tde 2

Pagina 1

1 1. Describe the spectral leakage using the convolution theorem, in less than 10 lines. The leakage is a result of not having the precise frequency of the signal in our discrete frequencies, multiple of 1/T. It is caused by the convolution in frequency from the window spectra and the signal spectrum. Since in time we have to simply multiply them, the discrete frequencies are instead result of the multiplication in frequency of the circular convolution spectrum and one of the signal, since to periodicize the signal we have to make the convolution in time between those two functions. The windowing affects leakage in represented in the spectrum, since once the window spectrum is centered on the signal bin, the discrete frequencies has to be taken until they reac h the window spectrum. The leakage can be reduced using a hanning window, which almost cancels the side lobes due to higher attenuation than the rectangular one. 2. The Fourier Transform of a rectangular window: o is periodic  is complex ✕ o none of the others o is real 3. The 99th percentile of a Gaussian distribution with mean= 0 and variance= 1 is: o -1.475 o -0.034 o 0.134  None of the other ✔ 2 4. A purely harmonic signal has a frequency of 10.51 Hz with amplitude 4 V, the signal is acquired with an accelerometer with full-scale range of ± 10 V. The ADC used for the acquisition has a fsamp of 20 Hz. A configuration that allows to correctly reconstruct the amplitude of the spectral component is: o Number of samples = 200. Hanning window o Number of samples = 40. Hanning window  None of the other ✔ o Number of samples = 40. Rectangular window 5. If an operator is linear: o the coherence is always 1, independently from the frequency o cannot accept multiple inputs  it is always additive ✔ o none of the…