23/24 Q1.

Question 1

A person records a human talking using a sampling rate of 6KHz.
Listening back to the recording, the person hears distortions. What are
these distortions called? What sampling rate would you recommend in
order to avoid such distortion? Briefly justify your choice.

Answer 1

1. Distortions -> aliasing. This is when one frequency component interferes with another.
2. Increase the sampling rate to fulfill NQ rate.
3. The NQ rate is when the sampling frequency is double the highest frequency of the signal.

Question 2

Identify two examples of DSP operations where finite wordlength
can impact the implementation.

Answer 2

Note: finite wordlength -> can only represent sample amplitudes with finite number of values.

1. Rounding and truncation
2. Quantization of arithmetic operations.

Question 3

Give an example of a signal processing application where analog
filtering remains the dominant approach. Briefly explain why digital filtering
is not used in the application you have given.

Answer 3

1. When transmitting an RF signal.
2. RF is too fast and therefore need fast and expensive ADC for digital filters.

Can use analogue filters instead.

Question 4

Define phase delay, both mathematically and in words. Identify all
parameters clearly. What unit is it measured in?

Answer 4

The phase delay is a measure of how much each frequency component is shifted by.

The unit is measured in samples.

omega(w) = <H(ejw)/w

Question 5

Outline two reasons why the DFT rather than the DTFT, is more
typically used in signal processing applications?

Answer 5

1. The DTFT;
   - input -> discrete, infinite
   - output -> continuos, periodic

DFT
- input -> discrete, finite
- output -> discrete, finite

i/p and o/p of DFT are periodic with the DFT length 2pi.

2. The FFT is derived from the DFT, which is a fast computation.