Kontrollküsimused 1. osa kohta

The Fourier spectrum calculated of a discrete argument signal with Discrete Fourier Transform is also always a discrete argument function.

The Discrete Fourier Transform of a periodic discrete argument signal is always discrete and periodic.

The Discrete Fourier Transform of a non-periodic discrete argument signal is continuous and periodic.

The Discrete Fourier Transform of a non-periodic discrete argument signal is periodic discrete argument function.

Real part of the Fourier transform corresponds to even portion of the signal.

Imaginary part of the Fourier transform corresponds to odd portion of the signal.

Real part of the Fourier transform corresponds to odd portion of the signal.

Imaginary part of the Fourier transform corresponds to even portion of the signal.

Imaginary and even part of the Fourier transform corresponds to even portion of the signal.

Negative frequencies contain the phase information of the signal. By comparing the positive and negative counterparts it is possible to tell the complex phase of each frequency component.

Negative frequencies of the Fourier spectrum show the phase spectrum, whereas positive frequencies correspond to power spectrum.

Negative frequencies of the Fourier spectrum do not contain additional information. The negative side is exact copy of the positive spectrum side.

Negative frequencies of the Fourier spectrum do not contain additional information. It is possible to calculate the negative frequencies side by taking complex conjugate of the positive side and reflecting the result to negative side.

By up-scaling the time-domain representation by a factor of 3 all the corresponding frequency components will be scaled up by a factor of 3.

Superposition holds for Fourier Transform. It is equivalent to take the Fourier transforms of n signals and sum the spectra after that

with

adding n signals and computing the Fourier Transform after that.

By up-scaling the time-domain representation by a factor of 3 all the corresponding frequency components will be scaled down by a factor of 1/3.

Superposition do not hold for Fourier Transform, because Fourier Transform is not a linear operation.

Fourier Transform is not linear, because additivity does not hold.

Even signals in time domain are purely real and even in the frequency domain.

Odd signals in the time domain are purely imaginary and odd in the frequency domain.

Odd signals in time domain are purely real and even in the frequency domain.

Even signals in the time domain are purely imaginary and odd in the frequency domain.

Even signals in the time domain are purely imaginary and even in the frequency domain.

Complex conjugate property holds only for continuous case, e.g. x*(t)  <-->  X*(-w)

Complex conjugate property holds only for discrete case, e.g. x*[n]  <-->  X*(-Ω)

Complex conjugate property holds for both discrete and continuous case, e.g. x*[n]  <-->  X*(-Ω) and x*(t)  <-->  X*(-w)