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1answer
42 views

Frequency Change with Tape Speed

I recorded my own voice in an old tape recorder. When I put the device in fast forward mode my voice turned a little squeaky. I wonder if the fundamental frequency of the voice had changed? Is that ...
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1answer
66 views

Determining the Discrete Fourier Transformation of signal.

I'm studying signal analysis and now I'm at the Fourier series/transformations. I'm following an example but can't understand the last step. This problem is divided in two steps. FIRST From this ...
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1answer
65 views

Signal Processing Convolution Summation Calculation

I am learning convolution of signals, and need to do a lot of summations and math. Because y[n]=Sum(x[k]h[n-k]) from negative infinity to infinity. I am always stuck at math procedures. Also, I am ...
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1answer
65 views

Reconstructing signal without aliasing

$$x[n]=2\sin\left(0.2\pi n-\frac{\pi}{2}\right)+4\cos(0.5\pi n-\pi)+\cos(0.8\pi n)$$ This signal is the result of sampling $x(t)$ with a frequency of 40Hz. I have to see if this frequency can ...
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0answers
202 views

Convolution property in terms of fft (matlab)

I am working on some signal processing and I have the following data: ...
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1answer
83 views

Bounds on least squares and weighted least squares estimator

I was wondering if I can get some help in getting bounds on the parameters estimated by least squares (LS) and weighted least squares (WLS) methods. Suppose our observation model is: $\mathbf{y} = ...
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1answer
120 views

Fourier transform of a signal sequence?

Desparately, I am trying to calculate the Fourier transform of the following signal sequence. What can it be? $$f(x)=\left(\frac{\sin(\pi x)}{x\ln(T)\sin[\pi\ln(x)/\ln(T)]}\right)^2$$ while $x > ...
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0answers
80 views

Proof of Caratheodory's theorem about the unique determination of a linear combination of sinusoids

Following is a statement of Caratheodory's Theorem about a positivelinear combination of sinusoids :- Any positive linear combination of k sinusoids is uniquely determined by its value at time t ...
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1answer
87 views

Signal compression

I believe I have an extremely simple question but I can't seem to figure it out. This image shows $x[n]$ and I have to draw $y[n]=x[2n-4]$ by first doing a compression and then a time shift. The ...
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0answers
232 views

Relationship between DFT and FFT/DTFT

Question 1: Assume we already know $x(t):[0,2\pi]\to\mathbb{R}$'s Fourier series $x[n]_{n=-\infty}^\infty$. Perform DFT on $x[n]_{n=0}^N$. How is the result connected to $x(t)$? WHY? Question 2: ...
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3answers
489 views

Bases in compressed sensing (signal reconstruction)

I have been posting this kind of question in Cross Validated, but since this one deals almost entirely with mathematics, I will post it here. In signal reconstruction using compressed sensing, we ...
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2answers
248 views

Given one sine wave in time domain, how to find its frequency?

Given one sine wave in time domain, I want to find its frequency. Because I observe only a very small part of the sine wave ~1 cycle, FFT methods have a poor spectral resolution. Has there been work ...
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1answer
286 views

How do I compute “AUC” Area under the curve number, if all I have are my TPR and FPR values?

I am trying to rank my neural network, which is trained for binary classification. That is, given a set of input signals, it outputs either a 1 or a 0. I have a training set, where I have the actual ...
2
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1answer
380 views

Using FFT in matlab

I am not completely sure if this is where a MatLab question belongs, so if not, please direct me where I should ask. But onto my question. I am working on trying to deconvolution a signal with ...
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1answer
618 views

Approximation of Saturation function

"Saturation" or "clipping" function: clip(x)=min(max(x, -1), 1) The context where I encountered this is LTI (linear time-invariant) system analysis (in classic ...
2
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1answer
79 views

What are Autoregressive Coefficients?

Can anyone explain what are Autoregressive Coefficients? What is their meaning that is. Consider a method: public double[] calculateARCoefficients(double[] inputseries, int order) When this method ...
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2answers
67 views

Max frequency of a signal?

Having $$ f(x) = \cos(x) + \sin(10x)$$ How Can I know which is the max frequency of this signal? I need it to set the right Nyquist frequency ($2\cdot\max\text{frequency}$) I can use Matlab if ...
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1answer
268 views

Sawtooth wave spectrum

Could a good soul help me? I heard that the fourier transform of a periodic signal is a pulse train, but for a sawtooth wave: what is the fundamental frequency of the spectrum? Thanks
3
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2answers
522 views

How do I find transfer function of a discrete-time system when its state-space form is given?

I read this and this Wikipedia pages, but both of them are explaining continuous-time systems. My question is about discrete-time case. For example, given the state-space equations of the second ...
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1answer
249 views

Find peak output value using transfer function

I have a filter with Transfer function $H(z)=(1-0.5z^{-1})(1+0.5z^{-1})$ designed for a sampling rate of 800 samples/s. How to find peak output if a sine of 200Hz and amplitude 4 is applied as input? ...
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1answer
68 views

Transfer Function from input to node.

From the IIR filter flow graph below i don't understand how the transfer function is calculated in every node: The circles contains 'X' inside are multiplications. The circles contains 'Σ' inside ...
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0answers
58 views

Why process noise model is$ \dfrac{T^4}{4}$ in Kalman filter.

I am using Kalman filter for filtering noise on 2D object movement. I read a lot of examples, but no one has been explained, why noise model is distance powered by 2: $$ s \times s = \dfrac{T^2}{2} ...
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1answer
68 views

Find the transform

I have the paper with 3 points on it. I have also a photo of this paper. How can I determine where is the paper on the photo, if I know just the positions of these points? And are 3 points enough? It ...
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1answer
104 views

Signal approximation using linear combination of functions

How I can approximate the signal $x(t)=0.001\,t^3 \exp(-0.1t)$ in the interval $[0,100]$ using a linear combination of the following functions: $f_1(t)=A_1$ $f_2(t)=A_2\cos(0.05t)$ ...
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2answers
2k views

What is the inverse z transform of 1/(z-1)^2?

I'd like to know how to calculate the inverse z transform of $\frac{1}{(z-1)^2}$ and the general case $\frac{1}{(z-a)^2}$
3
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2answers
584 views

Problem with Discrete Parseval's Theorem

I think I must be missing something obvious, but I can't for the life of me see what it is. The discrete version of Parseval's theorem can be written like this: $\sum_{n=0}^{N-1} |x[n]|^2 = ...
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1answer
199 views

Mathematically inclined books on Signal Processing Theory

First off, i know this may seem off topic but i could not find help in signal processing communities so i was hoping there would be people here who both love mathematics and have interest in signal ...
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2answers
1k views

Scale Space - Scales and Octaves

So I'm desperately trying to understand scale space for signals, specifically for 2D images... I'm having trouble with algorithms that discuss creating a pyramid. Specifically, I don't understand how ...
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1answer
30 views

How to show quantisation error for frequency coefficient

I have the following question from an exam which reads: For the second question my answer is: 24 5 2 3 9 2 1 3 2 3 2 2 1 1 1 0 I am unsure of what formula ...
5
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2answers
113 views

partially reconstruct information of function convoluted with boxcar kernel

the function (f) I want to reconstruct partially could look like this: The following properties are known: It consists only of alternating plateau (high/low). So the first derivation is zero ...
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1answer
95 views

Nyquist criterion

When using the Nyquist stability criterion, amplitude-frequency characteristic etc. we go from the Laplace image $G(s)$ to $G(j\omega )$. By definition of the Laplace transform, $s=\sigma + j\omega$. ...
2
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2answers
328 views

I need to calculate the period, I need help to verify my answer

I need to determine if $x(t) = 9\cos(2t) + 4\sin(\pi t)$ is periodic. If it is periodic I need to find the period. this what I have done \begin{align*} T_0 &= 2\pi/w\\ T_1 &= 2\pi/2 = \pi \\ ...
0
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1answer
341 views

Is the convolution an invertible operation?

If I have a signal $f(x,y)$ (discrete) and I convolve this signal with a kernal $h(x,y)$: $y(x,y) = f(x,y) \star h(x,y)$ (where $\star$ is the convolution operator) Can I obtain $f(x,y)$ given only ...
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1answer
46 views

Extracting independent sources from available signals.

I have four signals in time domain, in the format of 4 vectors (a,b,c,d). I know there are 3 sources contributing these signals. One is a source that is shared between all four signals. One is a ...
2
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0answers
241 views

Checking if (discrete) signal is stationary, BIBO stable and

I have this discrete signal y[n] = sum (x[k+1]h[k-1]), where k goes from -inf to +inf. I need to check if this signal is stable, stationary, and if it's invertible, i need to find it's inverse ...
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0answers
303 views

How can I find the compact trigonometric Fourier series from these signals?

I've been stuck on this for a while, but how exactly would I go about calculating the compact trigonometric Fourier series for both of these signals? I have a general formula down for it, but I just ...
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2answers
114 views

Complex expression for periodic binary sequences

We have infinite binary sequences of type $$\langle g_n \rangle_{j=4}=\{0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,...\} \,;\, n\to\infty$$ where $j$ indicates the length of a period that starts/ends with a $1$; ...
2
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1answer
71 views

FFT for a single frequency

I was looking for a more efficient way of finding the magnitude and phase of a signal at a certain frequency without performing an FFT because it produces more information than I need and I came ...
2
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1answer
331 views

Check the orthogonality of two functions

This is a part of two Passband Signals. My question involves inner product. Is $$ \left < \cos(2\pi ft + \phi) , \sin(2\pi ft + \phi) \right> $$ where $\phi \in [-\pi, \pi)$ equal to zero, i.e. ...
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1answer
586 views

solve an difference equation's particular solution with unit step input

I have a question like this $y[n] - \frac 2 5y[n-1] = 2x[n]$ and $x[n] = 2u[n]$, the manual say that $y^p[n] = k u[n]$ and subtitute it into the equation will become $ k - \frac 25k = 4$. But I think ...
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1answer
262 views

How can I calculate the bode magnitude and frequency as well as their plots?

I've been trying to figure this problem out for a while now. I've been given a transfer function $$H(s) = \frac{s(s+100)}{(s+2)(s+20)}.$$ I'm supposed to calculate the bode magnitude and frequency for ...
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0answers
50 views

Discrete time fourier transform of partial sum

I came across the following property of the DTFT: $ \mathcal{F} \Bigg(\sum_{m=- \infty}^{n}x[m]\Bigg) = \frac{1}{1- e^{-j \omega}} X(e^{-j \omega}) + \pi X(e^{-j0}) \sum_{m= ...
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1answer
8k views

Prove of the Parseval's theorem for Discrete Fourier Transform (DFT)

If $x[k]$ and $X[r] $ are the pair of discrete time Fourier sequences, where $x[k]$ is the discrete time sequence and $X[r]$ is its corresponding DFT. Prove that the energy of the aperiodic sequence ...
0
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1answer
87 views

Find the non null complex Fourier coefficients

I'm doing my homework on signal processing in MatLab and I'm stuck on an exercise. I'm given this signal $x(t)=1 + 2\sin(12\pi t+\frac{\pi}{4})\cos(21\pi t);$ and I have to get the non null complex ...
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1answer
119 views

The science of pearson product moment correlation coefficient

I need to compare two sound signals for similarity, I took cross-correlation of both the signals and I got a cross-correlation signal, now I intend to use pearson correlation coeff formula to get the ...
2
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2answers
54 views

Express $\cos(5t)$ with the help of Euler formula

I can't figure out, how to express $\cos(5t)$ in the form $e^{j\omega t}$. I don't even know the right answer. How would you deal with this task?
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1answer
54 views

How does one verify if a vector is really recovered?

In compressed sensing, how to verify if a vector is really recovered or how does one plot the figures on recovery rate? Since in numerical experiments, there is always a difference between the ...
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1answer
140 views

How to determine the function of this “black-box”?

Imagine a black box which accepts a digital input signal which is a pure sine wave and outputs the area between this input signal and some constant data set over a sample window. Given the input ...
0
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1answer
109 views

response impulse function

my question is related to time series modeling in signal form,i have such question,suppose we have time series data $y_1........y_n$,how can we represent in impulse response form?as i ...
3
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1answer
321 views

Find the expression and the system impulse response

I've started to learn signal fundamentals and I have to do one exercise and I can't understand something. It is said that $$x[n]=1.5\cos(0.025 \Pi n)(u[n+40]-u[n-40]))$$ and that the signal $u[n-m]$ ...