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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
117 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 ...
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1answer
91 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 ...
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1answer
88 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, ...
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1answer
260 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 ...
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2answers
549 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 ...
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1answer
462 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
97 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 ...
2
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1answer
348 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|} ...
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2answers
518 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 $f_0,f_1,f_2 ...f_{n-1}$ $f_0$ = ...
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0answers
144 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} ...
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0answers
237 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 ...
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0answers
211 views

What is the purpose and usage of convolution?

I am curious of what the purpose and usage of convolution are. Why is convolution created? In layman's term (and in mathematical term), what defines convolution?
5
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1answer
587 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 ...
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0answers
180 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 ...
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2answers
269 views

Usage of inverse Laplace transform

At my current study level in college, use of inverse Laplace transform is not mentioned well - textbooks say "use tables." So, can anyone show me how to use inverse Lapalce transform? And also proof? ...
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1answer
4k views

Hamming Window - Understanding Formula

I'm trying to understand the Hamming window concept (Signal Processing) and the equation looks like the following: Where: N = number of Samples in each frame Y[n] = Output Signal X(n) = Input ...
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3answers
386 views

Removing noise when the signal is not smooth

Suppose we have (an interval of) a time series of measurements: We assume it can be explained as a "simple" underlying signal overlaid by noise. I'm interested in finding a good algorithm to ...
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3answers
265 views

Pre–emphasis - Signal Processing

I am trying to compute the Pre-emphasis of a signal and the formular is below: y[n] = x[n] - 0.95 x[n-1] Let: ...
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1answer
307 views

how can I get minimum error probability for this decision problem?

I have the decision problem for 4 hypotheses as follows: $$H_j: Y_k=N_k-s_{jk},\ k=1,2,\ldots,n;\ j=0,1,2,3.$$ where signals are $s_{jk}=E_0\sin(w_cT(k-1)+(j+\frac{1}{2})\frac{\pi}{2}).$ $$$$ In ...
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1answer
124 views

Number of Zero-crossing

I have written an algorithm that calculates the number of zero-crossings within a signal. By this, I mean the number of times a value changes from + to - and vise versa. The algorithm is explained ...
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2answers
86 views

Algorithm as Equation

I have developed an algorithm that counts the number of times a particular block (within a 2D Matrix) crosses zero. Here's an example: ...
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1answer
143 views

What does it mean to convolve a matrix with a kernel?

I have a Matrix, M, of dimensions width x height. The problem is to apply the [-1, 0, 1] filter along the x and y axis (i.e. convolve the image with [-1, 0, 1] kernel along horizontal and vertical ...
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1answer
313 views

How does convolution/deconvolution with gaussian affect signal mean

I have a discrete signal (an image actually), which I am convolving/deconvolving with a zero-mean Gaussian kernel. I would like some proof that these operations do not alter the signal mean. Well, it ...
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1answer
56 views

Nonlinear single-input single-output model

Assume a single-input single-output model $y = f(x)$ where time series $x = (x_0, .., x_{n})$ is the input, time series $y = (y_0, .., y_n)$ is the output and $f$ a function mapping $x$ to $y$. If ...
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1answer
134 views

ROC analysis: detection probability when false alarm is maximized.

I am wondering if detection probability always goes to 1 as false alarm probability goes to 1. Let's assume binary hypothesis problem: $\mathcal{H}_0: x(t) =n(t)$ $\mathcal{H}_1: x(t) = s(t) + ...
3
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1answer
105 views

A question about infinities and distribution functions

Let $\mathcal{P}_i$ be the set of probability density functions to which $f_i$ belongs, $(i=0,1)$. Furthermore assume that $$L(y)=\frac{f_1(y)}{f_0(y)}$$ is an increasing function for any chosen ...
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1answer
159 views

Why doesn't repeating a signal give rise to a finer resolution of DFT/FFT?

If x = [1 2 3 4 3 2]; and x1= [x x x x x x x x x]--that a new vector made of duplicating copies of x, then why is it that the FFT of x and x1 are essentially the same. When I plot the FFTs of each ...
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0answers
47 views

System stability

I need to do an absolute integral of my impulse response of my LTI system so I can find out if the system is stable or not. The general formula is: $\int_{-\infty}^{\infty} \! |h(t)| \, \mathrm{d} t$ ...
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1answer
48 views

Using Product rule to take derivative

I'm trying to take the derivative of: $\frac{-1}{6}(e^{-3t}-1) u(t)$ The $u(t)$ is the step response. So the answer I get is by just doing product rule: ...
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0answers
283 views

Understanding Discrete Cosine Transformation

I'm currently working on some software and a key component is 2D DCT. But my question is more general, as I'm trying to understand the DCT in general, let's say from engineers point of view. For ...
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0answers
388 views

Fourier Series Coefficients for Signals

The question is: We specify the fourier series coefficients of a continuous-time signal that is periodic with period 4. Determine the signal x(t). $a_k=\begin{cases} 0, & k=0\\ ...
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1answer
130 views

Fourier Series with Signals

So the question is: Determine the fourier series representations for the following signal: Here the formula for the fourier series $$C_k=\frac{1}{T}\int_T \! x(t)e^\frac{-j2\pi kt}{T} \, \mathrm{d} ...
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1answer
194 views

Should mean be subtracted before convolution?

Suppose I have a signal in the form of N real numbers. I am searching for a continuous pattern within this signal. The pattern is represented by M real numbers. (M < N) To find the pattern's ...
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1answer
63 views

what is an integral multiple of a period?

Suppose i have a sinusoidal waveform. What does it mean when I need to truncate it corresponding to an integral multiple of a period?
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2answers
196 views

Chirp: Why do you need to integrate the frequency function?

From the Wikipedia page on chirp, if I provide some time-dependent frequency function $f(t)$, this has to be integrated if I want to use it as the argument to, say, a sinusoid. Suppose $f(t) = ...
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1answer
325 views

Maximum Eigenvalue of Autocorrelation Matrix Bound

I am reading Detection and Estimation by Kay. In problem 2.7, one of the parts is to show that the maximum eigenvalue of the autocorrelation matrix is less than the maximum value of the PSD. The ...
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0answers
214 views

Projection Slice theorem getting rid of artifacts?

I have employed the fourier(projection) slice theorem in matlab. I have a 3D image, P(x,y,z) defines their pixel intensities at a given location int he image volume, it is discrete and uniform. I ...
2
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1answer
3k views

How to plot this signals or functions?

i´m taking a course in signals and systems, and i really don´t know how to plot this signals Consider the pulse signal written as $p(t)=u(t+0.5)-u(t-0.5).$ where $u(t)$ is the Heaviside step ...
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2answers
129 views

Why is $1 - 2\cos^2(\frac{\pi n} {4})$ the same as $ -\cos(\frac{\pi n} {2}) $?

Why is $$1 - 2\cos^2(\frac{\pi n} {4})$$ the same as $$ -\cos(\frac{\pi n} {2}) $$ I think the 1 in here, I can just neglect when I look at borders from $[-\infty , \infty]$. But what's going on ...
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1answer
484 views

Autocovariance of white noise convolved with function on L2

I want to compute the autocovariance of a Gausian zero-mean white noise process convolved with a function $f(t) \in L^2$. Could anyone show me how I'd do this or provide a reference? $L^2$ is the ...
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3answers
10k views

square wave matlab code

I'm having some trouble generating a square wave in matlab via my equation. Just wondering if anyone has some insight on what I am missing here in my code? I was thinking I could easily generate a ...
3
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1answer
707 views

Is there a time-domain proof of Nyquist sampling theorem?

For a continuous-time signal $x(t)$ that is bandlimited (in the baseband) to $[-W,W]$, the standard proof of Nyquist sampling theorem proceeds in the frequency domain by examining the Fourier ...
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2answers
12k views

Integration of sawtooth, square and triangle wave functions

Context After a discussion about how to plot the results of a frequency modulation between two signals on Stack Overflow, I understood that I need to find the time-integral of the following wave ...
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1answer
673 views

What is the difference between FWHH and FWHM?

The title says it all really. I wanted to know if there is a situation where full width half height half maximum is more appropriate than full width half height or vice versa. Thank you
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1answer
94 views

Boundary condition error, correlation of a function with a wavelet.

I'm trying to compute some wavelet transforms and I seem to be running into some boundary condition errors. I have a randomly generated signal pictured at the top of the figure, and the real part of ...
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2answers
734 views

Need a formula for a quadratic spline

I'm trying to reproduce some results from a paper and I need an explicit formula for a specific quadratic spline to do so. The problem is, I've only got a plot of it. The quadratic spline is from ...
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1answer
637 views

FFT with a real matrix - why storing just half the coefficients?

I know that when I perform a real to complex FFT half the frequency domain data is redundant due to symmetry. This is only the case in one axis of a 2D FFT though. I can think of a 2D FFT as two 1D ...
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2answers
954 views

How can I apply a low pass filter to a Fourier Series?

I have a square wave signal and its Fourier Series. This signal pass through an ideal low pass filter,H(f), which has a cutoff frequency of 4KHz. What is the resulting baseband bandwidth of the ...
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2answers
3k views

How do you calculate the frequency perceived by humans of two sinusoidal waves added together?

I'm not sure if this is on topic or not. The tag may also not actually fit. If you add together two sinusoidal waves of different frequencies, how do you calculate the frequency of the resulting ...