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0
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1answer
109 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: $f_1(t)=A_1$ $f_2(t)=A_2\cos(0.05t)$ ...
2
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2answers
4k 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
votes
2answers
848 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 = ...
4
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1answer
282 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 ...
4
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2answers
2k 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 ...
1
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1answer
31 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 ...
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2answers
124 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 ...
1
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1answer
113 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
388 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 \\ ...
3
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2answers
528 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 ...
1
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1answer
50 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
309 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
435 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 ...
0
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2answers
148 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
81 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
384 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
959 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
472 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
55 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= ...
2
votes
1answer
11k 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
91 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 ...
0
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1answer
146 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
votes
2answers
57 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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2answers
61 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
173 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
138 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
votes
1answer
508 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 $u[n-m]$ ...
2
votes
1answer
964 views

Relationship between DFT index values, frequency in a Fourier series and Hz.

I have a sound file recorded at 44.1 K samples per sec, and some FFT and IFFT algorithms. The sound file is a vector with about $ 2^{17} $ elements. My objective is to find which of the index values ...
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0answers
162 views

Pre-Emphasis of a signal

I'm trying to describe the process of Pre-Emphasis (of a signal) in my equations, but I don't know whether or not this makes sense. $Y[n] = X[n] - 0.95 \cdot X[n-1]$ Where Y = pre-emphasis after, X ...
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1answer
119 views

Discrete time signal and unit step

I've started to learn signal fundamentals and I have to do one exercise and I can't understand something. It is said that $$x[n]=3\cos(0.1 \Pi n)(u[n+55]-u[n-55]))$$ and that the signal $u[n-m]$ is a ...
1
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1answer
3k views

How to determine the step response using convolution of the signal's impulse response?

The step response can be determined by recalling that the response of an LTI to any input signal is found by computing the convolution of that signal with the impulse response of the system. ...
1
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1answer
87 views

Finding two highest peaks in a chunk of samples

Supose I have a list of 600 samples of numbers, and the histogram of the samples looks like the following: As can be seen, there are two 'mountains' of values around 16 and 48, and a outlier in 95. ...
0
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1answer
87 views

Cleaning a signal and computing period

I am working with a signal which is a periodic square signal with some kind of noise and some outliers. I would like to know which is the best solution in order to get the period and clean the ...
1
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2answers
257 views

What course sequence should I study in order to build a foundation for studying cryptography and signal processing?

I studied mathematics about two decades ago, but unfortunately, I remember little of it. I'm hoping to start studying cryptography and signal processing, but I'm not entirely sure what ...
0
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2answers
366 views

When writing out the wave equation isn't the phase shift just adding to the frequency?

I hope someone here could clarify for me. With the waveform function f()=(A)sin(wt + theta) where A=magnitude of the wave, sin= type of wave form, wt=frequency rads/sec, theta = phase shift ...
0
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1answer
395 views

Power spectrum for discrete signals.

If $x(t)$ is a real (aperiodic) power signal, i.e. \begin{equation} 0<\lim_{T\rightarrow\infty} \frac{1}{T}\int_{-T/2}^{T/2}|x(t)|^2 dt<\infty \end{equation} $x_T (t)$ is a truncated version of ...
1
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1answer
5k views

What does upside down “v” ($\wedge$) mean in this equation?

I have a simple question, but it is hard to google it. I have this equation here: $$y(t, x) = \sum_{i=1}^{d}(|x_i| \wedge t)^{2} $$ Here $x$ is a size $d$ signal and $t$ is just a scalar. I am not ...
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3answers
125 views

Recover filter coefficients from filtered noise

I have a digital signal which may be represented as noise filtered with an FIR (finite impulse response) filter. Let us suppose that the noise consists of pulses (nonzero samples on a zero ...
0
votes
1answer
105 views

Filter signal through convolution

I am a little bit unsure if I've set up the following problem correctly: Consider the signal $$f(t) = e^{-t}(\sin(5t) + \sin(3t) + \sin(t) + \sin(40t)) \quad 0 \leq t \leq \pi$$ Filter this signal ...
0
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1answer
96 views

(geometric) intuition of whitening

I found this http://cis.legacy.ics.tkk.fi/aapo/papers/IJCNN99_tutorialweb/node26.html But I still don't have an intuition of whitening. A diagonal covariance matrix means uncorrelated distributions, ...
6
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1answer
299 views

Does this curve tend to a square wave?

I have put some Mathematica code here: http://pastebin.com/cY6r7skS that uses this algorithm: $$y1 = Sin[x];$$ $$y2 = Sin[y1];$$ $$y3 = Sin[y1 + y2];$$ $$y4 = Sin[y1 + y2 + y3];$$ $$y5 = Sin[y1 + y2 ...
2
votes
2answers
1k views

Interchange of sums and integral

Suppose I have a function $x:\mathbb{R}\rightarrow\mathbb{R}$ such that is square-integrable: $$\int_{-\infty}^\infty|x(t)|^2dt<\infty$$ Suppose also that $x(t)$ contains no higher frequencies ...
2
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1answer
514 views

Can the differentiating and squaring process in the cochlea explain a reported dichotic stimulation experiment?

On this math.stackexchange on url What is Octave Equivalence? in an answer on the related ( octave equivalence ) question is stated: Mathematically, this signifies that the mammalian cochlea ...
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1answer
123 views

Region of convergence of Z-Transform connected area?

Shouldn't the Region of Convergence of the Z transform be a connected area ? In Oppenheim solution manual, I've found this answer of a question that asks to determine the different forms of the ...
3
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1answer
616 views

Upper and lower bounds of a ratio involving vector norms

I'm working on a signal processing problem and need to analyze the following expression $$ G = \frac{n}{\sum\limits_{i=1}^n |w_i|} \frac{ \sum\limits_{i=1}^n g_i w_i^2}{\sum\limits_{i=1}^n g_i |w_i|} ...
2
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2answers
903 views

Combining bins of FFT ouput

I was trying to combine output of a $2n$ point Real FFT to generate custom FFT bins. For example the FFT generates components at equally spaced frequencies $f_0,f_1,f_2 ...f_{n-1}$ $f_0$ = ...
0
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0answers
255 views

Explain the existence of limit in Persistence Excitation — mostly zero and non-existent?

Definitions Persistence Excitation on page 121 here or shortly here and here. A signal is PE if this limit exists $$r_u(\tau)=\lim_{N\rightarrow\infty}\frac 1 N \sum_{t=1}^{N} ...
2
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0answers
392 views

Lloyd-Max Quantizer Problem

Consider the function $z = x^2 + y^2$ , for $0 \leq x \leq 10$ and $0 \leq y \leq 10$. Take a regular discretization with steps $\Delta x = \Delta y = 0.1$ and its histogram as the probability ...
6
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1answer
824 views

Zero-padding data for FFT

If I take a discrete Fourier transform of $\{ c_1, c_2, \ldots, c_n\}$ where $n$ is prime, I am rather limited in the FFT algorithms available to me and their performance. Additionally, having ...
2
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0answers
292 views

MFCC - Why 13 Coefficients

Basically I am trying to computer a MFCC and wondered if you can help. This is the FFT of 1 of the Frames (After I have multiplied the Hamming Window by the Mel Bank Filters) : Here is the DCT of ...