Discrete Definition and 897 Threads

I'm reading the text Understanding Digital Signal Processing Second Edition and in the text they give the IDFT without any proof and so I tried to do a quick proof, but I have not been able do it here is my attempted steps: X(m)=\sum^{N-1}_{n=0}x(n)e^{-i2\pi mn/N} \\ Considering x(1)...

Homework Statement Two point particles separated by 0.4 m carry a total charge of 185 µC. (a) If the two particles repel each other with a force of 80 N, what are the charges on each of the two particles? Homework Equations F = k* (q1*q2)/(r^2) The Attempt at a Solution I tried...

Homework Statement find the domain and image of f such that f(x) = {(x,y) \in R \times R \vert x = \sqrt{y+3} and domain and image of g such that g = { (\alpha,\beta) \vert \alpha is a person, \beta is a person, \alpha is the father of \beta Homework Equations the domain and image...

Let A be a set. For every set B and total function f:A->B we define a relation R on A by R={(x,y) belonging to A*A:f(x)=f(y)} *belonging to - because i don't know how to make the symbole... Prove that f is one-to-one if and only if the equivalence classes of R are all singletones

"Sliding DFT" discrete Fourier transform... I was wondering if any of you had had experience with the sliding DFT algorithm. It is somewhat similar to the Goertzel algorithm. I am having some trouble understanding the mathematics of the algorithm, and I also cannot seem to identify a useful...

Homework Statement a.) F = {(1, a), (2, b), (3, a), (4, c)} G = {(b, 1), (a, 2), (c, 3)} i. Find F o G ii. Find G o F b.) A function F: N x N --> N is represented 2(m + n) + 1 for F(m, n) i. Is F one-to-one? ii. Is F onto? c.) Prove by Mathematical Induction...

Preface: This homework assignment was due long ago. At this point I am only trying to understand the problem (or really if the posted solution follows the problem) before my exam. I have no real indication that this problem (or even one like it) will be on my final, but I feel that my inability...

For each n \in \omega, let X_n be the set \{0, 1\}, and let \tau_n be the discrete topology on X_n. For each of the following subsets of \prod_{n \in \omega} X_n, say whether it is open or closed (or neither or both) in the product topology. (a) \{f \in \prod_{n \in \omega} X_n | f(10) = 0 \}...

Homework Statement use combinatorial methods to determine the smallest amount of money that using cents, nickels, dimes, or quarters, requires a) four coins b) five coins c) six coins d) seven coins e) eight coins Hint: Consider the ways to partition sets of those respective...

Homework Statement What is the 15th term of (X3 + Y)25? Homework Equations The Attempt at a Solution

Homework Statement What is the 15th term of (X3 + Y)25? Homework Equations The Attempt at a Solution

Homework Statement How many points in ΣN are fixed by σkN? Homework Equations σkN is the kth iteration of the shift map σN. The Attempt at a Solution I'm not sure where to start. I probably just need a hint.

Homework Statement Let G be a discrete group in which every element is orientation-preserving. Prove that the point group G' is a cyclic group of rotations and that there is a point p in the plane such that the set of group elements which fix p is isomorphic to G' The Attempt at a...

Homework Statement Prove that a discrete group G cosisting of rotations about the origin is cyclic and is generated by \rho_{\theta} where \theta is the smallest angle of rotation in G The Attempt at a Solution since G is by definition a discrete group we know that if \rho is a...

I've been thinking about one of the postulates about one particle quantum mechanics, it says that whenever we measure an energy value, we get one of those eigenvalues. Firstly, pretty much 99% of the stuffs I know in nonrelativistic QM applies in the realm of electromagnetism. I just don't...

Homework Statement Prove that for all integers a >= 1, a^n - 1 is divisible by a - 1 for all n >= 1. Homework Equations None. The Attempt at a Solution Proof - Let P(n): a^n - 1 is divisible by a - 1, then P(1): a^1 - 1 is divisible by a - 1 is TRUE since a^1 - 1 = a - 1, and...

Hi, My problem is very simple, I have a project in which I have to design a voltage regulator out of discrete BJTs, Zeners and resistors etc. the only limitation is that I cannot use an IC. I would prefer not using a zener because i would like to make the output variable through a voltage...

Homework Statement Consider the families of iterating functions Fλ(x) = λ(x3 - x). Fλ(x) undergoes a bifurcation at λ=1, about the fixed point x=0. Figure out what ilk of bifurcation is occurring for Fλ(x) and prove your assertion rigorously.Homework Equations My book says this about...

Homework Statement a 1= 2, a k+1, 2ak-1 Homework Equations What is the 5th term The Attempt at a Solution a1= 2 a2=2(2)-1= 3 a3=2(3)-1=5 a4=2(4)-1=7 a5=2(5)-1=9 5th term =9?

confused:Given the simple LTE (less then equal) relation on S= {1,2,3,4} defined by [less and equal ], we define a complex NTG (not grater then) relation on S x S by (w,x) NTG (y,z) if w[less and equal) y or x [less and equal z. (this or confusing me ) Show that NTG is (R) reflexive, but not...

:confused: Construct a formal proof of the theorem: If (p-> q), (neg [r] -> s), and (neg [q] V neg [s], then (p-> r). [refer to table of logical equivalences (p62) and the table of logical implication (p62)]The tables are in the textbook Kenneth Ross, 5th edition, Discrete Math's...

I'm going to mix a couple questions together instead of creating a new topic for each question. I hope you don't mind. I'm an electrical engineer(micro-electronics), so while I got the basics of QM in my studies I had to do most of my more 'in depth' learning on my own by reading books/ocwm...

Prove or disapprove that the product of two rational numbers is irrational How do you solve this? Thanks

page.130 Ex.20 Ex.20 Show that if A and B are sets, then (A\capB) \bigcup (A\capB) = A. how do u solve this? The Attempt at a Solution

I recently came across a page named "Gems of Discrete Probability" - http://www.cse.iitd.ernet.in/~sbaswana/Puzzles/Probability/exercises.html Being a mathematics enthusiast, I tried the first question. Being very rusty in probability, I failed to come up with a satisfying answer: the best I...

Ok, so after a little discussion with my discrete math teacher today, he sent me on a little "quest". Here is how it happened: The topic we were covering was set theory, and as I had been studying very basic combinatorics the night before, I noticed something about the powerset, namely...

Homework Statement Alright here it is: Theorem: if there exists an x belonging to reals such that (x^2)-x-2=(x^2)-4 then 1=2. Remark: note that there is such an x belonging to reals. Proof: 1) by hypothesis assume there exists an X belonging to reals such that (x^2)-x-2=(x^2)-4...

Homework Statement Suppose that a discrete-time signal x[n] is given by the formula x[n] = 10cos(0.2*PI*n - PI/7) and that it was obtained by sampling a continuous signal at a sampling rate of fs=1000 samples/second. Determine two different continuous-time signals x1(t) and x2(t)...

Can anybody help me find a paper? The name is "The discrete self-trapping equation", or "J.C. Eilbeck, P.S. Lomdahl, A.C. Scott, Physica D 16 (1985) 318." Thank you very much !

I know I have to write an equation to solve the problem down. But I really don't know how to use the given information. I did it by enumeration, but I don't get it how this will be shown by an algebriac argument. Please some one help me at least with an idea. If S = {1,2,3,4}, consider the...

Homework Statement I have to prove the following claim. Claim: For any positive integers m and n, m and n both greater than 1, if n|m and a≡b(mod m), then a≡b(mod n).Homework Equations n/aThe Attempt at a Solution so i first changed each equation (ex: a≡b(mod m)) to a=b+qm and a=b+qn I...

Dear all, I have an example taken from the book titled "Discrete Mathematics For Computer Science" by Kenneth Bogart. In the book, page 11, example 1.2-2, it says: Write down all the functions from the two element set {1,2} to the two element set {a,b}. I couldn't understand the...

OK this is the first assignment I have in this class and I can't figure out how to negate and simplify the logical structure of W <--> S (bi-conditional implication) I got this so far: ~[(W --> S) ^ (S --> W)] by Definition ~(W --> S) v ~(S --> W) by DeMorgan's Law ~(~W v S) v ~(~S v W)...

I've been reading that it is, there is a smallest volume of space, if this is so then there is also a smallest length. So what i was wondering is that if there is a smallest length than any length could be measures exactly, like the circumfrence of a circle and the diameter, so if...

I'm currently studying this topic at school... I'm a 12th grader. So I just want to ask, does anyone know how to comprehend the topic in an easier way? or probably anyone know a guide somewhere in the net? I am just confused at binomial distribution, and poisson. I understand a little bit...

Hi, Im after some advice on what materials to use in order to gain a fairly 'decent' understanding of the following topics: Elementary Set Theory, Subsets, Unions, Intersections, Complements. Logic, Functions, Mappings, Injectivity. Subjectivity. Bijectivity, Permutations, Proof techniques...

Hi I need some help with the following problem: 1. Find all functions f: Z+ -> Z+ such that for each n Є Z+ we have f(n) > 1 and f(n + 3)f(n + 2) = f(n + 1) + f(n) + 18 2. I've been reading everywhere and I can't seem to find anything like this. I was wondering if anybody knew where to start 3...

Homework Statement Compute the unit-pulse response h[n] for n= 0,1,2,3 for the following discrete time system: y[n+2] + 1/2y[n+1] + 1/4y[n] = x[n=1] - x[n] Homework Equations I think i am supposed to replace the functions of x with delta functions, which are zero at all except n=0...

i have an exam in a few days and am certain a question like this is going to pop up but i have no solutions to this question and no idea how to work it out the question is as follows Find the equations of the line L1 through the point with position vector (4,2,1) and parallel to the vector...

starting with the iterated map derived in the notes for calculating rootp(p>0) Xn+1=1/2(Xn+(p)/(Xn) calculate root 7 starting with x0=1 so ok starting with that i get x0=1 x1=4 and then something strange happens the sub in looks like this X2=1/2(4+2/4)=9/4 i was under the...

I want to choose either one of these as a second major. Problem is, I'm undecided. My current major is pure math; I want another major so that I have a escape door to the corporate job market in case I decide to stir away from academia. Which one of these two disciplines would benefit me the most?

Hi, there! That's probably the most relevant forum thread where I can consult pros about my problem. Well, I'm a visual programmer and quite far of Spectra Physics to what my issue's dramatically related to. Specifically, I need to implement in C# the frequency-domain signal filtration (with a...

From the people I've spoken to, the general consensus is to take the class in separate semesters if possible. What do you guys recommend? I have 3 semesters left before I finish my AA and I want to get as many math courses in as possible... Thanks.

Hey all, I just started my Junior year at Florida International University this summer and decided to start light by taking Programming I and Discrete Math to kick things off with and get used to the university. Programming class is going fine, but Discrete Math class is really giving me a...

Does anyone know of any analytical expression for the upper bound on the Kullback–Leibler divergence for a discrete random variable? What I am looking for is the bound expressed as 0 <= S_KL <= f(k) Where k is the number of distinguishable outcomes. Ultimately I am also looking for...

please help me in this problem: two discrete signals x[nT]={0 0 1 0 0 2 2 2 2} h[nT]=[-1 2 3 3 2 1] find there convolution if the impulse response doesn't start from zero ,use the table or the matrix

If I use the following code in Mathematica f1[t_] := Cos[w t + d1]; f2[t_] := Cos[w t + d2]; data1 = Table[f1[t], {t,1,10000}]; data2 = Table[f2[t], {t,1,10000}]; ft1 = Fourier[data1]; ft2 = Fourier[data2]; To take the Fourier transform of two data sets, how can I use the resulting data...

Homework Statement The problem is as shown in the attatchment. Homework Equations The relevant equations are also given in the attatchment. The Attempt at a Solution My problem is how to adapt the given formula in order to find the sum of the function k(40-r) Do i use the...

So, I am interested in majoring in math at Georgia Tech starting this summer, and was wondering what the difference between discrete and applied mathematics is. Any information is greatly appreciated. Also, what does anyone think about double majoring in math and physics?

I need advice with my "Discrete Structures" class Hi everyone, I'm a sophomore undergraduate student at the Polytechnic University Of Puerto Rico, currently majoring in "Computer Engineering", for the record this university works by trimesters. I'm currently getting a bit frustrated with my...