You are a neuroengineer interested in developing better A/D convertors for biome
ID: 2262999 • Letter: Y
Question
You are a neuroengineer interested in developing better A/D convertors for biomedical sensors, hearing aids, and neural signal processing systems. A/D conversion involves quantization, the process by which continuous amplitudes of signal are diitized. Quantization involves redcing the number of possible signal amplitudes to a finite # a computer can store. Signal amplitudes are sampled, and stored as binary numbers. The resolution of the A/D conversion is determined by the # of available bits, typically, 8, 12, 16, 24, or 36 bits. The greater the # of bits vailable, the greater the resolution. For example, for audtory, sound wave applications, the quality of sound improves with the # of bits used by a signal processor.
*Assume the:
a.) A quantizer, or A/D convertor with N bits, can represent 2^N possible signal amplitude values
b.) The resolution of an A/D convertor can be determined as: Signal Input Range divided by the # of Signal Amplitude values that can be represented by the A/D convertor.
c.) To accurately represent a signal, the signal needs to be quantized, or digitized by an A/D convertor at a sampling rate of atleast twice the frequency of the signal
1.) How many amplitude levels can 16-bit A/D convertor represent?
2.) How many amplitude levels can a 8-bit A/D convertor represent?
3.) Which of these two A/D convertors has a higher resolution?
4.) If an input has a range of 36 volts, find the resolution of an 12-bit A/D convertor for digitizing that signal.
5.) The frequency content of an analog signal to be digitized has a range roughly covering that range of the auditory system of a young child: 200Hz to 20,000 Hz. For accurate sampling, what is the minimal sampling rate necessary for an A/D convertor?
Explanation / Answer
1. 2^16 = 65536 levels.
2. 2^8 = 256 levels.
3. The 16 bit A/D converter has a higher resolution.
4. Resolution=36V/(2*12) = 0.0088V = 8.8 mV
5. We need double the highest frequency present, thus we need to sample at a rate of at least 2x20,000Hz = 40,000 Hz.
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