A continuous time signal has the spectrum shown below. The x-axis is in Hz. The

Question

A continuous time signal has the spectrum shown below. The x-axis is in Hz. The sampling rate must be greater than what frequency to be certain that this signal can be perfectly reconstructed? The signal is sampled at 800 Hz. Sketch the corresponding spectrum of the discrete-time signal. Note, that the spectrum given is continuous and the x-axis is in Hz. Carefully label all points of interest on the plot! Label the magnitude of both the horizontal and vertical points of interest. (The vertical amplitudes do not need to be exact, but in the correct ratios.)

Explanation / Answer

(a). The maximum frequency present in the givens signal is fm=500 Hz. According to Nyquist's Sampling theorem, a signal can be reconstructed from its samples if and only if sampling frequency fs is greater than or at least equal to 2fm.

So, in this case, in order ensure that perfect reconstruction will be done, sampling frequency should be at least 2*500Hz=1000Hz.

(b). First of all, if the signal is sampled at 800 Hz, it would be below the specified rate as mention by Nyquist. Now, sampling should be done in time domain in order to obtain the discrete time representation of the signal. Now, unfortunately, in this question x(t) corresponding to X(f) is not given. Without that information, the time domain characteristic cannot be plotted.

But is is sure that since 800 Hz is less than the minimum Nyquist's sampling rate, the signal cannot be reconstructed from its samples in this case.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.