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# Exercises

1. A signal is 1 for and otherwise (an impulse). What is its ( -point) Fourier transform as a function of ?

2. Assuming further that is an even number, what does the Fourier transform become if is 1 at instead of at ?

3. For what integer values of is the Fourier transform of the -point Hann window function nonzero?

4. 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)?

5. 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)?     Next: Classical waveforms Up: Fourier analysis and resynthesis Previous: Phase vocoder time bender   Contents   Index
Miller Puckette 2006-12-30