You are a Neuroengineer interested in developing better A/D convertors for biome
ID: 1769842 • 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 a signal are digitized. Quantization involves reducing 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 available, the greater the resolution. For example, for auditory, sound wave applications, the quality of the sound improves with the # of bits used by a signal processor. Assume that: A quantizer, or A/D convertor with N bits, can represent 2N possible signal amplitude values 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 To accurately represent a signal, the signal needs to be quantized, or digitized by an A/D convertor at a sampling rate of at least twice the frequency of the signal a) b) c) Problem 1) How many amplitude levels can a 16-bit A/D convertor represent? 2) How many amplitude levels can a 4-bit A/D convertor represent? 3) Which of these two A/D convertors has a higher resolution? 4) If an input signal has a range of 46 Volts, find the resolution of an 8-bit A/D convertor for digitizing that signal. 5) The frequency content of an analog signal to be digitized has a range roughly covering the range of the auditory system of a young child: 200 Hz to 20,000 Hz. For accurate sampling, what is the minimal sampling rate necessary for an A/D convertor?Explanation / Answer
1. The number of amplitude levels that a 16-bit A/D convertor represent are = 2^N =2^16 = 65536 levels
2. The number of amplitude levels that a 4-bit A/D convertor represent = 2^4 = 16
3. The 16-bit A/D converter has a higher resolution.
4. Given input range = 46 volts,
The resolution ofd 8-bit A/D converter is R= V/2^8 = V/256 = 46/256 = 0.179 volts/bit
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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