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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
369 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
250 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
288 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
117 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
139 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
298 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
128 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) + ...
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1answer
103 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
147 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
122 views

Wavelet Transforms

I don't know as much as I would like to about Fourier analysis and I know almost nothing about wavelets. So just have a few conceptual questions to determine whether I should pursue their study or ...
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0answers
46 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
274 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
362 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
122 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
187 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
62 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
188 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
314 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
210 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 ...
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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
465 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
9k 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 ...
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1answer
680 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
11k 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
644 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
701 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
616 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
922 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
2k 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 ...
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1answer
78 views

Estimating the input to a system from a system state

[ Cross-posted to: http://dsp.stackexchange.com/questions/3098/estimating-the-input-to-a-system-from-a-system-state-using-ekf ] I have a system for which I have obtained a non-linear time-varying ...
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1answer
162 views

Solving Difference Equation

I have the following equation: $$\frac{Z-1}{{Z^2}-2Z+6}$$ I tried to apply difference equation on it: $$y_{n+2}-5y_{n-1}-6y_n = x_{n+1}-x_n$$ I need to find equation expressed as $y_n$ I have the ...
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1answer
4k views

Plotting a one-sided amplitude spectrum

I have a continuous signal $x(t)$ such that $$x(t)=12\cos(6\pi t)+6\cos(24\pi t)+3\cos(30 \pi t)$$ and is asked to sketch a $1$-sided Amplitude Spectrum of the signal $x(t)$ if sampled above the ...
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1answer
728 views

Finding Fourier series with function not centered at the origin

I am trying to find both Fourier cosine and sine series which represent the function F(t) in the interval $(0, \pi)$ where $F(t)=\begin{cases} \frac{\pi}{2} & \ \ 0<t< \frac{\pi}{2}\\ 0 ...
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1answer
82 views

Is that a counterexample to sampling theorem?

Sampling points are $\mathbb{Z}$. Sampling theorem tells us that functions with bandwidth lower than $\frac{1}{2}$ will have no aliases. Take functions with pure frequency $\frac{1}{4}$ as an ...
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2answers
140 views

Z-Transform Identity

I've come across an identity and would like to know if it has some sort of formal name or derivation or explanation or something! Also, I'm curious as to whether others are aware of such an identity. ...
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1answer
1k views

Visualize a difference equation with Matlab [closed]

I have a difference equation for a Single Pole Infinite Impulse Response Filter, defined on a discrete time-series: $y[n]-(1-\alpha)*y[n-1]=\alpha*x_n$ While the []s brackets refer to a position n ...
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3answers
121 views

Detecting significant decreases in a signal

I'd like to find a way to detect a significant drop/decrease in a signal. Below is an actual example of what I'd like to accomplish, with the arrow denoting the change that I'd like to detect (only ...
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1answer
5k views

$y(n) = x(-n)$ , causal or not , memory or memoryless?

$y(n) = x(-n)$ , causal or not , memory or memory-less ? it's a question in digital signal processing course . My guess it's memory less , causal because $x(-n)$ is only the inverse of the ...
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119 views

Worst-case error related to Cramer-Rao bound

I would like to understand the relation (if any) between the Cramer-Rao Lower Bound of estimation theory and the following simple definition of "reconstruction accuracy" which doesn't use any ...
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1answer
499 views

95% of energy of Bessel Functions

How can we determine what which Bessel function amplitudes contain the majority of the the energy? Similar to the Carson bandwidth rule, I want to determine which sidebands help make up the 95% of ...
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437 views

proof that orthogonal signals not interrupting each other

I know that signals that are orthogonal do not disturb each other. What I am curious is what is the proof behind why orthogonal signals in a single signal (i.e. a single signal can be broken down ...
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1answer
114 views

MA process ACF proof - don't understand it

I've got the proof but I don't understand a small detail. As you know for an MA process: $X_n = \sum _{i=0} ^q \beta_i Z_{n-i}$ where $Z_n$ is WGN (pure Gaussian random process). Then the ACF is: ...
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0answers
176 views

How to solve the recursive relation in Kalman filter?

I was wondering how to solve the Kalman filter's recursive equation (also see the appendix at the end of this post) for the estimated state $\hat{\textbf{x}}_{n|n}$ at time $n$, over discrete times ...
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2answers
400 views

Nyquist-Shannon sampling theorem - original version and modern version difference?

I just found out that the original version of Nyquist-Shannon sampling theorem differs from the modern version.. In the original version, it states that the bandlimited signal $x(t)$ can be ...