answer
20 views

Convergence property of DTFT toward DFT when function is periodic

from Wikipedia: When the input data sequence $x[n]$ is $N$-periodic, DTFT can be computationally reduced to a discrete Fourier transform (DFT), because: $ X_{1/T}(f)$ converges to zero ...
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1answer
22 views

Is it possible for continuous fourier transform of a function to have values only on finite number of frequencies?

Is it possible for continuous fourier transform of a function to have values only on finite number of frequencies? Or do these values necessarily impulse values, not complex numbers?
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1answer
33 views

What is a window function with positive spectrum?

I need a real, symmetric window function $x(t) = x(-t)$ whose Fourier transform $\hat{x}(\omega)$ (also real and symmetric) is non-negative $\hat{x}(\omega) \ge 0$ for all $\omega$. The function does ...
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1answer
20 views

Is the DTFT of a sampled Gaussian a positive function?

I have an infinite sequence $x_{n}$ for $n \in \mathcal{Z}$ which is a sampled Gaussian function $x_{n} = \exp(-n^2/a)$ with a > 0. I need to check whether its DTFT $x(\theta) = \sum_{n \in ...
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1answer
25 views

What is the relationship between DTFT and continuous fourier transform?

As title says, what is the relationship between DTFT and continuous fourier transform? Let's say there is continious signal $f(t)$. Continuous Fourier transform convert this into $F(\omega)$. Now let ...
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0answers
16 views

Help understanding Wiener filtering formula

I would like some help interpreting the following formula, equation 1 from this paper: https://www.math.uni-bielefeld.de/~rehmann/ECM/cdrom/3ecm/pdfs/pant3/strela.pdf $\hat{X} = ...
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10 views

How to work with 4-1 multiplexer In digital logic?

Here is my image of multiplexer, http://d18khu5s3lkxd9.cloudfront.net//wp-content/uploads/2014/04/GATECS2014Q55.png and this one ...
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0answers
16 views

Understanding, Non-Negative Sparse Coding algorithm

I have a question regarding sparse coding, Non-negative sparse coding. Iterate until convergence: $ \mathbf{A_i} \leftarrow \arg \! \min_{A \geq 0} || \mathbf{X}_i - \mathbf{B}_i\mathbf{A}||_F^2 + ...
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1answer
49 views

Fourier transform and splitting frequency range into 4 channels

I have code example that divides audio frequency into 6 channels. It uses Fast Fourier Transform (FFT). Algorithm process the frequency range using 6 capture[x] samples based on the range of n between ...
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1answer
61 views

Discrete Fourier Transform question

Let $R_{M\times N}$ be a space of size $M\times N$. Define the 2D Discrete Fourier Transform of $f\in R_{M\times N}$ to be \begin{equation} ...
2
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1answer
46 views

About integrating product of two sinc function using Fourier transform

So the problem is which I think is pretty straight-foward by using Fourier transform and convolution property of two sinc functions and evaluating the convolution at 5. However, I got sinc(t) for ...
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1answer
38 views

Deriving the autocorrelation function for the ARMA model

Definitions The ARMA model $$x_n=-\sum_{p=1}^P a_px_{n-p}+\sum_{q=0}^Qb_qw_{n-q} \tag{1}$$ where $w_n$ is zero mean stationary white noise with unit variance. Question To derive the ...
2
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1answer
39 views

Yule walker equation limited matrix size

Definitions For an ARMA model $$x_n=-\sum_{p=1}^P a_px_{n-p}+\sum_{q=0}^Qb_qw_{n-q} \tag{1}$$ where $w_n$ is zero mean stationary white noise with unit variance. It is straightforward to show that ...
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0answers
22 views

If the signal's frequency is multiples of the first harmonic frequency, transform method similar to DFT but use less number of samples?

Suppose that a continuous signal $f(t)$ has the first harmonic frequency $f_1$. $f(t)$'s frequencies that are not integer multiples of $f_1$ are known to have zero signal magnitude $|F(\omega)|$. This ...
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1answer
25 views

DSP Time domain and frequency domain

I'm new here and wish to say hello to this great community. I'm starting to learn DSP, I don't have a lot of Maths background but I'm trying to learn. I am new to DSP too and I am reading this great ...
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1answer
22 views

Which of arithmetic, geometric or harmonic mean is the most appropriate in this case?

I have a software that periodically detects tempo out of an audio signal and I would like to compute the average tempo out of all the generated values. Example: ...
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1answer
74 views

$E[x_i^2 x_j^2]$ for white Gaussian noise

If $x_n$ is a discrete time random signal and is white Gaussian noise (ergodic and WSS) so $$E[x_n x_{n+l}]=\sigma ^2 \delta (l)$$ and $$E[x_n]=0$$ Where $n \in \mathbb{R}$ and $l\in\mathbb{R}$ ...
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1answer
42 views

matlab problem - removing frequencies after FFT, signal processing

I want to stress that this is not a coding problem, my problem is that i don't fully understand the mathematics surrounding the subject and that's why I believe I have a problem. I was given an ...
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1answer
46 views

convolution and associativity

Ok Let talk about this,... I am now so confused. 1-$$\mathcal{F}\Big\{c(x-x_0)b(x-x_0)\Big\}=\mathcal{F}\Big\{c(x-x_0)\Big\}\circ\mathcal{F}\Big\{b(x-x_0)\Big\}\\=\Bigg[e^{-2ix_0y}C(y) ...
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1answer
81 views

How one can show $P(ax+n|x)=P(n)$? [closed]

Let $x$ be a signal and $n$ be an independent noise. How one can show $P(ax+n|x)=P(n)$? Thanks. Well, let $y=ax+n$, so we have $n=y-ax$. Now if the probability density function (PDF) of $n$ for ...
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2answers
50 views

Convolution sum. Compute $y[n]=x[n]\ast h[n]$

Compute $y[n]=x[n]\ast h[n]$ $x[n]=(-\frac{1}{2})^2u[n-4]$ $h[n]=4^nu[2-n]$ In this question, when I try to calculate the convolution sum. I face with: ...
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0answers
24 views

Calculate Distance between Fourier Transforms

I'm working with signal data (specifically data from accelerators and gyroscopes), and I take their Fourier transforms to get a better idea of the dominant frequencies. I'd like to compare the ...
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1answer
19 views

DFT by $n$ samples of a continuous periodic signal with more than $n$ frequencies

It is known that if we only have $n$ samples and take DFT, we only get at most $n$ distinct frequency data. But let's say that there is a continuous periodic signal with more than $n$ frequencies, ...
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2answers
27 views

If a signal is periodic, can the error of approximation by Discrete Fourier Transform be avoided when using finite number of samples?

As title says, if a signal $f(t)$ is periodic, can approximation errors of approximation by discrete Fourier transform (DFT) be avoided when only finite number of samples are used?
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1answer
23 views

Why are discrete-time Fourier series and discrete Fourier transform only defined on integer $k$?

In ordinary Fourier series/transform of a continuous signal $f(t)$, fourier frequencies $\omega$ of series/transforms can be any of $\mathbb{C}$, not just $\mathbb{Z}$. But why is it the case that ...