I am a senior in high school and am currently trying to conduct an exploration on Fourier Analysis, specifically using the Discrete Fourier Transform to analyze a chord played on my piano. Basically, I'd play a chord of 3 notes, deduce the different frequencies of the sound wave, and estimate the chord played. According to the formula below, I have recorded the sound wave of Amplitude-time domain however I do not understand what is meant by the "index of data points" and how to find it from this graph. Is there any way someone could help with that as I am a bit unfamiliar to this. Thanks. This is the DFT formula and the index of data points fj
2026-02-23 07:54:10.1771833250
FOURIER TRANSFORM: How can I find the index of data points
18 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
Related Questions in DISCRETE-MATHEMATICS
- What is (mathematically) minimal computer architecture to run any software
- What's $P(A_1\cap A_2\cap A_3\cap A_4) $?
- The function $f(x)=$ ${b^mx^m}\over(1-bx)^{m+1}$ is a generating function of the sequence $\{a_n\}$. Find the coefficient of $x^n$
- Given is $2$ dimensional random variable $(X,Y)$ with table. Determine the correlation between $X$ and $Y$
- Given a function, prove that it's injective
- Surjective function proof
- How to find image of a function
- Find the truth value of... empty set?
- Solving discrete recursion equations with min in the equation
- Determine the marginal distributions of $(T_1, T_2)$
Related Questions in FOURIER-ANALYSIS
- An estimate in the introduction of the Hilbert transform in Grafakos's Classical Fourier Analysis
- Verifying that translation by $h$ in time is the same as modulating by $-h$ in frequency (Fourier Analysis)
- How is $\int_{-T_0/2}^{+T_0/2} \delta(t) \cos(n\omega_0 t)dt=1$ and $\int_{-T_0/2}^{+T_0/2} \delta(t) \sin(n\omega_0 t)=0$?
- Understanding Book Proof that $[-2 \pi i x f(x)]^{\wedge}(\xi) = {d \over d\xi} \widehat{f}(\xi)$
- Proving the sharper form of the Lebesgue Differentiation Theorem
- Exercise $10$ of Chapter $4$ in Fourier Analysis by Stein & Shakarchi
- Show that a periodic function $f(t)$ with period $T$ can be written as $ f(t) = f_T (t) \star \frac{1}{T} \text{comb}\bigg(\frac{t}{T}\bigg) $
- Taking the Discrete Inverse Fourier Transform of a Continuous Forward Transform
- Is $x(t) = \sin(3t) + \cos\left({2\over3}t\right) + \cos(\pi t)$ periodic?
- Translation of the work of Gauss where the fast Fourier transform algorithm first appeared
Related Questions in FAST-FOURIER-TRANSFORM
- Translation of the work of Gauss where the fast Fourier transform algorithm first appeared
- Arcsin of a number greater than one
- Unable to solve nonlinear equation using scipy.optimize.fsolve
- Fourier transform on formal series
- Optimization of a Fast Fourier Transformation-based correlation function?
- Example of 1-D Poisson Equation in physics field, engineering field, or others in daily life
- Fourier Curve Fitting
- The best textbook on Fourier Transformation for beginners
- What is the intuition of FFT for polynomial multiplication?
- Which part of formula is FFT changing the basis?
Related Questions in MUSIC-THEORY
- Is there a name for this exponential analog to modular arithmetic? (octave equivalency)
- Musical and combinatorial proof
- Algorithm for converting complex sine wave to constituent simple sine waves
- Find three points on a scale using golden ratio
- What is the solution of normalized harmonic series based on $4/3$ between one and two?
- Is there an arithmetic mean limit on the symmetrical items of the harmonic series?
- Fourier Transform on Musical Notes
- (Music) List of all possible "types of set" of 12 musical notes
- How many ways can you generate 12 who's pairwise modulus difference is also a unique rank?
- The Complexity of "The Baby Shark Song".
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?