Part 1: Signals and Spectra This part of the Major Assignment is going to examine the concept of spectrum and consider s

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Part 1 Signals And Spectra This Part Of The Major Assignment Is Going To Examine The Concept Of Spectrum And Consider S 1 (55.63 KiB) Viewed 54 times

Part 1: Signals and Spectra This part of the Major Assignment is going to examine the concept of spectrum and consider some of the Fourier analysis techniques including the Fourier Series and Fourier Transforms. Fourier Series: In this task you will be analyzing a periodic sawtooth wave and explain the decomposition of this sawtooth into its harmonically related components. The type of sawtooth you will be analyzing will relate to the 5th number in your student number (see table below) and have the mathematical form: X16) = A, sawtooth (2 71 (fo)of ) 0.5 5th Student Amplitude (Ao) Frequency (fo) Number 1 100 Hz 2 1 40 Hz 3 1.5 200 Hz 4 2 250 Hz 5 2.5 500 Hz 125 Hz 7 3.51 200 Hz 8 25 Hz 9 4.5 400 Hz 0 50 Hz 6 ON 100 4 For example, if your student number was 3210987 your 5th student number would be 9 so your square wave would be:
X(t) = 4.5 x sawtooth (800 mt-) = 2 RMIT Classification: Trusted Tasks: • Manually calculate the Fourier Series coefficients (2. & au) for this waveform (use the exponential Fourier Series notation). • Now convert this exponential form of the Fourier series into trigonometric form. • In MATLAB confirm your calculations by plotting the original sawtooth wave and the sum of the first 6 weighted sines/cosines you calculated from the previous task (use a simulation accuracy of Ts = 0.00001;). • Label all MATLAB figures including x and y axes. Discussion: 1) What number harmonics are contained in a sawtooth wave? Contrast this with what you have been doing in Laboratory Experiment 2 where you have been looking at the Fourier series of a square-wave.
a Discussion: 1) What number harmonics are contained in a sawtooth wave? Contrast this with what you have been doing in Laboratory Experiment 2 where you have been looking at the Fourier series of a square-wave. 2) Explain how many weighted sines/cosines would need to be added together to accurately synthesize the original sawtooth waveform.