# Tagged Questions

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

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### 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 ...
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### Looking for a Calculus Textbook

I want to start signal processing and I need a book that satisfies my mathematical requirements: I am in the third grade of high school and I don't know any useful thing about limit, differential, ... ...
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### How do I exactly project a vector onto a subspace?

I am trying to understand how - exactly - I go about projecting a vector onto a subspace. Now, I know enough about linear algebra to know about projections, dot products, spans, etc etc, so I am not ...
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### 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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### Rapid approximation of $\tanh(x)$

This is kind of a signal processing/programming/mathematics crossover question. At the moment it seems more math-related to me, but if the moderators feel it belongs elsewhere please feel free to ...
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### 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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### 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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### Complex filter factorizations - continued

Continuing from this rather silly trivial question factoring real valued filters into shorter complex ones, hoping this won't be as trivial. If we modify it a bit: $$z_0 = e^{2\pi i / 8}$$ and ...
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### Kolmogorov-Zurbenko filter - Calculation of coefficients

I'm currently researching the Kolmogorov-Zurbenko filter and trying to implement it myself as a way to smooth one-dimensional signal strength values. The basic filter per se is pretty easy to ...
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I am sampling a continuous signal $x_c(t)$ that follows a triangle function in the time domain, meaning: $$x_c(t)=\left\{\begin{array}{rl}1-|t/a|,&|t|<|a|\\ ... 3answers 1k views ### Fourier transform of \left|\frac{\sin x}{x}\right| Is there a closed form (possibly, using known special functions) for the Fourier transform of the function f(x)=\left|\frac{\sin x}{x}\right|? \hspace{.7in} I tried to find one using ... 5answers 6k 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 ... 1answer 434 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 ... 4answers 4k 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 ... 1answer 13k views ### Prove of the Parseval's theorem for Discrete Fourier Transform (DFT) If x[k] and X[r]  are the pair of discrete time Fourier sequences, where x[k] is the discrete time sequence and X[r] is its corresponding DFT. Prove that the energy of the aperiodic sequence ... 1answer 861 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 ... ... 2answers 897 views ### Physical interpretation of L1 Norm and L2 Norm In signal analysis, students have no qualms about associating the L2 norm of a square integrable function f(t) as the energy associated with that signal. A good understanding of whether a function ... 1answer 515 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 ... 0answers 123 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)$$Here, the e_i are point light sources at locations r_i in the object and P is a point ... 3answers 17k views ### square wave matlab code I'm having some trouble generating a square wave in matlab via my equation. Just wondering if anyone has some insight on what I am missing here in my code? I was thinking I could easily generate a ... 2answers 72 views ### Help needed with the integral of an infinite series Can you please help me with the integral of this series? I came across it in a signal processing paper and haven't been able to figure out the solution myself.$$ ...
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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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### Derivative of a random variable w.r.t. a deterministic variable

I'm reading about time series and I thought of this procedure: can you differentiate a function containing a random variable. For example: $f(t) = a t + b + \epsilon$ where $\epsilon \sim N(0,1)$. ...
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### Fourier transform of a certain equality / discrete time Fourier transform of Dirac delta?

This comes from Stephane Mallat's Wavelet Tour text; however, I will phrase my question independently of it. I apologize that this is sort of long-winded. We have a function $f$ which satisfies the ...
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### Detecting periodicity in point processes

I have data from a periodic one dimensional point process representing the times of events which is also mixed in with lots of data that I regard as noise. The total number of points is of order one ...
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### 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 $\frac{1}{(z-a)^2}$
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### 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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### Help in understanding a coding technique based on inverse mapping of a dynamical system

Based on paper titled : Simultaneous Arithmetic Coding and Encryption Using Chaotic Maps by Kwok-Wo Wong et. al The Authors use a non-linear dynamical system for generating keys to be used in ...
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### Is the sum of all cross-correlation samples representative of target existence likelihood?

Answers to this question take the peak in the cross correlation as the measure to the likelihood of the trigger signal exist in the received signal - this is pretty much text book. My question is ...
Let's say we have a random variable $X$ with a certain probability density function $f_x(x)$. 1) How should I find out the PDF of the random variable $X^2$? Problem background: $X_1 = s_1 + W$, ...