# Frequency spectrum



## sofaso (8 مارس 2010)

Frequency spectrum:-​​Familiar concepts associated with a frequency are colors, musical notes, radio/TV channels, and even the regular rotation of the earth.​​​​Electromagnetic emission spectrum of Iron in the visible region.​​A source of light can have many colors mixed together and in different amounts (intensities). A rainbow, or prism, sends the different frequencies in different directions, making them individually visible at different angles. A graph of the intensity plotted against the frequency (showing the amount of each color) is the *frequency spectrum* of the light. When all the visible frequencies are present in equal amounts, the effect is the "color" white, and the spectrum is a *flat* line. Therefore, flat-line spectrums in general are often referred to as _white_, whether they represent light or something else.​​Similarly, a source of sound can have many different frequencies mixed together. Each frequency stimulates a different length receptor in our ears. When only one length is predominantly stimulated, we hear a note. A steady hissing sound or a sudden crash stimulates all the receptors, so we say that it contains some amounts of all frequencies in our audible range. Things in our environment that we refer to as _noise_ often comprise many different frequencies. 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 domain (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.​​​​*Spectrum analysis:-*​​Example of voice waveform and its frequency spectrum​​A triangle wave pictured in the time domain (top) and frequency domain (bottom). The fundamental frequency component is at 220 Hz (A2).​​_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, making it 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 ******* (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


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## alexander18 (23 أبريل 2010)

thank you


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## bryar (6 يوليو 2010)

Thank you for your effort


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## ابوالبراء البغدادي (7 يوليو 2010)

شكرا لك


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