Sample Paper Short Questions Flashcards
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.
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.
What is a random process? Give one example of a real-world
signal that is modelled as a random process.
A collection of random variables, characterised by a set of probability distribution functions that are a function of time.
Real world signal: Speech signal
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.
- When transmitting an RF signal
- The RF signal is too fast and therefore need fast and expensive ADC. Therefore we use analog
Give three differences between IIR and FIR filters which explain
why FIR filters can be preferred in many applications.
FIR Filters:
- Impulse response is finite
- Inherently** stable - all zeros **
- Implementation through convolution
- Depends on past and present inputs
EXTRA:
5. Can have **linear phase **
6. Can be **made causal
**
IIR Filters:
- Infinite impulse response
- Stability depends on poles
- Implementation through recursion
- Output depends on current and previous inputs AND past outputs
EXTRA:
5. Few coefficients - faster, less memory
6. Usually non-causal
Outline how much more efficient the FFT is than a direct implementation of the DFT, with reference to the number of operations.
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
Explain what is meant by distortionless transmission in a system and how this relates to phase.
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.
If an FIR filter has linear phase, how will this manifest in its impulse response?
FIR is symmetrical around
Explain the difference between a Short-time Fourier transform and a regular Discrete Fourier Transform
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
What’s a random process.
A collection of random variables, characterised by a set of probability distribution functions that are a function of time.
