Espectro de frecuencias
El espectro de frecuencia de un fenómeno ondulatorio (sonoro, luminoso o electromagnético), superposición de ondas de varias frecuencias, es una medida de la distribución de amplitudes de cada frecuencia. También se llama espectro de frecuencia al gráfico de intensidad frente a frecuencia de una onda particular.
El espectro de frecuencias o descomposición espectral de frecuencias puede aplicarse a cualquier concepto asociado con frecuencia o movimientos ondulatorios como son los colores, las notas musicales, las ondas electromagnéticas de radio o TV e incluso la rotación regular de la tierra.
Epectro lumínico, sonoro y electromagnético
Un fuente de luz puede tener muchos colores mezclados en diferentes cantidades (intensidades). Un arcoiris, o un prisma transparente, deflecta cada fotón según su frecuencia en un ángulo ligeramente diferente. Eso nos permite ver cada componente de la luz inicial por separado. Un gráfico de la intensidad de cada color deflactado por un prisma que muestre la cantidad de cada color es el espectro de frecuencia de la luz o espectro lumínico. Cuando todas las frecuencias visibles están presentes por igual, el efecto es el "color" blanco, y el espectro de frecuencias es uniforme, lo que se representa por una línea plana. De hecho cualquier espectro de frecuencia que consista en una línea plana se llama blanco de ahí que hablemos no solo de "color blanco" sino también de "ruido blanco".
De manera similar, una fuente de sonido puede ser una superposición de frecuencias diferentes. Cada frecuencia estimula una parte diferente de nuestra cóclea (caracol del oído). Cuando escuchamos una onda sonora con una sóla frecuencia predominante escuhamos una nota. Pero en cambio un silbido cualquiera o un golpe repentino que estimule todos los receptores, diremos que contine frecuencias dentro de todo el rango audible. Muchas cosas en nuestro entorno que calificamos como ruido frecuentemente continen frecuencias de todo el rango audible. Así cuando un espectro de frecuencia de un sonido, o espectro sonoro,
Therefore, when the sound spectrum is flat, it is called white noise. This term carries over into other types of spectrums than sound.
Each broadcast radio and TV station transmits a wave on an assigned frequency (aka channel). A radio antenna adds them all together into a single function of amplitude (voltage) vs. time. The radio tuner picks out one channel at a time (like each of the receptors in our ears). Some channels are stronger than others. If we made a graph of the strength of each channel vs. the frequency of the tuner, it would be the frequency spectrum of the antenna signal.
The rotation of the earth has only one frequency and never changes. So the concept of "spectrum" is not particularly useful in that case.
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.