Discrete Definition and 829 Threads

1. Given: The DTFT over the interval |ω|≤\pi, X\left ( e^{jω}\right )= cos\left ( \frac{ω}{2}\right ) Find: x(n) 2. Necessary Equations: IDTFT synthesis equation: x(n)=\frac{1}{2\pi}\int\limits_{-\pi}^{\pi}X\left ( e^{jω} \right ) e^{j\omega n}d\omega Euler's Identity...

Hello all, I've breadboarded a simple astable multivibrator to generate 38kHz (identical to http://upload.wikimedia.org/wikipedia/commons/6/6a/Transistor_Multivibrator.svg) using 2N3904s. Upon power up, it's a solid 38Khz. After 60 seconds, it's drifted up to ~44Khz... and stabilizes to...

Homework Statement Hi Everyone, I am trying to show why the given sum is zero. I am pretty sure it is zero. Homework Equations sin[8*\pi*n/5]+sin[12*\pi*n/5] n is an integer. The Attempt at a Solution n----sin[8*\pi*n/5]----sin[12*\pi*n/5] 0 ----...

Hi all I need some assistance 1. Homework Statement with the attempt How many 5-digit briefcase combinations contain 1. Two pairs of distinct digits and 1 other distinct digit. (e.g 12215) I wasn't sure on which approach was correct. 10 * 9 * 8 (because there are three distinct...

All analitic function can be express how: f(x) = \frac{1}{0!} \frac{d^0f}{dx^0}(x_0) (x - x_0)^0 + \frac{1}{1!} \frac{d^1 f}{dx^1}(x_0) (x - x_0)^1 + \frac{1}{2!} \frac{d^2f}{dx^2}(x_0) (x - x_0)^2 + \frac{1}{3!} \frac{d^3f}{dx^3}(x_0) (x - x_0)^3 + ... that is the taylor series of the function...

I am a math major and I need to take Methods of Discrete Mathematics. What is methods of discrete mathematics? Should I take it after My calculus series( including linear/ diff. equations)? Is it easy enough to take with Calculus 2? Thanks

Hello, I have a question I am trying to figure out how it works and I am so confused I need a break down of what is exactly going on with this problem the Question. "Concern three persons who each randomly choose a locker among 12 consecutive lockers" What is the probability that no two...

Homework Statement \sum_{x} x^k for k ∈ Q Homework Equations \sum_{x} x=\frac{1}{2}x^2-\frac{1}{2}x\sum_{x} x^2=\frac{1}{3}x^3-\frac{1}{2}x^2+\frac{1}{6}x\sum_{x} x^{-1}=\Psi (x) The Attempt at a Solution I don't know. There isn't way to compute the antiderivative of any function and I...

Homework Statement Suppose A={ø,1,2,{1,2},{3}}. Determine if each statement is true or false. Give a brief justification for your answers. (I finished the majority of them except for the last two) g) A-ø=A h) A-ø={1,2,{1,2},{3}} Homework Equations The definition of difference between...

Does anything connect the discrete wave functions? I thought they were suppose to be connected.

How to have better discrete math "insight" Greetings: I came a cross a textbook example in a discrete math book that I have been reading on my own, and I thought this example in the book was a good example of what I want to be good at: Given integers from 0-9 arranged in a circle, is...

Hello I am trying to solve this problem: A coin is given with probability 1/3 for head (H) and 2/3 for tail (T). The coin is being drawn N times, where N is a Poisson random variable with E(N)=1. The drawing of the coin and N are independent. Let X be the number of heads (H) in the N draws...

Why parity is discrete transformation? ##Px=-x## ##P\psi(x)=\psi(-x)## when ##x## is continual variable. Could you explain me difference between discrete and continual transformation?

I'm trying to prove that the discrete form of the Fourier transform is a unitary transformation So I used the equation for the discrete Fourier transform: ##y_k=\frac{1}{\sqrt{N}}\sum^{N-1}_{j=0}{x_je^{i2\pi\frac{jk}{N}}}## and I put the Fourier transform into a N-1 by N-1 matrix form...

Homework Statement is it possible to have a topological space that is neither the indiscrete nor the discrete, and very set in the topology is clopen? Homework Equations The Attempt at a Solution let ##X## = {(0,1),(2,3)} with the ordinary topology on R. (0,1) is open, but...

I just want to make sure I understand the normal modes of a vibrating system of particles with discrete spacing. I have tried to drawn what I understand as the lowest and highest frequency mode of the standing waves. Is the drawing correct? Edit: actually I have drawn the maximum frequency where...

Hello! I was told, that there are no mainstream physics theories, in which time is discrete. My question is this: At any present or any given future scenario, there will always exist the smallest amount of time, that a machine is able to measure. How come this variable, is not a main...

Homework Statement There are a set number of marbles in a bag; the marbles consist of two colors. We are given the mean number of marbles of color 1 in the bag, as well as color 1's standard deviation. We are then asked to find the mean and standard deviation of color 2.Homework Equations How...

If two fair dice are rolled 10 times, what is the probability of at least one 6 (on either die) in exactly five of these 10 rolls? So this problem is hard to wrap my head around. I'm probably wrong on many counts, here's what I'm doing: Two fair dice are rolled 10 times but this question only...

Hi guys, I'm trying to solve the S.E. For a potential that's time dependent but the time variable is not continuous. Essentially the potential is a finite square well and it shifts over time but not continuously. I.e. At time 0<t<t' it's a finite square well centered about some x' At...

[FONT=arial]Definition: A subset $D$ of $\mathbb R$ is said to be discrete if for every $x\in D$ there exists $\epsilon>0$ such that $(x-\epsilon,x+\epsilon)\cap D=\{x\}$. Question: Does there exist a discrete subset $D$ of $\mathbb R$ such that the set of limit points of $D$ is an uncountable...

Corollary from book: if d= gcd(a,b), then there exists integers x and y such that ax + by = d. This is not an obvious statement to me. Are there any direct proofs to prove this statement? The book proves this by induction. My proof: Suppose d = gcd(a,b) and a and b are positive integers. a...

Hello. I am reading an introduction to induction example, and I am having the hardest time trying to determine what exactly happened in the proof. Can somebody please help? How can ##3^{k-1}## + ##3^{k-2}## + ##3^{k-3}## all of a sudden become ##3^{k-1}##+##3^{k-1}##+##3^{k-1}## and how can be...

Quantum Phys Homework: I am given a function: $$f(x)=\frac{1}{10}(10-x)^2\,;\,0\leq{x}\leq{10}$$ and $$f(x)=0$$ for all other \(x\). I need to find the average value of \(x\) where $$\bar{x}=\frac{\int_{-\infty}^{\infty}x\,f(x)\,dx}{\int_{-\infty}^{\infty}f(x)\,dx}$$ I am not really even sure...

Homework Statement Consider a discrete time birth and death process in which the maximal population size is N = 6. Birth rates and death rates are directly proportional to the current size Xt of the population at time t (t = 0; 1; 2; : : :). If the maximal population size is reached, no more...

Stuck on the induction step,please help

1. The problem statement, all variables and givenknown data We have a system of three atoms arranged in a circular arrangements. They each have a valence electron that can tunnel to the nearest neighbor. For a tunneling rate -A/\hbar we have the Hamiltonian (shifted by an energy E_a on the...

How would I go about solving this? We are starting to learn about venn diagrams so would creating a venn diagram be helpful? This is what I tried so far, I created a set C consisting of all people who have taken calculus and a set D consisting of all people who have taken discrete math...

Homework Statement . Prove that a metric space X is discrete if and only if every function from X to an arbitrary metric space is continuous. The attempt at a solution. I didn't have problems to prove the implication discrete metric implies continuity. Let f:(X,δ)→(Y,d) where (Y,d) is...

The N real numbers x0, ..., xN-1 are transformed into the N real numbers X0, ..., XN-1 according to one of the formula by DCT. I would ask what is the benefit and why should we do that?

Homework Statement Using the rules of inference, prove that if ∀x(P(x) ∨ Q(x)) and ∀x((￢P(x) ∧ Q(x)) → R(x)) are true, then ∀x(￢R(x) → P(x)) is true as well. Homework Equations The Attempt at a Solution The problem arises step 5. I feel this is correct but the...

To give you a sense of strong induction and the relationship between mathematical induction and recursion (next session), let's do the pile splitting problem: Take a bunch of beads, rocks, coins, or any kind of chips. Ten is a good number. Split the pile into 2 smaller piles and multiply their...

I took f(t) = SIN(10*t) +SIN(5*t) and got this f(0) = 0 f(1) = -1.5 f(2) = 0.4 f(3) = -0.3 now I tried to do the DFT Fs = 4Hz N = 4 samples 3 f[r] = Ʃ x[k]ε^(-j(2πkr/4) k=0 f[r] = 0 -1.5ε^(-j(2πr/4) + 0.4ε^(-j(2π(2)r/4) -0.3ε^(-j(2π(3)r/4) f[0] = 0 - 1.5 +...

h is a constant in Planck's equation but I have not seen anything written saying that the frequency cannot be arbitrarily small, thus making E arbitrarily small. Is it that v is only allowed to be integral (after all, when we're measuring a frequency we're essentially counting how many times...

I have these problems I need help with. Can anyone take a look at them? https://www.dropbox.com/s/vq8rk6z5ea5gpwd/Problems.docx

Having a hard time with this problem. Can anyone guide me in the correct direction? Random graphs are a fascinating subject of applied and theoretical research. These can be generated with a fixed vertex set V and edges added to the edge set E based on some probability model, such as a coin...

Use a truth table to determine that "division into cases" rule of inference is valid.

How many comparisons are performed to find 13 in the following list by using Binary Search? 7, 12, 5, 22, 13, 32 Is it true that there are 10 comparisons performed to find 13 in the following list by using Binary Search? If this isn't right, then can somebody please help explain this to me?

How many vcomparisons did you actually need?

I have just started working with discrete time signals, more specifically various system properties. I am wondering if their is a discrete time system that is homogeneous but not additive? This is basically testing the linearity of a signal with the additive and homogeneous criteria.

Link to theorem: http://en.wikipedia.org/wiki/Law_of_the_unconscious_statistician Suppose Y is a discrete random variable related to X, a continuous random variable by some function r (so Y = r(X) ). Let A be the following set: A_y = {x ∈ R ; r(x) = y}. Since Y is discrete, f_Y (y) = P(Y = y)...

Consider a discrete set of ##k## points. First, is it a manifold? I know that a manifold is a topological space that contains a neighborhood homeomorphic to Euclidean space for each point. Can we just consider each point's neighborhood to be a set containing only that point? Second, would the...

Hello everyone: I have some question using the FFT in MATLAB for data interpolating. I don't know what the relation between the normal Fourier series and the real, image number. For example, given a set of measurement data, I can use the curve fitting toolbox to fit a curve. The general...

Testing for chaos in data I have data for 3 variables ,each with respect to the discrete time values. How do I check for the existence of chaos for this discrete 3D system?(I don't have the analytic eqs.,just the data.) MY IDEAS ON CHECKING FOR CHAOS FROM DATA:(which of these are feasible...

Homework Statement Hi, this is not a homework question per se, but something I'm wondering. Let C be a circulant n x n matrix, let x, b, be vectors such that C x = b. We would like to find a solution x. One way is to use the DFT: According to section 5, In Linear Equations, in the wikipedia...

Hi all, I'm a complete novice when it comes to describing images in frequency space and i understand that it is a way of representing images as being composed of a series of sinusoids. So a horizontal striped pattern with a single spatial frequency would have a magnitude image in frequency...

Hi, I'm interested in building a breadboard version of the simplest comparator using transistors and resistors. Ultimately I'd like to understand the LM393 but looking at the datasheet schematic, it seems quite complicated. I was hoping there was a simpler comparator I could mimic to start out...

Wikipedia says it deals with distinct objects and is differentiated from continuous math, which has objects that "vary smoothly." For a layman, can someone explain what this means? And is all math discrete or continuous? No other options?

Hi, Homework Statement How may I find to what number Ʃ(m=1 to ∞) m/2m-1 converges? Further, suppose I know it converges to 4, why would then E(Y), given that P(Y) = 1/2m-1, be equal to 2 (thus asserted the answer) and not 4? Homework Equations The Attempt at a Solution I am...

Homework Statement Hi, for a project for school, I need to implement the Discrete Haar Wavelet Transform to compress an audio signal. This would be fine and dandy, but I do not really understand how to use the the DHWT. Could anyone direct me towards some resources that would be very helpful...