One application of this inverse procedure is to the compression of audio signals. In other words, we can recover the original signal by inverting the succession of DFTs that make up its spectrogram. (b) Similar graphs for the author's rendition of “twinkle, twinkle, little star.”
(a) Bottom graph displays data from a recording of a young girl singing “twinkle, twinkle, little star.” Top graph displays the spectrogram magnitudes for this recording. Specifies that the function handle to fun will have parameter t, where t is the time row-vector parameter, over which all the periodic functions will be defined.FIGURE 16. Really, most of the work is already done for you within the first three lines of code. When it comes time to substitute parameters into these functions, MATLAB will know what to do based on what you have first defined here. Here, a and b will have parameters, k, T, and t. You are generalizing something over which you will substitute another function into fun(t), and in fact, whenever you do see an it allows MATLAB to resolve what's actually going to be substituted in, to be delayed, until a later time, at which that information is available. The clues you want to look for are in your MATLAB workspace.īy the definition of the Fourier Series, the program is substituting and integrating (summing the values over an interval) the periodic functions needed to compute the Fourier coefficients. T = 1 %T =0.5 - (-0.5) where T is fundamental period of x(t) I don't know how to check if it is right, or what I am doing in general.
I have the following code, and while it doesn't give me any errors. I was told to use trigonometric form of continuous time Fourier series (CTFS) to calculate a and b of x(t), where k is harmonic number. I am trying to determine the approximation of the following function as a ctfs:
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