Fourier Vs Wavelet Transform What Is Fourier Transform? An idea you’ll find all over science, math and engineering is the Fourier Transform (FT) . The FT decomposes a function into simple sines and cosines (i.e, waves). In theory, any function can be represented in this way — that is, as a sum of (possibly infinite) sine and cosine functions of different amplitudes and frequencies. I’ve provided a toy example below. Here, I’ve translated the top signal from the time domain to the frequency domain. In other words, we change the x-axis from time to frequency. The way to interpret peaks in the bottom plot is that the original signal represents the sum of two simple sine waves with frequencies one and two Hz, respectively. What Is a Wavelet Transform A major disadvantage of the Fourier transform is it captures global frequency information, meaning frequencies that persist over an entire signal. This kind of signal decomposition may not serve all applications well,...
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