• Study Resource
  • Explore
    • Arts & Humanities
    • Business
    • Engineering & Technology
    • Foreign Language
    • History
    • Math
    • Science
    • Social Science

    Top subcategories

    • Advanced Math
    • Algebra
    • Basic Math
    • Calculus
    • Geometry
    • Linear Algebra
    • Pre-Algebra
    • Pre-Calculus
    • Statistics And Probability
    • Trigonometry
    • other →

    Top subcategories

    • Astronomy
    • Astrophysics
    • Biology
    • Chemistry
    • Earth Science
    • Environmental Science
    • Health Science
    • Physics
    • other →

    Top subcategories

    • Anthropology
    • Law
    • Political Science
    • Psychology
    • Sociology
    • other →

    Top subcategories

    • Accounting
    • Economics
    • Finance
    • Management
    • other →

    Top subcategories

    • Aerospace Engineering
    • Bioengineering
    • Chemical Engineering
    • Civil Engineering
    • Computer Science
    • Electrical Engineering
    • Industrial Engineering
    • Mechanical Engineering
    • Web Design
    • other →

    Top subcategories

    • Architecture
    • Communications
    • English
    • Gender Studies
    • Music
    • Performing Arts
    • Philosophy
    • Religious Studies
    • Writing
    • other →

    Top subcategories

    • Ancient History
    • European History
    • US History
    • World History
    • other →

    Top subcategories

    • Croatian
    • Czech
    • Finnish
    • Greek
    • Hindi
    • Japanese
    • Korean
    • Persian
    • Swedish
    • Turkish
    • other →
 
Profile Documents Logout
Upload
THE DEVELOPMENT OF THE PRINCIPAL GENUS
THE DEVELOPMENT OF THE PRINCIPAL GENUS

NUMBER THEORY
NUMBER THEORY

Lecture Notes for Analysis II MA131 with revisions by January 8, 2013
Lecture Notes for Analysis II MA131 with revisions by January 8, 2013

Lectures on Integer Partitions - Penn Math
Lectures on Integer Partitions - Penn Math

Full text
Full text

Finite and Infinite Sets
Finite and Infinite Sets

Linear independence of the digamma function and a variant of a conjecture of Rohrlich
Linear independence of the digamma function and a variant of a conjecture of Rohrlich

Full text
Full text

Nonnegative k-sums, fractional covers, and probability of small
Nonnegative k-sums, fractional covers, and probability of small

THE FRACTIONAL PARTS OF THE BERNOULLI NUMBERS BY
THE FRACTIONAL PARTS OF THE BERNOULLI NUMBERS BY

Midpoints and Exact Points of Some Algebraic
Midpoints and Exact Points of Some Algebraic

Section 4 Notes - University of Nebraska–Lincoln
Section 4 Notes - University of Nebraska–Lincoln

On the proportion of numbers coprime to a given integer
On the proportion of numbers coprime to a given integer

fermat`s little theorem - University of Arizona Math
fermat`s little theorem - University of Arizona Math

PARTITION STATISTICS EQUIDISTRIBUTED WITH THE NUMBER OF HOOK DIFFERENCE ONE CELLS
PARTITION STATISTICS EQUIDISTRIBUTED WITH THE NUMBER OF HOOK DIFFERENCE ONE CELLS

An Introduction to Real Analysis John K. Hunter
An Introduction to Real Analysis John K. Hunter

Notes on Combinatorics - School of Mathematical Sciences
Notes on Combinatorics - School of Mathematical Sciences

34(3)
34(3)

Still More on Continuity
Still More on Continuity

Full text
Full text

Automated Theorem Proving in Loop Theory
Automated Theorem Proving in Loop Theory

the nekhoroshev theorem and long–term stabilities in the solar system
the nekhoroshev theorem and long–term stabilities in the solar system

Detecting Mutex Pairs in State Spaces by Sampling
Detecting Mutex Pairs in State Spaces by Sampling

An explicit version of Birch`s Theorem
An explicit version of Birch`s Theorem

(pdf)
(pdf)

... meaning that it is a difficult function to work with, although easy to comprehend. On the other hand, the function ψ(x) is a very “natural” function. We will see later that ψ(x) is strongly related to a deceptively simple looking infinite sum known as the Riemann zeta function which is deeply rooted ...
< 1 2 3 4 5 6 ... 26 >

Nyquist–Shannon sampling theorem



In the field of digital signal processing, the sampling theorem is a fundamental bridge between continuous-time signals (often called ""analog signals"") and discrete-time signals (often called ""digital signals""). It establishes a sufficient condition for a sample rate that permits a discrete sequence of samples to capture all the information from a continuous-time signal of finite bandwidth.Strictly speaking, the theorem only applies to a class of mathematical functions having a Fourier transform that is zero outside of a finite region of frequencies (see Fig 1). Intuitively we expect that when one reduces a continuous function to a discrete sequence and interpolates back to a continuous function, the fidelity of the result depends on the density (or sample rate) of the original samples. The sampling theorem introduces the concept of a sample rate that is sufficient for perfect fidelity for the class of functions that are bandlimited to a given bandwidth, such that no actual information is lost in the sampling process. It expresses the sufficient sample rate in terms of the bandwidth for the class of functions. The theorem also leads to a formula for perfectly reconstructing the original continuous-time function from the samples.Perfect reconstruction may still be possible when the sample-rate criterion is not satisfied, provided other constraints on the signal are known. (See § Sampling of non-baseband signals below, and Compressed sensing.)In some cases (when the sample-rate criterion is not satisfied), utilizing additional constraints allows for approximate reconstructions. The fidelity of these reconstructions can be verified and quantified utilizing Bochner's theorem.The name Nyquist–Shannon sampling theorem honors Harry Nyquist and Claude Shannon. The theorem was also discovered independently by E. T. Whittaker, by Vladimir Kotelnikov, and by others. It is thus also known by the names Nyquist–Shannon–Kotelnikov, Whittaker–Shannon–Kotelnikov, Whittaker–Nyquist–Kotelnikov–Shannon, and cardinal theorem of interpolation.
  • studyres.com © 2025
  • DMCA
  • Privacy
  • Terms
  • Report