𝑦(𝑡) = 6 cos(23𝜋𝑡) + 3 sin(16𝜋𝑡)(a) State the Nyquist sampling rate of y(t).
Question
𝑦(𝑡) = 6 cos(23𝜋𝑡) + 3 sin(16𝜋𝑡)(a) State the Nyquist sampling rate of y(t).
Solution
To determine the Nyquist sampling rate of y(t), we need to consider the highest frequency component present in the signal. In this case, the highest frequency component is 23𝜋, which corresponds to a frequency of 23𝜋/2𝜋 = 11.5 Hz.
According to the Nyquist-Shannon sampling theorem, the sampling rate should be at least twice the highest frequency component in the signal. Therefore, the Nyquist sampling rate for y(t) would be 2 * 11.5 Hz = 23 Hz.
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