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1answer
248 views

Short question to a pole-zero plot

I worked out this output of a sequence: $$Y(z) = \frac{(z-1)(z+\frac{3}{2})}{z^2 (z-\frac{j}{2})(z+\frac{j}{2})(z-\frac{1}{2})}$$ My problem is the $z^2$. $$z^2 = z * z = (z - 0)(z-0)$$ So I think ...
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1answer
252 views

How to take the inverse of this signal?

I have a little problem computing the inverse of this signal: $$X(z) = \frac{(z-1)(z+\frac{3}{2})}{(z+\frac{j}{2})(z-\frac{j}{2})(z-\frac{1}{2})}$$ $$X(z^{-1}) = ?$$ I know how to take the inverse, ...
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1answer
320 views

Qualitative interpretation of Hilbert transform

the well-known Kramers-Kronig relations state that for a function satisfying certain conditions, its imaginary part is the Hilbert transform of its real part. This often comes up in physics, where ...
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1answer
2k views

Speech processing pre-emphasis: how does it work?

In speech processing, the original signal usually has too much lower frequency energy, and processing the signal to emphasize higher frequency energy is necessary. To perform pre-emphasis, we choose ...
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3answers
11k views

Matlab Speech Recognition - Mel-Frequency Cepstrum Coefficient (MFCC)

I'm following this Matlab Speech recognition tutorial. I'm stuck on page 5 on the term/concept of MFCC feature vectors. I'm unable to grasp the concept of what an MFCC is.. a matlab function, ...
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3answers
398 views

Fast computation/estimation of the nuclear norm of a matrix

The nuclear norm of a matrix is defined as the sum of its singular values, as given by the Singular Value Decomposition of the matrix itself. It is of central importance in Signal Processing and ...
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1answer
77 views

Can u tell me something about these signals?

I have a problem with these signals: $x[n]$ is given: $ x[n] = 3 \delta [n] - 2 \delta [n-1] + \delta [n-1] \text{, } n = 0,...,N \text{, N=8 }$ I computed the DFT and afterwards the 5 IDFT's of the ...
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2answers
6k views

FFT bins from exact frequencies

I'm trying to understand a few concepts about Fourier Transforms (mainly in the context of signal processing). Let's suppose a signal is sampled at 10kHz and that the FFT size is 1000. If 1000 ...
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1answer
129 views

Trouble finding the right DTFT pair

i have a periodic signal $x[n] = \cos (\frac{2 \pi}{10}n)$. I found this DTFT pair: That's the only pair for a cosine function i found. But what is $\delta _{2\pi}$ ? Is it just a Dirac $\delta$ ...
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1answer
106 views

Express a signal by another signal?

I am having trouble understanding and getting the solution to this question: Let $x : \mathbb Z \to \mathbb C$ denote a discrete-time sequence and for $N \in \mathbb N$ let $x |_N$ be the ...
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1answer
109 views

Derive the function for a given symmetric impulse response

i have a symmetric impulse response: $h[n]=-h[M-n]$ , $0\leq n \leq M$ Frequency response is: $H(e^{j\omega})=je^{-j\omega N}R(e^{-j\omega})$ $R(e^{-j\omega})$ is a real-valued function. I want ...
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0answers
226 views

FFT signal post processing

This is more a "post a suggestion" topic rather than a question. And thank you if you are willing to read this whole. I've been studing the code in the Nvidia Cuda SDK regarding how to operate a ...
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1answer
424 views

Is this a square wave signal?

i have a decomposition of a square wave signal: $$ y = \frac{4h}{\pi}(\sin(x) + \frac{1}{3}\sin(3x) + \frac{1}{5}\sin(5x) + ...) $$ I computed the fundamental wave and 2 harmonic waves: $$ U_{r0} = ...
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1answer
224 views

When has this sequence a triangular shape?

Can someone explain to me why y[n] has a triangular shape? From what I have found, there is a specific range $n_0$ where y[n] is triangular. But right now I have no clue where to start. $^2$ Search ...
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1answer
2k views

What is boxcar averaging?

This is an application in signal processing but what I don't understand is how it's done algorithmically. I've seen some stuff online but most of it is just pictures. I would like an example on some ...
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2answers
5k views

How to fit a curve to a sinusoidal wave

I am wondering how to fit a sinusoidal wave (approximation). I would like to fit it in the form: $y = A\sin(Bx + C) + D$ where $A,\,B,\,C$ and $D$ are constants. The only constants I really care about ...
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0answers
608 views

Partial differentiation of vector to find Jacobian (extended Kalman filter)

I am working through some coursework on self-tuning control and part of one of the questions requires the use of the extended Kalman filter for joint parameter and state estimation. For completeness, ...
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3answers
455 views

Simplifying the expressions for the magnitude and phase of a Fourier transform

$$h[n] = 2( \delta[n-2]-\delta[n-1]-\delta[n-3])$$ i computed my frequency response and i have this now: $$H[e^{j \omega}] = 2[ e^{-2 j \omega} - e^{-j \omega}-e^{-3 j \omega}]$$ $$H[e^{j \omega}] = ...
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1answer
92 views

LTI: What if my frequency response = 1

in my calculations i get to this solution: \begin{aligned} H(e^{j*\omega}) & =\frac{1}{1-0.5 e^{-j\omega}} - \frac{0.5e^{-j\omega}}{1-0.5 e^{-j\omega}} &= 1\ \end{aligned} Am i right that ...
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1answer
187 views

LTI: Is my calculation of the frequency response correct?

i am not sure if my computation is correct. Hope someone can have a look at it. Here is my problem: \begin{aligned} H[e^{j\omega}] & = \sum_{m=0}^{\infty} (\frac{1}{2} e^{-j\omega})^n = ...
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1answer
279 views

Summability of a sinc function power 'p', where 1<p<2

We know that a sum of the form $\sum_{n=0}^{\infty} \left|\frac{sin(a\pi n)}{a\pi n}\right|$ where $a$ is not an integer, is unbounded and tends to infinity. But what about the expression ...
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1answer
613 views

LTI: How to derive the impulse response of this system?

Well, i transform g and x into the frequency domain. u[n] = 1, n ≥ 0 u[n] = 0, n < 0 \begin{aligned} x[n] & = u[n] \\ h_1[n] & = (\frac{1}{2})^n u[n] \\ g[n] & = (\frac{1}{2})^n u[n] \\ ...
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1answer
1k views

LTI: How to calculate the step response of this impulse response?

i need to evaluate the convolution sum of x[n] * h[n]. x[n] is the step function u[n]. I know how the output should look like but i don't know how i can calculate it. I think the lower border is 0, ...
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1answer
1k views

How to sketch the following discrete time signal?

i need to sketch y[n] where * denotes the convolution operator and delta is the unit impulse. I know how to sketch x[n-1] and delta[n-2] but i have problems with the convolution. In my script i only ...
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1answer
513 views

How can I increase/decrease (frequency/pitch) and phase using fft/ifft

How can I increase/decrease (frequency/pitch) and phase using fft/ifft I think I have the basic code but I’m not sure what to do next PS: It's done in Octave/matlab code Example I have a signal that ...
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1answer
90 views

Signal processing and SNR

I am working on a problem where we measure some ripple over a huge constant. The problem is from electronics. You can think of as 100V DC always constant and we have a ripple of +/- couple mV over ...
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2answers
433 views

Which time-frequency coefficients does the Wavelet transform compute?

(I asked this on Stack Overflow a while ago and didn't get a satisfying answer, so I'm trying again here.) The Fast Fourier Transform takes O(N log N) operations, while the Fast Wavelet Transform ...
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0answers
92 views

Extracting the power of a frequency range in a signal

I have a heartrate signal which is a few hours long. I need to preform a spectral analysis to get the ratio high frequency (0.15Hz-0.4Hz) to low frequency (0.04Hz - 0.15Hz) changes in heartrate within ...
0
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1answer
408 views

Aliasing in DFT: mathematical expression

The Fourier transform of a sinc function is the top hat function. So, if $\{y_k\};\ k\in\{0,1,...,n-1\}$ are samples of the sinc function, sampled $T$ apart, the discrete Fourier transform is ...
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1answer
69 views

Given a set of 2D points (x,y) (cloud of points), find the points that, when connected, will contain all other points

Given a set of 2D points I have to find the points that when connected will form a polygon that contains all the points in the set. A quick example: imagine you have a set ...
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0answers
115 views

What is the difference between various kalman filters?

What is the difference between additive and multiplicative kalman filters, as well as some other kinds? I'm also looking for reference texts and articles that describe the algorithms, so ...
4
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1answer
385 views

Fourier Transforms

I'm having a terrible time trying to understand Fourier transforms. I'm very visual so leaving the $X,Y,Z,t$ domain is not working form me :) I'm trying to figure out the basics at the moment. ...
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2answers
4k views

MATLAB interpretation of Xcorr2 - Cross Correlation function

I have two vectors of matching lengths. They are readings from two different sensors (one is from a smartphone and the other is from a wiimote) of the same hand movement. I am trying to find the time ...
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1answer
1k views

Mathematics of a leading signal for a sine wave

Taken from elsewhere on the web : - "The derivative of a sine function is d SIN(ω*t) / dt = ω * COS(ω t) where ω = angular frequency = 2 π *frequency and this derivative leads the original function ...
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4answers
109 views

How much noise will the average of N noisy signals have?

(Inspired by this question on the photography site) Say you have N copies of the same signal, each with a layer of noise on top. You average these copies together in an attempt to reduce the effect ...
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2answers
477 views

Barker sequence

Hi I am learning about Barker sequence. I have a problem, because I do not know, why for example 5, in Barker Code looks like this: +++-+. What is the base of this code. I am looking for some ...
0
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1answer
733 views

Frequency Swept sine wave — chirp

I am experiencing what I think is really simple confusion. Take $y(t) = \sin(2 \cdot \pi \cdot t \cdot\omega(t))$ and $\omega(t) = a \cdot t+b$ for $t \in [0,p)$ and let $\omega(t)$ have a periodic ...
2
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2answers
188 views

Easy question about finite energy due to convergence

The infinite-length sequence $x_1[n]$ defined by \begin{multline} x_1[n]= \begin{cases} \dfrac{1}{n}& \text{if $n \geq $1},\ 0& \text{if $n \leq $0}. \end{cases} \end{multline} has an energy ...
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4answers
241 views

What probability distribution is this?

This image show a histogram (200 bins) of accumulated distances from a radar distance meter (very noisy). The peak around 7 meters is an object. At thought this looked kind of like a normal ...
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3answers
2k views

How to sketch a sinc function by hand?

I have to do this for an upcoming exam, but cannot find anywhere (in the textbook or online) how to do this. I only really need to know a couple points to plot it... when x = 0, and then the earliest ...
2
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1answer
588 views

Rigorous definition of convolution with the unit doublet

The unit doublet is a symbolic object whose convolution with a differentiable function is supposed to give the derivative: $$(x * u_1)(t) = \frac{dx(t)}{dt}$$ See also: ...
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4answers
2k views

Extracting exact frequencies from FFT output

Say I pass 512 samples into my FFT My microphone spits out data at 10KHz, so this represents 1/20s. (So the lowest frequency FFT would pick up would be 40Hz). The FFT will return an array of 512 ...
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1answer
2k views

Calculating the Savitzky-Golay Coefficients

I am working on a signal-smoothing algorithm for personal interest. I understand the basic concept of the Savitzky-Golay algorithm but I would like to understand how the coefficients were discovered. ...
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1answer
125 views

Kalman gain over one

Short question: Can an element in the Kalman gain vector ever be over one?
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3answers
420 views

How can I interpret “energy” in signals?

I am learning about various signal processing methods in my university course, and I can't seem to grasp what 'energy' in signals represent. I mean, I know that it is the integral of the absolute ...
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3answers
613 views

Sensor fusioning in Kalman filter

I'm interested, how is the dual input in a sensor fusioning setup in a Kalman filter modeled? Say for instance that you have an accelerometer and a gyro and want to present the "horizon level", like ...
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2answers
2k views

How do I apply a Gaussian Blur (low-pass filter) to an image made up from a set of points?

I have an image encoded in the form of a list of points, like so: ...
4
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1answer
1k views

Wiener filter: A good tutorial

I am interested in image analysis and am looking for an approachable tutorial to the Wiener filter. At some point I am interested in implementing such a filter but I would like to have a deeper ...
2
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2answers
266 views

Encoding a Discrete Signal to an Artificial Neural Network?

What might be some potential methods to encode a 100-point signal (curve) for input to a Artificial Neural Network? Example: we have a large number of 100-pt 'curves' ranging from flat-line to ...
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0answers
100 views

Analysing an optics model in discrete and continuous forms

A discrete one-dimensional model of optical imaging looks like this: $I(r) = \sum_i e_i P(r - r_i)$ Here, the $e_i$ are point light sources at locations $r_i$ in the object and $P$ is a point spread ...