Questions on the mathematical aspects of signal processing. Please consider first if your question might be more suitable for http://dsp.stackexchange.com/

learn more… | top users | synonyms (1)

4
votes
2answers
80 views

Reduce formula using Euler's?

I am performing a self-study, and I am lost as to a derivation that has taken place. I basically started with this equation: $$ \Upsilon(\phi) = e^{-j\frac{N-1}{2}\phi} \ \Big[ \frac{1 - e^{j N ...
2
votes
2answers
1k views

Adjustable Sigmoid Curve (S-Curve) from (0,0) to (1,1)

I feel like this is such a simple question but I am at such a loss. I currently have a set of values that I would like to weigh by an S Curve. My data ranges from $0$ to $1$ and never leaves those ...
0
votes
2answers
66 views

Which Method of Convolution (If Any) Is Most Appropriate Here?

I need to convolve (or otherwise get the impulse response h(t) of) the input signal $x(t) = 2u(t)$ and $y(t) = cos(4t) + 2e^{(t-1)}$. I have tried the Fourier Transform and the Laplace Transform, but ...
0
votes
2answers
33 views

What Does The Following System Do?

I have a system $y(t) = 0.5 \int^\infty _{-\infty} x(T)[d(t-T) - d(t+T) dT] $ Where d(x) is the Dirac Delta function (couldn't find the LaTEX representation - a little rusty there, so an edit to ...
1
vote
1answer
73 views

Can one zero-pad data prior to Fourier transformation, then reverse the change afterwards?

Suppose I have a set of $n$ points $\underline{x}\in\mathbb{C}^n$ with $n \in \mathbb{P}$ ($n$ is prime), and I want to find the Fourier transform of $\underline{x}$. There are some prime-length ...
0
votes
1answer
45 views

Determine negligible coefficients in spectrum

Suppose I have some function $f$ that I have sampled at $N$ points and I preform a transform on it (this could be a Fourier transform, or perhaps a Hadamard, or really anything eles - I'm hoping for a ...
4
votes
1answer
188 views

When does Discrete Fourier analysis fail to detect a frequency?

I'm using python to learn about Discrete Fourier Analysis. What I want to understand is when does the technique fail to recover some frequency of the signal? I understand how this can occur via the ...
1
vote
0answers
69 views

Output of wavelet transforms

I am working on a time sensitive computer science and fluid dynamics project that requires me to find applications of wavelet analysis. I know that at its core, a wavelet transform simply takes a ...
3
votes
0answers
88 views

Exponentials of chi-squared random variables (and their sums)

Let $X_1,X_2,\ldots,X_n$ be a sequence of i.i.d. chi-squared random variables with $t$ degrees of freedom, i.e. $X_i\sim\chi^2_t$. I am wondering what is known about the distribution of ...
32
votes
10answers
2k views

What's the difference between $\mathbb{R}^2$ and the complex plane?

I haven't taken any complex analysis course yet, but now I have this question that relates to it. Let's have a look at a very simple example. Suppose $x,y$ and $z$ are the Cartesian coordinates and ...
0
votes
1answer
41 views

Continuous Hidden Markov Modeling

I am writing a speaker recognition program in Matlab using Mel Frequency Cepstral Coefficients, and although I have gotten the problem to work using discrete time wrapping, I was interested in try to ...
0
votes
1answer
64 views

Finding the signal $y[n]$ that results from the linear transformation of $x[n]$

I have this two signals $$x[n]=4\delta[n+1]+\delta[n-2]-2\delta[n-5]$$ $$y[n]=(3n-5)(u[n-1]-u[n-4]$$ I know that $y[n]$ results by the linear transformation of $x[n]$ and I have to find the ...
0
votes
0answers
205 views

Autocorrelation of the rectangular function

Given the autocorrelation function of the signal "s": $$r(k)=\sum_{t=-\infty}^{+\infty}{s(t)\cdot s(t+k)}$$ The autocorrelation of a rectangular function $\Pi$ (t/2) is a triangle formed by the ...
1
vote
0answers
248 views

Creating intuition about Laplace & Fourier transforms

I've been reading up a bit on control systems theory, and needed to brush up a bit on my Laplace transforms. I know how to transform and invert the transform for pretty much every reasonable function, ...
1
vote
1answer
447 views

Discrete Convolution

Does someone know the equation for the discrete convolution? I found here that the formula is: $$\{x*h\}[k]=\sum_{t=-\infty}^{+\infty}{x[t]\cdot h[k-t]}$$ But when using in Matlab/Octave the command ...
0
votes
1answer
123 views

Harmonic mean of absolute value squared discrete Fourier transform

Let $X[k] \in \mathbb{C}$ be the discrete Fourier transform of $x[n] \in \mathbb{R}$, where $k,n = 0,1,2,...,N-1$. Parseval's theorem relates the arithmetic mean (AM) of absolute value squared ...
1
vote
1answer
46 views

n-correlation function.

So I was thinking of generalization of notions in statistics, like auto-correlation or cross-correlation (auto-correlation is a specific example of cross-correlation where we take the same proccess). ...
3
votes
2answers
81 views

Estimating time in harmonic signal

I hope someone can help me with the following problem: Assume a periodic signal of the form $$\begin{align} s(t) &= \sum\limits_{p=1}^P \sin(p\Omega_0t)\\ &= \sum\limits_{p=1}^P ...
0
votes
0answers
76 views

Calculating sum of a discrete signal (explain summation)

I have to find a convolution of two signals $h[n] = 0.5^nu[n]$ $x[n] = u[n]-u[n-3]$ the final sum, which is correct is: $$\sum_{m=n-2}^n 0.5^mu[m] $$ note that i replaced $n-k$ with $m$, that is ...
0
votes
1answer
40 views

Frequency Change with Tape Speed

I recorded my own voice in an old tape recorder. When I put the device in fast forward mode my voice turned a little squeaky. I wonder if the fundamental frequency of the voice had changed? Is that ...
0
votes
0answers
43 views

Create an objective function for the window length of an adaptive filter

I have a filter, when I place it on a sinusoid, and I use a certain window length (1/4 the period of the sinusoid, no matter the amplitude), it returns my desired result: the stationary points of the ...
0
votes
1answer
63 views

Determining the Discrete Fourier Transformation of signal.

I'm studying signal analysis and now I'm at the Fourier series/transformations. I'm following an example but can't understand the last step. This problem is divided in two steps. FIRST From this ...
1
vote
1answer
57 views

Signal Processing Convolution Summation Calculation

I am learning convolution of signals, and need to do a lot of summations and math. Because y[n]=Sum(x[k]h[n-k]) from negative infinity to infinity. I am always stuck at math procedures. Also, I am ...
0
votes
1answer
59 views

Reconstructing signal without aliasing

$$x[n]=2\sin\left(0.2\pi n-\frac{\pi}{2}\right)+4\cos(0.5\pi n-\pi)+\cos(0.8\pi n)$$ This signal is the result of sampling $x(t)$ with a frequency of 40Hz. I have to see if this frequency can ...
1
vote
0answers
148 views

Convolution property in terms of fft (matlab)

I am working on some signal processing and I have the following data: ...
0
votes
1answer
71 views

Bounds on least squares and weighted least squares estimator

I was wondering if I can get some help in getting bounds on the parameters estimated by least squares (LS) and weighted least squares (WLS) methods. Suppose our observation model is: $\mathbf{y} = ...
1
vote
1answer
112 views

Fourier transform of a signal sequence?

Desparately, I am trying to calculate the Fourier transform of the following signal sequence. What can it be? $$f(x)=\left(\frac{\sin(\pi x)}{x\ln(T)\sin[\pi\ln(x)/\ln(T)]}\right)^2$$ while $x > ...
2
votes
0answers
74 views

Proof of Caratheodory's theorem about the unique determination of a linear combination of sinusoids

Following is a statement of Caratheodory's Theorem about a positivelinear combination of sinusoids :- Any positive linear combination of k sinusoids is uniquely determined by its value at time t ...
1
vote
1answer
77 views

Signal compression

I believe I have an extremely simple question but I can't seem to figure it out. This image shows $x[n]$ and I have to draw $y[n]=x[2n-4]$ by first doing a compression and then a time shift. The ...
3
votes
0answers
160 views

Relationship between DFT and FFT/DTFT

Question 1: Assume we already know $x(t):[0,2\pi]\to\mathbb{R}$'s Fourier series $x[n]_{n=-\infty}^\infty$. Perform DFT on $x[n]_{n=0}^N$. How is the result connected to $x(t)$? WHY? Question 2: ...
4
votes
3answers
286 views

Bases in compressed sensing (signal reconstruction)

I have been posting this kind of question in Cross Validated, but since this one deals almost entirely with mathematics, I will post it here. In signal reconstruction using compressed sensing, we ...
0
votes
2answers
207 views

Given one sine wave in time domain, how to find its frequency?

Given one sine wave in time domain, I want to find its frequency. Because I observe only a very small part of the sine wave ~1 cycle, FFT methods have a poor spectral resolution. Has there been work ...
0
votes
1answer
72 views

How do I compute “AUC” Area under the curve number, if all I have are my TPR and FPR values?

I am trying to rank my neural network, which is trained for binary classification. That is, given a set of input signals, it outputs either a 1 or a 0. I have a training set, where I have the actual ...
2
votes
1answer
192 views

Using FFT in matlab

I am not completely sure if this is where a MatLab question belongs, so if not, please direct me where I should ask. But onto my question. I am working on trying to deconvolution a signal with ...
0
votes
1answer
449 views

Approximation of Saturation function

"Saturation" or "clipping" function: clip(x)=min(max(x, -1), 1) The context where I encountered this is LTI (linear time-invariant) system analysis (in classic ...
2
votes
1answer
70 views

What are Autoregressive Coefficients?

Can anyone explain what are Autoregressive Coefficients? What is their meaning that is. Consider a method: public double[] calculateARCoefficients(double[] inputseries, int order) When this method ...
1
vote
2answers
66 views

Max frequency of a signal?

Having $$ f(x) = \cos(x) + \sin(10x)$$ How Can I know which is the max frequency of this signal? I need it to set the right Nyquist frequency ($2\cdot\max\text{frequency}$) I can use Matlab if ...
1
vote
1answer
169 views

Sawtooth wave spectrum

Could a good soul help me? I heard that the fourier transform of a periodic signal is a pulse train, but for a sawtooth wave: what is the fundamental frequency of the spectrum? Thanks
3
votes
1answer
352 views

How do I find transfer function of a discrete-time system when its state-space form is given?

I read this and this Wikipedia pages, but both of them are explaining continuous-time systems. My question is about discrete-time case. For example, given the state-space equations of the second ...
0
votes
1answer
174 views

Find peak output value using transfer function

I have a filter with Transfer function $H(z)=(1-0.5z^{-1})(1+0.5z^{-1})$ designed for a sampling rate of 800 samples/s. How to find peak output if a sine of 200Hz and amplitude 4 is applied as input? ...
1
vote
1answer
63 views

Transfer Function from input to node.

From the IIR filter flow graph below i don't understand how the transfer function is calculated in every node: The circles contains 'X' inside are multiplications. The circles contains 'Σ' inside ...
1
vote
0answers
50 views

Why process noise model is$ \dfrac{T^4}{4}$ in Kalman filter.

I am using Kalman filter for filtering noise on 2D object movement. I read a lot of examples, but no one has been explained, why noise model is distance powered by 2: $$ s \times s = \dfrac{T^2}{2} ...
1
vote
1answer
61 views

Find the transform

I have the paper with 3 points on it. I have also a photo of this paper. How can I determine where is the paper on the photo, if I know just the positions of these points? And are 3 points enough? It ...
0
votes
1answer
87 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
votes
2answers
1k 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
367 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
votes
1answer
128 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 ...
1
vote
2answers
721 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
vote
1answer
28 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 ...
5
votes
2answers
93 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 ...