Discrete Definition and 829 Threads

Homework Statement The question is, simplify this equation: (A ∪ B ∪ C) ∩ ((A ∩ B) ∪ C) The correct answer is (A ∩ B) ∪ C Homework Equations We have been given the commulative, associative, distributive, identity, complement and idempotent laws and DeMorgan's laws, and I researched the...

Okay I have a question involving calculating the FFT of a signal from a sensor. I have simulated many different scenarios in MATLAB of various noise characteristics involving the signal. I want to take the FFT of a noisy signal. As long as my expected input signal has a higher amplitude than...

is the set of symbols that make up strings denoted by the symbol Σ or Σ* , also what is this difference?

Hey guys here is the question i'd appreciate if you could help me with it: it says that no one dies in planet X,some spies of planet Y were captured by planet X's police.They are so professional that won't say anything to police so their inspection will go on forever and their inspection has no...

Homework Statement Prove that the following four statements are equivalent: (a) n2 is odd. (b) 1 − n is even. (c) n2 is odd. (d) n2 + 1 is even. Homework Equations None really, just the use of different proofs ( indirect, etc...) The Attempt at a Solution I'm having trouble with this one...

Dear Physics Forum mentors, I am an undergraduate sophomore with double majors in mathematics and microbiology. I wrote this email to seek your recommendation on the discrete mathematics textbook that is in-depth, theoretical, proof-based, and also comprehensive. I am currently taking a...

Homework Statement We have a set of values: f(n)=f(0,1,2)=(1,3,2) so f(0)=1, f(1)=3, f(2)=2, where n=0,1,2the number of values N=3 The question is to calculate the FFT of this signal, the Fourier spectrum the power spectrum and phase spectrum. I'm not sure concerning FFT. And also about...

For a definite particle,the decay mode is determinant,finite kind,which embody the characteristic of quantum mechanics. But for a specific mode of a definite particle's decay,the decay spectrum,ie,energy of products,continuous,or discrete? Decay is a process which has unique initial...

Before I make a fool of myself let me just say I just had my first class today and the book/ teacher aren't helpful in my question. And I'm not even sure I'm in the right section, this is just my major 1. Homework Statement "If 1+1=3 then 2+2=4" Homework Equations We just covered conditional...

I have seen two characterizations of the problem in measuring a discrete variable of a state ψ exactly with each of two non-commuting Hermitian operators A and B: (1) that the product of the standard deviations ( = √(<ψ|A2|ψ>-<ψ|A|ψ>2), & ditto for B) ≥ 1 (2) that one cannot simultaneously...

Homework Statement A traffic signal operates in the following cyclic regime: amber (A) light for 5 seconds, then red (R) for 30 seconds, then amber again for 5 seconds, then green (G) for 40 seconds (thus making a cycle ARAG), and then in the cyclic manner, i.e. ARAGARAG... . Let us assume...

Why is the summation for the discrete Fourier series from 0 to N-1 (where N is the fundamental period of the signal) wheras it goes from minus infiniti to infiniti for continuous Fourier series...Thank you

For the discrete complex sinusoid with period N, how many distnict sinusoids are there? And why?

Hi everyone, I haven't been successful in Discrete Math this semester. I have finished all of the calculus I-III series and I did very well. I want to know if anyone can give me some tips on how to study for my final coming up in a few days. Now, I understand that is a vague question but I am...

Hey guys, I was reading Kenneth's Discrete Mathematics and I came across this definition in the function chapter: Let f be a function from A to B and let S be a subset of A.The image of S under the function f is the subset of B that consists of the images of the elements of S.We denote...

Prove the following theorem: Theorem For a prime number p and integer i, if 0 < i < p then p!/[(p− i)! * i] * 1/p Not sure how to go about this. I wanted to do a direct proof and this is what I've got so far. let i = p-n then p!/[(p-n)!*(p-n)] but that doesn't exactly prove much.

Homework Statement 2. Homework Equations [/B] So the sample mean is 2. the sample variance would be [[(3-1+1)-1]/12]/36 = 8/432. The Attempt at a Solution Is it, P[ (2.1-2)/sqrt(8/432) < z < (2.5-2)/sqrt(8/432)] = 0.232574. The book answer is 0.2312. I just want to be sure.

Homework Statement Show that, ∪n=2∞[0,1 - 1/n] = [0,1) Homework EquationsThe Attempt at a Solution

Show that A - (B intersection C) = (A - B) union (A - C) I went about this completely around on a test but here is what I have Right Hand Side = ( A - B) union ( A - C) = (A intersection B) union (A intersection C) = A - (B intersection C) ? Easy problem but confused..thanks

Hi there, I am reading a material on the application of Fourier transformation in physics. One application is to transform the position-dependent function to k-dependent function, i.e.## F(k) = FFT[f(x)]## We know that the in physics, the wavenumber could be written in momentum as...

Homework Statement Homework EquationsThe Attempt at a Solution I'd like to see if I have the right line of thinking in my solutions: a. The sampling frequency should be such that no aliasing or folding occurs, so it should be twice the frequency of the original signal. $$x(t) = -17...

Homework Statement Two test charges are located in the x–y plane. If q1 = -3.50 nC and is located at x = 0.00 m, y = 0.680 m and the second test charge has magnitude of q2 = 3.60 nC and is located at x = 1.00 m, y = 0.650 m, calculate the x and y components, Ex and Ey, of the electric field, ...

I am a math major currently in a community college reputed for having an outstanding math department, lucky me :D. I am taking Calculus 2 this semester. Next semester I'll be taking Calculus 3 with linear algebra or discrete math. Can I take all three at the same time or would it be an overkill...

The discrete random variable K has the following PMF: p(k) = { 1/6 if k=0 2/6 if k=1 3/6 if k=2 0 otherwise } Let Y = 1/(1+K), find the PMF of Y My attempt: So, I am really confused about what this is asking. I took...

Homework Statement Prove that in the 1D case all states corresponding to the discrete spectrum are non-degenerate. Homework Equations \hat{H}\psi_n=E_n\psi_n The Attempt at a Solution Okay so, what I am stuck on here is that the question is quite broad. I can think of specific...

Homework Statement Let ##X_k## be iid uniform discrete on ##\{0,...,9\}##. Find the distribution of ##\sum\limits_{k=1}^{\infty} \frac{X_k}{10^k}##Homework Equations The Attempt at a Solution I've tried a lot of things, I've tried decomposing ##X_k## into 10 bernoulli trials, I've tried using...

Homework Statement I need to write \begin{align*} N_{k+1} = \frac{\lambda N_{k} }{1+aN_{k} } \end{align*} in the form \begin{align*} N_{k+1} = N_{k} + R(N_{k})N_{k} \end{align*} Homework Equations As above The Attempt at a Solution I know that \begin{align*} N_{k+1} = N_{k} +...

Hi bros, so I feel like I am very close, but cannot find out how to go further. Q.1 Compute the DTFT of the following signals, either directly or using its properties (below a is a fixed constant |a| < 1): for $x_n = a^n \cos(\lambda_0 n)u_n$ where $\lambda_0 \in (0, \pi)$ and $u_n$ is the...

Homework Statement An electric circuit has 5 components. It is known that one of the componenets is faulty. To detremine which one is faulty, all 5 componenets are tested one by one until the faulty component is found, The random variable X represents the number of test required to determine...

Hi, New to this topic, and need some help. My task is to find the convolution between $ y= x ∗ h$ where $x = u_n - u_{n-N}$ and $h_n = u_n - u_{n-M}$ and $M\ge N$ are positive integers My understanding is that in general, $ y= x ∗ h = \sum\limits_{m=-\infty}^\infty x_m h_{n-m} $ so for my...

Homework Statement Here's the question: Given X is a discrete random variable. E(X-2) = 1/3 , VAR(X-2) = 20/9 . Detrmine value of E(X^2) the ans is 23/3 . but i ended up getting 3 . why i am wrong? Homework Equations The Attempt at a Solution

When I sample a certain digital signal with increasing sampling frequency, the fast Fourier transform of the sampled signal becomes finer and finer. (the image follows) Previously I thought higher sampling frequency makes the sampled signal more similar to the original one, so the Fourier...

Let's say I'm applying electrical currents to a certain part of a human test subject and measuring certain deflections in his heart readings during this period. Before I increase the electrical currents, which could be dangerous, I'm interested to see if the changes in electrical currents are...

Hi All, I have a problem I've been thinking about for a while, but I haven't come up with a really satisfactory solution: I want to do a discrete Fourier transform on data that has been sampled at 2 different sampling frequencies. I've attached a picture of what my data will look like...

How can a discrete time signal can be a vector? i cannot grasp the idea. i know MATLAB uses matrices which denote vectors, but how does a discrete time varying amplitudes be a vector?

Observation of the growth of some beetle population suggests that discrete logistic equation would be more appropriate since these animals have distinct breeding season. discrete logistic equation: Xn+1=Xn+rXn(1-(X2/K)) the result of this equation accounts for population only season to...

Suppose we have a function ##f:\mathbb{N}\times\mathbb{N}\to\mathbb{R}_+## that isincreasing: ##f(x+e_i)\geq f(x)## for any ##x\in\mathbb{N}^2## and ##i\in\{1,2\}##;convex: ##f(x+2e_i)-f(x+e_i)\geq f(x+e_i)-f(x)## for any ##x\in\mathbb{N}^2## and ##i\in\{1,2\}##.How could one show that a...

Hello, I am trying to develop a software control algorithm to compensate for oscillator imperfections/frequency drift. I have a NTP server which I can get a pretty good estimation (@1Hz) of the "true" time and compare it to my system's time. I can differentiate the offset-error to calculate...

Homework Statement The probabilities of blood types O, A, B and AB are 0.46, 0.39, 0.12, 0.03 respectively. If a clinic is seeking either type O or B from six random individuals, what is the probability that at least 2 people have the desired blood type? Homework Equations The...

Hi all, Now naturally after completing a physics degree I am very familiar with the form and function of the Fourier Transform (FT) but never have grasped it quite conceptually. I understand that given a function f(x) I can express every functional value as a linear combination of complex...

I am simulating an ODE where the differential function is a function of sampled data points and are having trouble obtaining data in between sampled points (for the step computations of RK4). The first thing that I tried was to linearly interpolate the data, but that introduced large...

In a Hilbert-space whose dimensionality is either finite or countably infinite, we have the discrete resolution of identity \sum_n |n\rangle \langle n| = 1 In many cases, for example to obtain the wavefunctions of the discrete states, one employs the continuous form of the resolution...

A problem i made up for some of my friends who need help with discrete distributions tables. Can you do it? Dice Generator Part I: 1. Construct a discrete probability distribution table for a fair six-sided dice. (Round according to example) 2. Calculate the mean, variance, and standard...

I'm trying to do some extra course work to prepare for my final next week but I'm having a lot of trouble with the book problems. They talk about a lot of things we weren't taught. Can someone help me out here? Prove: n\niZ, n= a multiple of gcd(a,b) ⇔ n is a linear combination of a and b This...

Hello, I have a question regarding discrete energy levels of atoms. If electrons must inhabit certain energy levels, when they are excited up to a higher energy level, do they instantaneously jump to that level, or do they exist for some short time 'in between'? Furthermore, if the...

Hi everybody, I am interested to do some DEM(Discrete Element Method) simulation for my miniproject. So far I have seen that the most available opensource codes require large computation resource for parallel calculation. I don't have access to such facility and also my initial problem...

Hi guys, so I'm trying to create this thing that gets accelerometer values and integrate those values at about 25 samples a second. From what I understand if I integrate the values, that means each second I have 25 values I want to integrate. I read this research paper where someone used the...

I have a 3 rad/s sine wave that I am sampling every 2 seconds. The slow sampling has created an alias of -0.14 rad/s. I have plotted this over the top of the original continuous time signal, please see attachment. My problem is that I only want to plot the first period of the discrete signal...

How do you calculate the intersection of discrete data points and an equation? Actually I have two ways already, one is to just take the equation of the discrete points then solve it using a root-finding technique. The other would be substituting the x values of the discretized points to the...

I am currently enrolled in Calculus 1. Will be taking Calculus 2 in summer and Calculus 3 in Fall. I have already registered for these courses. One of the Math electives I have a choice in Fall Semester is either Discrete Math or Linear Algebra. Any suggestions would be greatly appreciated...