Sample Paper Short Questions

Question 1

You need to make a recording of birdsong. The particular species
sings at frequencies up to 10 kHz. Is a sampling rate of 16 kHz suitable for
the task? Explain why.

Answer 1

The sampling rate is not suitable for the task, due to the Nyquist Rate.

The sampling rate frequency has to be twice the highest frequency to produce a reliable measure.

Question 2

What is a random process? Give one example of a real-world
signal that is modelled as a random process.

Answer 2

A collection of random variables, characterised by a set of probability distribution functions that are a function of time.

Real world signal: Speech signal

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. The RF signal is too fast and therefore need fast and expensive ADC. Therefore we use analog

Question 4

Give three differences between IIR and FIR filters which explain

why FIR filters can be preferred in many applications.

Answer 4

FIR Filters:

1. Impulse response is finite
2. Inherently stable - all zeros
3. Implementation through convolution
4. Depends on past and present inputs

EXTRA:
5. Can have linear phase
6. Can be made causal

IIR Filters:

1. Infinite impulse response
2. Stability depends on poles
3. Implementation through recursion
4. Output depends on current and previous inputs AND past outputs

EXTRA:
5. Few coefficients - faster, less memory
6. Usually non-causal

Question 5

Outline how much more efficient the FFT is than a direct implementation of the DFT, with reference to the number of operations.

Answer 5

A DFT can be performed as O(N^2) in time complexity

The FFT reduces this time complexity in the order of O(NlogN)

Where N represents the number of inputs

Question 6

Explain what is meant by distortionless transmission in a system and how this relates to phase.

Answer 6

A system is meant to be distortionless when the output of the system is an exact replica of the input signal.

The phase response would be a straight line. This means that the phase shift introduced by the system is constant across all frequencies.

Question 7

If an FIR filter has linear phase, how will this manifest in its impulse response?

Answer 7

FIR is symmetrical around

Question 8

Explain the difference between a Short-time Fourier transform and a regular Discrete Fourier Transform

Answer 8

The short-time Fourier transform is a Fourier-related transform used to determine the sinusoidal frequency and phase content of local sections of a signal as it changes over time.

• STFT is a method of taking a ‘window’ that slides along the time series and performing the DFT