(20 points) Consider the continuous time signal a (t) sin (2 fot) and consider t
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Question
(20 points) Consider the continuous time signal a (t) sin (2 fot) and consider the sampling and reconstruction system 1 Let wa be the sampling frequency. a. What is the Nyquist rate/frequency wn for z(t)? b. Consider the ideal sampling system where Ho 1 and Hr(w) /2(w). Plot rp (t), zs(t), and Tr(t) for rectw./2 I. w 2w. III. ws wn/2 c. Repeat previous part for H1 and H2 being the Hold sampling interpolation system and recon- struction system, i.e. 2 sin (wT/2) Ho(w) jwT/2 Hr (w) rectua/2 (w)e 2 sin(wT/2)Explanation / Answer
Digital Circuits
A digital circuit is a circuit where the signal must be one of two discrete levels. Each level is interpreted as one of two different states (for example, on/off, 0/1, true/false). Digital circuits use transistors to create logic gates in order to perform Boolean logic. This logic is the foundation of digital electronics and computer processing. Digital circuits are less susceptible to noise or degradation in quality than analog circuits. It is also easier to perform error detection and correction with digital signals. To automate the process of designing digital circuits, engineers use electronic design automation (EDA) tools, a type of software that optimizes the logic in a digital circuit.
I don't know the details. I'll write the method anyway. Sinc function has a freq spectrum of rectangular pulse . I'm not sure sure about the width of the pulse. Say the max freq is Fmaxsinc . And cos has an impulse in freq domain. Now you are multiplying them in time domain. So you need to convolve the two freq spectrums. Now convolving with an impulse will only shift the waveform . So the final answer should be 2*(Fmaxsinc+the shift caused by cos).
It's actually interesting if you think about the nyquist freq when u multiply cos with a rectangular pulse in time domain. Now the rectangular pulse has sinc in freq domain. Now because the sinc has freq throughout, no matter what freq you use for sampling , there will be some aliasing and some info will be lost
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