Any function can be represented as a sum of simpler functions.

Any function can be represented as a product of simpler functions.

Any function can be represented as a quotient of simpler functions.

Any function can be represented as a difference of simpler functions.

A representation of a periodic function as a sum of sine and cosine functions.

A representation of a periodic function as a sum of exponential functions.

A representation of a periodic function as a sum of polynomial functions.

A representation of a periodic function as a sum of rational functions.

A mathematical operation that converts a function of time or space into a function of frequency.

A mathematical operation that converts a function of time or space into a function of amplitude.

A mathematical operation that converts a function of time or space into a function of phase.

A mathematical operation that converts a function of time or space into a function of wavelength.

A small wave-like function that is used for analyzing signals.

A large wave-like function that is used for analyzing signals.

A periodic function that is used for analyzing signals.

A non-periodic function that is used for analyzing signals.

The more precisely the position of a particle is known, the less precisely its momentum can be known.

The more precisely the momentum of a particle is known, the less precisely its position can be known.

The more precisely the energy of a particle is known, the less precisely its time can be known.

The more precisely the time of a particle is known, the less precisely its energy can be known.

The overshoot of a Fourier series at a discontinuity.

The undershoot of a Fourier series at a discontinuity.

The ringing of a Fourier series at a discontinuity.

The cancellation of a Fourier series at a discontinuity.

The energy of a signal is equal to the sum of the squares of its Fourier coefficients.

The energy of a signal is equal to the product of its Fourier coefficients.

The energy of a signal is equal to the difference of its Fourier coefficients.

The energy of a signal is equal to the quotient of its Fourier coefficients.

The Fourier transform of a function is equal to the Fourier transform of its inverse Fourier transform.

The Fourier transform of a function is equal to the inverse Fourier transform of its Fourier transform.

The Fourier transform of a function is equal to the product of its Fourier transform and its inverse Fourier transform.

The Fourier transform of a function is equal to the quotient of its Fourier transform and its inverse Fourier transform.

The power spectral density of a stationary random process is equal to the Fourier transform of its autocorrelation function.

The power spectral density of a stationary random process is equal to the inverse Fourier transform of its autocorrelation function.

The power spectral density of a stationary random process is equal to the product of its autocorrelation function and its Fourier transform.

The power spectral density of a stationary random process is equal to the quotient of its autocorrelation function and its Fourier transform.

A signal can be perfectly reconstructed from its samples if the sampling rate is at least twice the highest frequency component of the signal.

A signal can be perfectly reconstructed from its samples if the sampling rate is at most twice the highest frequency component of the signal.

A signal can be perfectly reconstructed from its samples if the sampling rate is equal to twice the highest frequency component of the signal.

A signal can be perfectly reconstructed from its samples if the sampling rate is less than twice the highest frequency component of the signal.

A function is bandlimited if and only if its Fourier transform is supported on a finite interval.

A function is bandlimited if and only if its Fourier transform is supported on an infinite interval.

A function is bandlimited if and only if its Fourier transform is supported on a semi-infinite interval.

A function is bandlimited if and only if its Fourier transform is supported on a quarter-infinite interval.

A function that assigns to each point in a function the supremum of the function over all intervals containing that point.

A function that assigns to each point in a function the infimum of the function over all intervals containing that point.

A function that assigns to each point in a function the average of the function over all intervals containing that point.

A function that assigns to each point in a function the median of the function over all intervals containing that point.

A kernel used to approximate the Fourier series of a function.

A kernel used to approximate the Fourier transform of a function.

A kernel used to approximate the wavelet transform of a function.

A kernel used to approximate the Hilbert transform of a function.

A kernel used to approximate the Fourier series of a function.

A kernel used to approximate the Fourier transform of a function.

A kernel used to approximate the wavelet transform of a function.

A kernel used to approximate the Hilbert transform of a function.