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112 views

Solving multiple phase angles for multiple equations

I have several equations and each have their own individual frequencies and amplitudes. I would like to sum the equations together and adjust the individual phases, ...
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1answer
358 views

What is a moving average system?

Can someone elaborate on what a moving average system is? I know that the system is defined as: $$y[n] = \frac{x[n] + x[n-1] + x[n-2]}{3}$$ How would we draw $y[n]$ given that we have a graph with ...
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1answer
602 views

What is a cardinal basis spline?

Wikipedia says: the normalized cardinal B-splines tend to the Gaussian function and writes them as "Bk". Meanwhile, cnx.org Signal Reconstruction says: The basis splines Bn are shown ... ...
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1answer
55 views

Calculating Basis Functions for DFTs (64 Samples)

I am attempting to graph some 64 sample'd basis functions in MatLab, and getting inconsistent results -- which is to say, I'm getting results that are still sinusoidal, but don't have the frequency ...
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3answers
643 views

Describing a Wave

I have this wave in front of me, and I am to describe this into a math description such as its function that is equivalent to representing this wave. I have no idea how to start and could use some ...
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1answer
45 views

Function to take discrete sample of a continuous sinusoid function?

Say I have continuous sinusoid function such as: $$x(t) = \cos(2\pi f_0 t)$$ where $f_0$ is the frequency and $t$ is some time in the function. I want to take samples of this function at some sample ...
2
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1answer
844 views

Hilbert transform of white noise

What is the Hilbert transform of a white noise $\xi(t)$? By the Hilbert transform I mean: http://mathworld.wolfram.com/HilbertTransform.html Thank you.
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1answer
362 views

Signal extraction from multivariate normal

Define: $y= \theta + \varepsilon + a,$ where $a$ is a choice variable in a behavioral economic model, with equilibrium solution $a^e$, and $\theta$ and $\varepsilon$ are independently distributed ...
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1answer
1k views

Combining Sine Waves on Chart

I would like to combine multiple sine waves with differing amplitudes, frequencies and phases into a single curve that I can display as a graph. What formula will I need to create the points for the ...
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0answers
69 views

Means to classify data streams or compare similarity

Last year I converted some Matlab code into c to run on embedded Linux. I'm an engineer and normally shy away from maths, but this got me thinking about different ways to classify data or compare the ...
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2answers
235 views

Can it be proven that such functions don't exist?

We are given $x_1,x_2 \in \mathbb{R}$ and we want to find two functions $v_1(t),v_2(t)$ such that: $$x_1x_2 = \int_{-\infty}^{\infty} v_1(t)-v_2(t) dt$$ A very interesting restriction that we have ...
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2answers
90 views

Should I combine the negative part of the spectrum with the positive one?

When filtering sound I currently analyse only the positive part of the spectrum. From the mathematical point of view, will discarding the negative half of the spectrum impact significantly on my ...
2
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2answers
490 views

normalization of a linear combination

I'm a newbie at this forum, so I hope, that this question is not so silly. Let's have some filter $F$, which is a linear combination, thus $F = \sum_{i=0}^{i=N}\alpha_ib_i$, where $\alpha_i$ are ...
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1answer
275 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
499 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
397 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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2answers
3k 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
16k 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
545 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
83 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
11k 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
137 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
124 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
117 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
278 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
522 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
230 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
4k 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
9k 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
901 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
557 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
99 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 ...
0
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1answer
199 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
351 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
804 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
2k 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
2k 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
766 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 ...
0
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1answer
101 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
594 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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1answer
554 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
90 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
166 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 ...
5
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1answer
464 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
5k 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 ...
3
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4answers
135 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 ...
1
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2answers
803 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
897 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 ...
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2answers
207 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 ...