Because pure sinusoidal signal only contains impulses, I was wondering what happens to the fourier transform of the sample output from the sinusoidal input of $26$kHz if the sampling is done with sample frequency of $44.1$kHz.
2026-03-27 10:12:49.1774606369
What happens to fourier transform of the sampled output of pure sinusoidal input of 26kHz if sampled with 44.1kHz sample frequency?
51 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
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 SIGNAL-PROCESSING
- What is the result of $x(at) * δ(t-k)$
- How is $\int_{-T_0/2}^{+T_0/2} \delta(t) \cos(n\omega_0 t)dt=1$ and $\int_{-T_0/2}^{+T_0/2} \delta(t) \sin(n\omega_0 t)=0$?
- 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?
- Fast moving object, how to remove noise from observations?
- Computing convolution using the Fourier transform
- Find Fourier Transform of $\cos^2(ωt)x(t)$
- Finding closed expression for the output of an LTI system
- Is there an intuitive way to see that $\mathbb{E}[X|Y]$ is the least squares estimator of $X$ given $Y$?
Related Questions in SAMPLING
- Defintion Ideally sampled image
- What is expected value of a sample mean?
- Why does k-fold cross validation generate an MSE estimator that has higher bias, but lower variance then leave-one-out cross-validation?
- Sampling Question
- Limit of chi square distribution.
- Sampling Distribution of Difference of Normal Random Variables
- Sampling Distribution and Chi Squared Random Variables
- Variance of $S^2$ taken from Normal Distribution
- Sample Variance Definition Disparity
- [data generating process]-[sampling from an infinite population]-[i.i.d.]: some clarifications
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?
Because the sampling rate is less than two samples per cycle, the input will be aliased down to $26-44.1=-18.1$ kHz. If the wave is a sine wave, the minus sign just inverts the signal. If $t$ is a multiple of $1/(44.1$ kHz), $\sin (2\pi t 26$ kHz$)=\sin (-2\pi t 18.1$ kHz). If you have a large duration, you will see (almost all the) energy in frequencies near to $-18.1$ kHz. If you don't have an integral number of cycles, the discontinuity between the start and end of the interval will make other artifacts.