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Fourier transform: Quiz


Question 1: As alternatives to the Fourier transform, in ________, one uses time-frequency transforms to represent signals in a form that has some time information and some frequency information – by the uncertainty principle, there is a trade-off between these.
Wigner distribution functionTime–frequency analysisTime–frequency representationFourier analysis

Question 2: When the independent variable x represents time (with ________ unit of seconds), the transform variable ξ  represents frequency (in hertz).
Systems of measurementMetric systemConversion of unitsInternational System of Units

Question 3: The Fourier transform is also used in ________ (NMR) and in other kinds of spectroscopy, e.g.
Nuclear magnetic resonanceAtomNMR spectroscopyStable nuclide

Question 4: The ordinary-frequency convention (which is used in this article) is the one most often found in the ________ literature.
GeometrySet theoryMathematical logicMathematics

Question 5:
Which of the following titles did Fourier transform have?
Fourier Transform
The Transformers: Stormbringer
Euler transformation
KIR Transformation

Question 6: A locally compact abelian group is an ________ which is at the same time a locally compact Hausdorff topological space so that the group operations are continuous.
Group homomorphismGroup (mathematics)Simple groupAbelian group

Question 7: In the case when the distribution has a ________ this definition reduces to the Fourier transform applied to the probability density function, again with a different choice of constants.
Probability density functionProbability distributionNormal distributionCumulant

Question 8: This passage from sines and cosines to ________ makes it necessary for the Fourier coefficients to be complex valued.
ExponentiationComplex numberEuler's formulaLeonhard Euler

Question 9: These can be generalizations of the Fourier transform, such as the short-time Fourier transform or fractional Fourier transform, or can use different functions to represent signals, as in wavelet transforms and ________, with the wavelet analog of the (continuous) Fourier transform being the continuous wavelet transform.
Time–frequency representationChirplet transformSegal-Shale-Weil distributionWavelet series

Question 10: The usual interpretation of this complex number is that it gives you both the ________ (or size) of the wave present in the function and the phase (or the initial angle) of the wave.
Electrical engineeringCrest factorAmplitudeMeasuring instrument


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