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Spectrum analysis Analysis means decomposing something complex into simpler, more basic parts. As we have seen, there is a physical basis for modeling light, sound, and radio waves as being made up of various amounts of all different frequencies. Any process that quantifies the various amounts vs. frequency can be called spectrum analysis. It can be done on many short segments of time, or less often on longer segments, or just once for a deterministic function (such as ). The Fourier transform of a function produces a spectrum from which the original function can be reconstructed (aka synthesized) by an inverse transform. So it is reversible. In order to do that, it preserves not only the magnitude of each frequency component, but also its phase. This information can be represented as a 2-dimensional vector or a complex number, or as magnitude and phase (polar coordinates). In graphical representations, often only the magnitude (or squared magnitude) component is shown. This is also referred to as a power spectrum. Because of reversibility, the Fourier transform is called a representation of the function, in terms of frequency instead of time, thus, it is a frequency domain representation. Linear operations that could be performed in the time domain have counterparts that can often be performed more easily in the frequency domain. It is also helpful just for understanding and interpreting the effects of various time-domain operations, both linear and non-linear. For instance, only non-linear operations can create new frequencies in the spectrum. The Fourier transform of a random (aka stochastic) waveform (aka noise) is also random. Some kind of averaging is required in order to create a clear picture of the underlying frequency content (aka frequency distribution). Typically, the data is divided into time-segments of a chosen duration, and transforms are performed on each one. Then the magnitude or (usually) squared-magnitude components of the transforms are summed into an average transform. This is a very common operation performed on digitized (aka sampled) time-data, using the discrete Fourier transform (see Welch method). When the result is flat, as we have said, it is commonly referred to as white noise. Physical acoustics of music Spectrum is one of the determinants of the timbre or quality of a sound or note. It is the relative strength of pitches called harmonics and partials (collectively overtones) at various frequencies usually above the fundamental frequency, which is the actual note named (eg. an A). See also | ||||||||||
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