A biological signal is recorded at a sample rate of 500 Hz, and the duration of

Question

A biological signal is recorded at a sample rate of 500 Hz, and the duration of the recording is 10 seconds. To show the frequency content of the signal, in this case by an amplitude spectrum, the discrete Fourier transformation (DFT) is computed, and a plot of X[k]| is made. 1) What does k represent. That is, what is the logical unit, or the interpretation of the unit, on the x-axis of your plot? 2) What is the frequency resolution of |X[k]|, meaning the frequency step between each value of the 'spectrum'? 3) What does it mean in the time domain (i.e. in the signal), if one frequency component in the amplitude spectrum (frequency A) has twice the amplitude of another component (frequency B)? The following is an example of an amplitude spectrum of an ECG signal contaminated by 50 Hz mains noise. A filter for removing this noise is required. amplitude spectrum 50 100 150 frequency [Hz] 4) Given that the amplitude at of the 50 Hz noise in the spectrum is 2, and that the signal components around 50 Hz have amplitudes of approximately 0.1, how many decibels does the filter need to attenuate the 50 Hz noise?

Explanation / Answer

k is used to denote the frequency domain ordinal.

The DFT is a numerical variant of the fouruer transform and yields a set of n frequency magnitudes. n is used to represnt the time dominant ordinal. N is the length of the sequence to be transformed.

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