Module Code : NG2S800
Module Title : Analogue And Digital Communications
Assignment Type : Assessment
Learning Outcomes to be assessed (as specified in the validated module
1) To be able to analyse and synthesise a range of periodic and non-periodic signals in the time and frequency domains
2) To be able to understand the requirements of analogue and digital communications systems for designing and evaluating their system performance
NG2S800 Analogue And Digital Communications Assessment – South Wales University UK.
Task 1 : Mathematical analysis of a Fourier series
Any periodic waveform, , can be represented as the sum of an infinite number of sinusoidal and cosinusoidal terms, this make sine and cosine signals as a special wave forms among other, especially in the frequency domain. Fourier series is the mathematical function which explain the relationship between time domain and the frequency domain. Fourier series can be given by the following formula.
The equation (1) compute infinite series, where is an independent variable which often represent time. is the varying voltage against . Here , where f is the frequency of the wave form. is the often refer to as DC voltage or the offset from oscillating waveform. are amplitude of the sine and cosine wave for the given instant of a frequency dependant term.
NG2S800 Analogue And Digital Communications Assessment – South Wales University UK.
1.Examine the formula and explain its property in frequency and time domains.
Hints: You may analyse the following properties
1. Amplitude
2. Phase
3. Sine and Cosine properties (from the formula)
4. Frequency ()
Task 2 : Discrete Fourier Transform (DFT)
An industrial manufacturing process control unit required a measurement system needed to be test for quality control for the manufactured crystal resonators. The manufacturing process involve in rage of crystals resonant frequency from 32.7kHz – 10MHz. The resonant crystal accuracy must be 20 ppm is specified by the manufacture.
Design team found this process can be automated through implementing a DFT and the frequency components can be identified within the given range for a validating the components. As you re part of the Electronic design team required to analyse the practical of the Fourier series.
NG2S800 Analogue And Digital Communications Assessment – South Wales University UK.
You are required to simulate the DFT using Matlab or similar simulation platform and discuss in detail how the above Equation (1) can be transformed to a Discrete Fourier Transform and then it can be transformed into DFT for digital computation.
Analyses the DFT you described above for the suitability for the application given above. Hints: you may consider the frequency resolution point of view, which is crucial for the application to measure the crystal accuracy.
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