Okay so need you to write my Maths IA, the exact question you need to decide how to phrase it. “Noise-cancelling headphones with trigonometric functions, the algorithm used for it.” “exploring the math behind active noise canceling headphones with Fourier transform“. attach the marking criteria for it that you have to follow and below i will paste some ideas that ive researched and what my teacher
proposed:”exploring the math behind active noise canceling headphones with Fourier transform,” and while researching it seen many people recommend focusing less on explaining the actual concept and more on the application of it. Why so?
plan on using Fourier transforms to explore how my Bose qc45 headphones achieve this.
Also, does anyone have any idea how can obtain the data (frequency in different environments, noise before vs after using the ANC feature) for this and show how the Fourier transform applies to my device? I am kind of stuck on this and would really appreciate the help.
The Fourier transform is an operation that transforms data from the time (or spatial) domain into the frequency domain. In this chapter, the Fourier transform is related to the complex Fourier series. It is demonstrated that the transform can be considered as the limiting case of the complex Fourier series.
In brief, Fourier transform is based on the idea that functions of suitable properties can be represented with a linear combinations of trigonometric functions. This decomposition using trigonometric functions can be seen as extracting frequency-domain information from a time-domain signal, allowing for alternative or more efficient ways of investigating or modifying a signal.
Discrete Fourier transform to fast Fourier transform
Two sets of synthetic data sets are used to validate the applicability of the noise reduction techniques by comparing the obtained results to the underlying smooth functions used to generate the data sets.
Analysing measured data has its own challenges involving unpredictable conditions and sys- tematic measurement errors. These factors introduce noise into the data, thereby complicat- ing analysis and possibly causing biased or incorrect conclusions. For many application, it can be considered useful to find a function to model the background process instead of using noisy measurements themselves. In mathematics and engineering, white noise is a widely used tool used to model effects of stochastic processes in measured data [3].
Smoothing algorithms reduce noise by smoothing the curve using various techniques. One way this can be accomplished is by calculating mean value of three consecutive points, thereby reducing noise by partly averaging out the noise.
One could consider smoothing or noise reduction in the frequency domain. As previously mentioned, this can be achieved by the use of Fourier transforms.
Noise filtering via Fourier transforms has seen numerous applications. Examples of such applications are canceling out electromagnetic conditions in radar measurements [5], echo suppression in audio processing [6], and 2D noise filter in image processing [7]. In the above, Fourier transform has proven to be functional and efficient tool for noise reduction.
TEACHER’S NOTES:
Noise-cancelling headphones with trigonometric functions, the algorithm used for it.Extention – can we make a wave that takes away the jet engine wave and leaves the music one?
Please look at the criteria, , so it has to be done using concepts and topic we used in it, so please research the course content. And make sure to follow the criteria very carefully. Search up good IA examples so that you have examples to follow.
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