351 Midterm Exam solutions

12 amplitude 8 4 1 0 1 15 c what is the nyquist rate

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Unformatted text preview: π : ω = 2π rad/s --> f = ω /2π = 1 Hz (b) Plot the discrete amplitude spectrum (amplitude vs. frequency) of y(t); clearly label the axes values. 12 amplitude 8 4 1 0 1 1.5 (c) What is the Nyquist rate for y(t)? 2 2.5 Frequency (Hz) fmax = 2.5 Hz --> Nyquist rate = 2fmax = 5 Hz (d) What is the lowest sampling rate you can use to avoid aliasing when measuring y(t)? fs ≥ Nyquist rate to avoid aliasing = 5 Hz (e) For the sampling frequency chosen in (d), what is the Nyquist frequency? fN = fs/2 = 2.5 Hz (f) For your chosen sampling rate, what is the smallest number of samples you must take to yield the most accurate reconstruction (both frequency and amplitude) of y(t)? To avoid frequency leakage, the number of samples (N) times the sampling period (T = 1/fs) must coincide with an integer multiple of the fundamental period: N/fs = 1 s (for 1 Hz fundamental frequency in part a) --> N = 5 Hz/Hz = 5 samples 4...
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