Real-Time Signal Processing and Quantization Noise

Question 1

1. a) Give two examples of 'hard’ real-time systems and discuss the deadlines associated with them.
2. b) The ‘Highway Code’ for England, Scotland and Wales sets out rules intended to reduce road casualties. The general guidance in the Highway Code states that the typical ‘thinking distance’ (from the instant the driver identifies potential danger and applies the brakes) associated to braking a car going at 70 miles per hour is 21 metres (plus 75 metres of actual breaking time). (NB: 1 mile = 1609 metres)
3. i) What is the ‘deadline’, in milliseconds, associated with that ‘thinking distance’?
4. ii) Given the above, you are required to design a computerised automatic braking system for cars as a feature to reduce serious accidents further. What latency/ deadline would you aim for? Justify your answer.

Question 2

1. a) What is the maximum frequency component of signals that can be sampled reliably by a 16-bit A/D converter that is part of a data acquisition system that uses a sample-and-hold with a time jitter of 1 ns?
2. b) If you are collecting audio signals (fmax = 20 kHz), which are sampled using a data acquisition system with a sample-and-hold that has a time jitter of 1 ns, how many bits of a linear A/D converter are reliable?
3. c) Say we want to implement a digital filter with equation

Would you use a linear memory buffer or a circular memory buffer for the input samples? Justify your answer.

Question 3

1. a) Explain why all interrupts are disabled automatically by the hardware of a microprocessor / microcontroller / DSP chip when an interrupt is accepted and serviced.
2. b) What is ‘interrupt priority’?
3. c) Is it possible to implement a real-time system without using interrupts? Explain your answer.
4. d) Explain the difference between ‘event triggered systems’ and ‘time-triggered systems’.

Question 4

Regarding the concept of using buffers in memory to acquire samples and process them in real-time,

a)Explain the idea of using a linear buffer for real-time signal processing.

b)Explain the idea of using a circular buffer for real-time signal processing.

c)Explain the use of two pointers for implementing circular buffering for real-time signal processing and explain the tests necessary for these two pointers in order to verify that no overrun has occurred.

Question 5

Signal-to-noise ratio (SNR) is generally expressed in decibels as

For the sampling of sinusoidal signals using a linear A/D converter with N bits, that results in the following expression for the SNR due to ‘quantisation noise’:dB eqn. Q5_2021

a)Explain what ‘quantisation noise’ is.

b)Why is eqn. Q5_2021 not suitable for non-sinusoidal signals (say, speech or music)?

c)Derive (and explain your derivation) the corresponding ‘quantisation noise’ equation for speech signals if we want to cater for 3 standard deviations of the amplitude distribution without clipping.

d)For a discrete system intended for storing speech signals where the analogue electronics (amplifier) has a SNR of 88 dB, specify the number of bits to use, so that the discretisation does not add additional quantisation noise.