A fundamental problem in signal processing that we encountered in our study of radar systems is to estimate the frequency of a sinusoidal signal after observing the signal for a limited observation time. Suppose we have a system with the following parameters: Expected range of observed sinusoidal frequencies: 0 ≤ 𝑓 < 10 𝑘 𝐻 𝑧 Sampling rate: 𝑓 𝑠 = 20 𝑘 𝐻 𝑧 ⟶  time between samples = 50 𝜇 𝑠 𝑒 𝑐 . Observation time: 3.2 𝑚 𝑠 𝑒 𝑐 ⟶   𝑁 = 64  samples. If the system shown below is used to estimate the frequency of the incoming sinusoid, how much zero padding is needed to guarantee that the error in the frequency estimate is no more than ± 100 𝐻 𝑧 ? Provide the minimum value of 𝑀 needed.数值题

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