Solving Sampling Frequencies: Discrete Time Signal & Nyquist Frequency

[Whoohw]

Homework Statement

x(t) = 3*sin(1000*pi*t)

Suppose that the signal is sampled at a rate of fs = 2000Hz. What is the discrete time signal obtained after sampling (i.e., the signal expressed as a function of sample number n, x[n])

What discrete time frequency, f-hat will the signal x[n] be at if x(t) is sampled at its nyquist frequency?

Homework Equations

From the previous parts of this problem:
Original Frequency in hertz: 500 Hz
Niquist frequency: 1000 Hz

The Attempt at a Solution

I do not understand what a discrete time signal is, and as such, i have no idea what to do for these two steps of the problem.

 

[berkeman]

Homework Statement

x(t) = 3*sin(1000*pi*t)

Suppose that the signal is sampled at a rate of fs = 2000Hz. What is the discrete time signal obtained after sampling (i.e., the signal expressed as a function of sample number n, x[n])

What discrete time frequency, f-hat will the signal x[n] be at if x(t) is sampled at its nyquist frequency?

Homework Equations

From the previous parts of this problem:
Original Frequency in hertz: 500 Hz
Niquist frequency: 1000 Hz

The Attempt at a Solution

I do not understand what a discrete time signal is, and as such, i have no idea what to do for these two steps of the problem.

The discrete time signals are just the sample values at each sample time. So if you sample a sine wave twice per cycle, and happen to hit the correct phase to sample the + and - peaks of the waveform, your discrete time samples will alternate +/-1. If you sample at 4 times the period of the sine wave, what are the possible discrete time snapshot values that you can get (there is more than one set, depending on the phase of the sampling, right?)?