Lecture #4 - Sampling and Reconstruction

Question 1

How do you get a discrete-time representation of a continuos-time signal?

Answer 1

Obtained via a periodic sampling

Question 2

What is the disadvantage of a discrete-time representation?

Answer 2

1. There’s ambiguity
2. For certain sample, two signals could have the same samples, even though they are completely different.

Question 3

What does impulse train sampling do?

Answer 3

It’s a method used in signal processing to convert continuos-time signal into a discrete-time signal.

Question 4

What is aliasing in a signal

Answer 4

Aliasing is the overlapping of frequency components resulting from a sample rate below the Nyquist rate

Question 5

What is the nyquist rate?

Answer 5

The sample rate must be at least twice the bandwidth of the signal to avoid aliasing distortion.

Question 6

When trying to reproduce a sine wave, how many points do you need to construct?

Answer 6

Two

Question 7

Give the terminology for the Nyquist frequency and the Nyquist rate

Answer 7

/omega_N - Nyquist Frequency (the highest frequency you have in the signal)

2/omega_N - Nyquist Rate

Question 8

Explain the following terms on the effect of sampling in the frequency domain:

1. Oversampling
2. Undersampling
3. Critical sampling

Answer 8

Oversampling:
- The sampling frequency is higher than the Nyquist rate

Undersampling
- The sampling frequency is lower than the Nyquist rate

Critical sampling
- The sampling frequency is equal to the Nyquist rate

Question 9

What is interpolation?

Answer 9

Interpolation involves generating new data points within the range of existing data points to provide a more detailed or higher-resolution representation of a signal.