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3) An analog signal xa(t) = 2*cos(180*pi*t) is sampled at 270HZ. Find: a) The frequency of the analog signal b) The minimum sampling rate for the analog signal c) The discrete-time signal obtained using the Nyguist rate

3) An analog signal xa(t) = 2*cos(180*pi*t) is sampled at 270HZ. Find: a) The frequency of the analog signal b) The minimum sampling rate for the analog signal c) The discrete-time signal obtained using the Nyguist rate

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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3) An analog signal xa(t) = 2*cos(180*pi*t) is sampled at 270HZ. Find: a) The frequency of the analog signal b) The minimum sampling rate for the analog signal c) The discrete-time signal obtained using the Nyquist rate d) The discrete-time signal obtained using the given sampling rate. e) Give at least two (2) other signals with frequencies different from the given analog signal, which when sampled with the given sampling rate, and then the result is converted back to analog, gives the same original analog signal. Consider the analog signal xa(t) = 3 sin(320 pi*t) - 5 sin(3040 pi*t) + 2 sin(5280 pi*t) – 4 sin(8640 pi*t). a) What is the Nyquist rate? b) If sampled at 560HZ, determine the discrete-time signal obtained c) From the result in (b), determine the analog signal ya(t) derived when subjected to an 4) ideal DAC 5) An analog signal is defined as xa(t) = 2*exp(-2t)*cos(2pi*3t). Using 10 samples per second with 8 levels of quantization: a) Determine the Nyquist rate b) Determine the discrete time signal using the given sampling rate of 10 Hz c) Using Vmax as the initial value of xa(t) and with a dynamic range of 4 volts, compute for the step size (A) d) Tabulate the values of the discrete-time signal, the quantized discrete-time signal using rounding-off, the discrete-time signal using truncation, and the respective quantization errors for each type of quantization for n=0 to 10.
Transcribed Image Text:3) An analog signal xa(t) = 2*cos(180*pi*t) is sampled at 270HZ. Find: a) The frequency of the analog signal b) The minimum sampling rate for the analog signal c) The discrete-time signal obtained using the Nyquist rate d) The discrete-time signal obtained using the given sampling rate. e) Give at least two (2) other signals with frequencies different from the given analog signal, which when sampled with the given sampling rate, and then the result is converted back to analog, gives the same original analog signal. Consider the analog signal xa(t) = 3 sin(320 pi*t) - 5 sin(3040 pi*t) + 2 sin(5280 pi*t) – 4 sin(8640 pi*t). a) What is the Nyquist rate? b) If sampled at 560HZ, determine the discrete-time signal obtained c) From the result in (b), determine the analog signal ya(t) derived when subjected to an 4) ideal DAC 5) An analog signal is defined as xa(t) = 2*exp(-2t)*cos(2pi*3t). Using 10 samples per second with 8 levels of quantization: a) Determine the Nyquist rate b) Determine the discrete time signal using the given sampling rate of 10 Hz c) Using Vmax as the initial value of xa(t) and with a dynamic range of 4 volts, compute for the step size (A) d) Tabulate the values of the discrete-time signal, the quantized discrete-time signal using rounding-off, the discrete-time signal using truncation, and the respective quantization errors for each type of quantization for n=0 to 10.
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