In other cases, it can identify the regular contributions to a fluctuating signal, thereby helping to make sense of observations in astronomy, medicine and chemistry. In some cases, the Fourier transform can provide a means of solving unwieldy equations that describe dynamic responses to electricity, heat or light. The Fourier transform has become a powerful analytical tool in diverse fields of science. Figure 1 illustrates this time to frequency domain conversion concept. Plotting the amplitude of each sinusoidal term versus its frequency creates a power spectrum, which is the response of the original waveform in the frequency domain. This process, in effect, converts a waveform in the time domain that is difficult to describe mathematically into a more manageable series of sinusoidal functions that when added together, exactly reproduce the original waveform. The Fourier transform accomplishes this by breaking down the original time-based waveform into a series of sinusoidal terms, each with a unique magnitude, frequency, and phase. Simply stated, the Fourier transform converts waveform data in the time domain into the frequency domain. The Fourier transform is the mathematical tool used to make this conversion. The brain then turns this information into perceived sound.Ī similar conversion can be done using mathematical methods on the same sound waves or virtually any other fluctuating signal that varies with respect to time. The ear formulates a transform by converting sound-the waves of pressure traveling over time and through the atmosphere-into a spectrum, a description of the sound as a series of volumes at distinct pitches. The human ear automatically and involuntarily performs a calculation that takes the intellect years of mathematical education to accomplish. To calculate an FFT (Fast Fourier Transform), just listen. Calculate FFTs with WinDaq Waveform BrowserĪvailable for free with every DATAQ Instruments data acquisition device.
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