Write a short report (3 three pages maximum) on the data analysis. This should concentrate upon what meaningful information you can find from the data, especially the spectral content of the data. You have two thrust settings, try and make some meaningful comment upon the relationship between the sound intensity and the thrust level (if there is one). In your report you need to verify that your data analysis methodology is correct, that is why the square wave signal data have been sampled. Your report needs to include at least one figure showing plotted data. Notes to guide you how to write a technical report are in the file 'write_a_report'.

A. Student School of Engineering University of Glasgow Abstract In this coursework, we have performed the Fourier analysis on the signal, which is loaded to the system and also, we have created square wave signal and performed Fourier analysis and then harmonics are plotted with correct frequency. In the next step, conversion of microphone signal into pressure in Pa, and we found maximum sound pressure level magnitude (SPL) & root-mean-square of the signal. I. Introduction The term "Fourier analysis" refers to a procedure that can be used to define periodic waveforms using trigonometric function names. During the 18th and 19th centuries, a French mathematician and physicist by the name of Jean Baptiste Joseph, Baron de Fourier, was active. This individual is where the method gets its name. The fields of electronics, acoustics, and communications all make use of Fourier analysis. Numerous waveforms include energy both at a fundamental frequency and at harmonic frequencies in addition to the fundamental frequency (multiples of the fundamental). The form of the wave is determined by the proportions of energy that are present in the fundamental and the harmonics relative to one another (Hales., 2000) . The wave function (typically amplitude, frequency, or phase versus time) can be expressed as a sum of sine and cosine function s known as a Fourier series,(Lee., 2004) which is uniquely defined by constants known as Fourier coefficient s. This can be done by plotting the wave function against the amplitude, frequency, or phase versus time. Then co-efficient are represented by a, a1, a2 … and b, b1, b2. Where F(x) is the Fourier, in which x is the independent variable and represented as follows: F ( x ) = a /2 + a 1 cos x + b 1 sin x + a 2 cos 2 x + b 2 sin 2 x + ... + a n cos nx + b n sin nx + ... In Fourier analysis, the goal is to calculate the coefficients a, a 1, a 2, all the way up to an, and b 1, b 2, all the way up to bn, all the way up to the highest feasible value of n. The Fourier series representation of the waveform is said to be more accurate when the value of n is increased. This is because there are more terms in the series whose coefficients can be calculated when n is increased. 2. Experimental Method To do an FFT, listen. The human ear calculates subconsciously what the mind can only do after years of math. The ear transforms sound, which is pressure waves flowing through air over time, into a spectrum, a range of volumes at different pitches. The brain translates this into sound. Mathematical approaches can convert sound waves or any other time-varying signal. The Fourier transform does this. The Fourier transform converts time-domain waveform data to frequency. The Fourier transform breaks the original waveform into sinusoidal terms with their own amplitude, frequency, and phase. This procedure turns a hard-to-describe time-domain waveform into a sequence of sinusoidal functions that, when put together, duplicate the original waveform. Power spectrum is the waveform's frequency-domain response. It's made by charting each sinusoidal term's amplitude vs. frequency. Figure 1 displays time-to-frequency conversion. In several scientific fields, the Fourier transform is employed for analysis. The Fourier transform may solve equations that describe how electricity, heat, or light affects things dynamically. In other cases, it can locate the regular parts of a shifting signal, which helps astronomers, doctors, and chemists interpret what they observe. Because it's useful, the Fourier transform works on a PC. Algorithms link the PC's ability to assess many integers with the Fourier transform. This shows PC-based waveform data in the frequency domain. 3. Results In this coursework, we have analysed data148 and data192 in which we have performed following experiments and obtained the results. Created python script to load square wave signal with Time-dependent. execute a Fourier analysis of the square wave and check the fundamental and harmonic frequencies. Find the microphone's maximum sound pressure level (SPL) and root-mean-square. Converted them to dB (you'll need to conduct some research). Analysis on the microphone signal as the square wave. Plot Fourier mode amplitudes vs. frequency on semi-logarithmic axes. 4. Discussion We have successfully performed the Fourier analysis, where we got knowledge about Fourier analysis and the microphone signal processing. 5. Conclusion During the course of this coursework, we have performed the Fourier analysis on the signal that is put into the system. In addition to this, we have constructed a square wave signal, performed the Fourier analysis on it, and then plotted the harmonics with the appropriate frequency. Converting the signal from the microphone into pressure measured in Pa was the next step, after which we determined the maximum sound pressure level magnitude (SPL) and the root-mean-square of the signal. 6. References Hales, L., & Hallgren, S. (2000). An improved quantum Fourier transform algorithm and applications. Proceedings 41st Annual Symposium on Foundations of Computer Science. https://doi.org/10.1109/sfcs.2000.892139

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Write a short report (3 three pages maximum) on the data analysis. This should concentrate upon what meaningful information you can find from the data, especially the spectral content of the data. You have two thrust settings, try and make some meaningful comment upon the relationship between the sound intensity and th