Name: 1. A signal is made up of different frequencies 30 Hz, 90 Hz, and 300 Hz.

Question

Name: 1. A signal is made up of different frequencies 30 Hz, 90 Hz, and 300 Hz. What is the minimum sampling frequency that should be used for the signal? 2. What does aliasing prevent? How far apart are aliasing images (replicas) located in the frequency domain? 3. 4. Why is a signal quantized? 5. If a 6-bit ADC is used, what is the resolution given that the ADC operates from 0 V to 10 V? 6. What is the T Hidden equation of a 12-bit ADC? 7. What do the a terms (coefficients) represent in Fourier series? What do the b terms (coefficients) represent in Fourier series?

Explanation / Answer

1) According to Shannon's Sampling theorem minimum sampling frequency should be atleast twice the maximum frequency content of signal to be sampled.

Now maximum frequency content of signal is 300 Hz.

Hence minimum sampling frequency required is 300*2 Hz i.e 600 Hz

2)Aliasing is an effect that causes different signals to become indistinguishable ( or aliases of one another ) when sampled.If aliasing occurrs then it prevents faithful reconstruction of original continous signal from sampled.signal.

Reconstructed signal turns out to be different from original signal.

3)In frequency domain aliasing images(replicas) are far apart by sampling frequency fs as signal is undersampled hence images(replicas) are separated by sampling frequency fs.

4)In signal processing,during the analog to digital process,amplitudes of the analog signal to be converted have infinite precision.The continuous amplitude must be converted into digital data with finite precision.Hece the signal is quantized.

5)Resolution of ADC = Range / 2n ( n = number of bits of ADC )

Resolution = 10 / 26 = 10 / 64 = 0.15625 Volts

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