The frequency spectrum of a vibration signal is shown in the figure below. We wo

Question

The frequency spectrum of a vibration signal is shown in the figure below. We would like to sample and analyze the low frequency spectral peaks around 1kHz but our sampling rate is limited up to 5kHz.

1. Justify the feasibility of this task.

2. Define approximately the cutoff of an ideal AntiAliasing Filter to implement this sampling system.

3. Assuming that a reasonable level of high frequency noise is -60dB of the peak magnitude of the signal, estimate the parameters of a practical filter to achieve this objective (cutoff, order). (Hint: for simplicity, you may approximate the filter frequency response by its asymptotes.)

Problem 4: The frequency spectrum of a vibration signal is shown in the figure below. We would like to sample and analyze the low frequency spectral peaks around lkHz but our sampling rate is limited up to 5kHz. 1. Justify the feasibility of this task. x 10 2. Define approximately the cutoffof an ideal Anti- 15 Aliasing Filter to implement this sampling system. 3. Assuming that a reasonable level of high frequency noise is -60dB of the peak magnitude of the signal, 10 estimate the parameters of a practical filter to achieve this objective (cutoff, order). (Hint: for simplicity, you 3 may approximate the filter frequency response by its asymptotes.) 2000 4000 6000 8000 10000 frequency (Hz)

Explanation / Answer

1.To analyze the signal around 1khz and sampling at frequency greater than twice the frequency provides better resolution , reduce noises , avoids alliasing and phase distortion. Here sampling rate is limited to 5Khz. As sampling can be done above 2khz, it will give better result.

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