Parseval's theorem

Target entity: Parseval's theorem
Context triple: [Wiener–Khinchin theorem, relatedTo, Parseval's theorem]

• A. Wiener–Khinchin theorem
  The Wiener–Khinchin theorem is a fundamental result in signal processing and probability theory that relates a wide-sense stationary random process’s autocorrelation function to its power spectral density via the Fourier transform.
• B. Fourier inversion theorem
  The Fourier inversion theorem is a fundamental result in harmonic analysis that guarantees, under suitable conditions, that a function can be exactly reconstructed from its Fourier transform.
• C. Fourier transform
  The Fourier transform is a mathematical operation that decomposes a function or signal into its constituent frequencies, widely used in engineering, physics, and signal processing.
• D. Poisson summation formula
  The Poisson summation formula is a fundamental result in harmonic analysis that links sums of a function over the integers to sums of its Fourier transform, with deep applications in number theory, signal processing, and physics.
• E. convolution theorem
  The convolution theorem is a fundamental result in Fourier analysis stating that convolution in one domain corresponds to pointwise multiplication in the Fourier-transformed domain (and vice versa), greatly simplifying the analysis of linear systems.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Parseval's theorem
Target entity description: Parseval's theorem is a fundamental result in Fourier analysis that equates the total energy of a function in the time (or spatial) domain with the total energy of its representation in the frequency domain.

• A. Wiener–Khinchin theorem
  The Wiener–Khinchin theorem is a fundamental result in signal processing and probability theory that relates a wide-sense stationary random process’s autocorrelation function to its power spectral density via the Fourier transform.
• B. Fourier inversion theorem
  The Fourier inversion theorem is a fundamental result in harmonic analysis that guarantees, under suitable conditions, that a function can be exactly reconstructed from its Fourier transform.
• C. Fourier transform
  The Fourier transform is a mathematical operation that decomposes a function or signal into its constituent frequencies, widely used in engineering, physics, and signal processing.
• D. Poisson summation formula
  The Poisson summation formula is a fundamental result in harmonic analysis that links sums of a function over the integers to sums of its Fourier transform, with deep applications in number theory, signal processing, and physics.
• E. convolution theorem
  The convolution theorem is a fundamental result in Fourier analysis stating that convolution in one domain corresponds to pointwise multiplication in the Fourier-transformed domain (and vice versa), greatly simplifying the analysis of linear systems.
• F. None of above. chosen