Question 1: Given the engineering context of an autonomous underwater vehicle (AUV) communication system operating under limited bandwidth constraints, you are tasked with transmitting a data signal represented by x(t)=3sin(140πt)-2cos(80nt) through the AUV's acoustic transmitter, which operates at a fixed sampling rate of 30 samples per second. To achieve this, perform the following tasks: a) Find the discrete-time signal, x(n), by sampling x(t) at 30 samples per second. b) Determine the period of the discrete-time signal x(n) and explain its significance within the context of AUV communication.

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Author:Robert L. Boylestad
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Question 1: Given the engineering context of an autonomous underwater vehicle (AUV)
communication system operating under limited bandwidth constraints, you are tasked with
transmitting a data signal represented by x(t)=3sin(140лt)-2cos(80πt) through the AUV's
acoustic transmitter, which operates at a fixed sampling rate of 30 samples per second. To
achieve this, perform the following tasks:
a) Find the discrete-time signal, x(n), by sampling x(t) at 30 samples per second.
b) Determine the period of the discrete-time signal x(n) and explain its significance
within the context of AUV communication.
Transcribed Image Text:Question 1: Given the engineering context of an autonomous underwater vehicle (AUV) communication system operating under limited bandwidth constraints, you are tasked with transmitting a data signal represented by x(t)=3sin(140лt)-2cos(80πt) through the AUV's acoustic transmitter, which operates at a fixed sampling rate of 30 samples per second. To achieve this, perform the following tasks: a) Find the discrete-time signal, x(n), by sampling x(t) at 30 samples per second. b) Determine the period of the discrete-time signal x(n) and explain its significance within the context of AUV communication.
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