Consider a continous time signal given below. The signal is digitized and carried via the link operating at the rate of 20 Kbits/sec, and each input sample is quantized into 2048 different voltage levels. x(t) = 2cos(2pi50t) + cos(2pi150t) + sin(2pi35t) a. What is the sampling frequency of the given acquisition? b. Is the sampling frequency sufficient for the given signal to avoid aliasing? If not, what are the aliased frequencies going to be? and from which original frequencies would they come from? c. Assume a bipolar 10-V A/D. What is the resulting quantizer resolution?
Quantization and Resolution
Quantization is a methodology of carrying out signal modulation by the process of mapping input values from an infinitely long set of continuous values to a smaller set of finite values. Quantization forms the basic algorithm for lossy compression algorithms and represents a given analog signal into digital signals. In other words, these algorithms form the base of an analog-to-digital converter. Devices that process the algorithm of quantization are known as a quantizer. These devices aid in rounding off (approximation) the errors of an input function called the quantized value.
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1. Consider a continous time signal given below. The signal is digitized and carried via the link operating at the rate of 20 Kbits/sec, and each input sample is quantized into 2048 different voltage levels.
x(t) = 2cos(2pi50t) + cos(2pi150t) + sin(2pi35t)
a. What is the sampling frequency of the given acquisition?
b. Is the sampling frequency sufficient for the given signal to avoid aliasing? If not, what are the aliased frequencies going to be? and from which original frequencies would they come from?
c. Assume a bipolar 10-V A/D. What is the resulting quantizer resolution?
d. What is the SNRdb of the aquired signal?
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