Fourier Transform Test 1 Questions with Correct Answers
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Course
Fourier Transform
Institution
Fourier Transform
Fourier Transform Test 1 Questions with Correct Answers
Why doesn't the normalisation vectors apply to the DC-component (values at t=0)? - Answer-Because the DC component don't have a negative counterpart. It's the average value of all data points.
How does amplitude in time and frequency doma...
Fourier Transform Test 1 Questions with
Correct Answers
Why doesn't the normalisation vectors apply to the DC-component (values at t=0)? -
Answer-Because the DC component don't have a negative counterpart. It's the average
value of all data points.
How does amplitude in time and frequency domain differ? - Answer-The amplitude is
the length of the complex vector in frequency, hence it cannot be negative.
Amplitude in time-domain, however, indicates direction in addition to magnitude and can
therefore be negative.
How do the Fourier transform work, mathematically? - Answer-it loops through the
different timepoints (corresponding to the length of the signal). Where the time point is
the only variable in a complex exponential. This complex exponential gets point-wise
multiplied with the signal and added together which will give the Fourier coefficients.
This syntax then gets repeated for the remainder of iterations in the loop.
How do the invers Fourier transfer work, mathematically? - Answer-The same as
regular Fourier transform but with a sign flip in the complex exponential which will
cancel out the "i*sin" component.
What's the fast Fourier transform? (FFT) - Answer-The same as fourier transform but
the computations are done with vector algebra instead of point-wise multiplication which
is SUPER DUPER faster.
What's the frequency resolution? - Answer-how well the signal is represented. sampling
rate divided by data points. The higher amount of data points the better the resolution.
What's zero padding? (*förklara bättre*) - Answer-Data points of zeroes added to the
end of a signal which increases the sampling length and thus will increase the sinc-
interpretation i.e the resolution.
Note that the normalisation factor should be of the original length and NOT the added
zero-padded length.
What does the sample frequency determine? - Answer-it determines the span of
frequencies that can be evaluated. This span corresponds to the nyquist frequency
(f_samp /2) at best.
What does the amount of data points correspond to when sampling? - Answer-the
duration of the sampling which solely will increase the frequency resolution greatly.
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