- A signal is 1 for and otherwise (an impulse). What is
its (-point) Fourier transform as a function of ?
- Assuming further that is an even number, what does
the Fourier transform become if is 1 at instead of at ?
- For what integer values of is the Fourier transform of the -point
Hann window function nonzero?
- In order to Fourier analyze a 100-Hertz periodic tone (at a sample rate
of 44100 Hertz), using a Hann window, what value of would be needed to
completely resolve all the partials of the tone (in the sense of having
non-overlapping peaks in the spectrum)?
- Suppose an N-point Fourier transform is done on a complex sinusoid of frequency
where is the fundamental frequency. What percentage
of the signal energy lands in the main lobe, channels and ? If the signal
is Hann windowed, what percentage of the energy is now in the main lobe (which
is then channels 1 through 4)?