Bandwidth & Frequency Components

Bandwidth & Frequency Components The basic definition of bandwidth is that it is the width of the spectrum that a signal occupies. The human ear can only hear sounds with frequencies up to around 20kHz and this value reduces slowly as people grow older. The bandwidth of a radio signal is generally related to the audio quality for either analogue or digital radio systems but that is not the whole story because bandwidth has very definitions for analogue bandwidth and digital bandwidth. If you’re not interested in the definition of bandwidth then skip the rest of this section but just remember that kbps means thousand bits per second, and Mbps means million bits per second.  Because bandwidth is an often used word these days I think it would be best to define what it is first because it crops up so often. The term bandwidth is used for both analogue and digital systems and means similar things but is used in very different ways. In a digital system it is used as an alternative term to bit rate, which is the number of bits per second, usually displayed as kilobits per second (kbps, kbit/s, or kb/s) or megabits per second (Mbps, Mbit/s, or kb/s). Here kilo = thousand, and mega = million, so 2 kbps equals 2,000 bits per second and so on. By the way, using ‘K’ means 1,024 bits, just to confuse things. This is the way approximately 1,000 is used in the computing industry because it is equal to 2 to the power of 10 = 1024 and base 2 is the base used for digital because it can take on 2 values, just as decimal numbers consist of 10 numbers, the numbers 0-9.  Analogue bandwidth is very different to this and more complicated. In communications engineering a concept called Fourier Theory is used to analyze signals as the sum of sinewaves with different frequencies. That is, if you wanted to make a square wave signal (like a digital signal where alternate ones and zeros are transmitted), you could add up a few sinewaves with different frequencies and different amplitudes and if you added enough together the resulting waveform would look like a square waveform. This can be applied in the other direction so that a signal that you receive can be analysed as a bunch of sinewaves at different frequencies with different amplitudes. The technique that makes this possible is called the Fourier Transform, named after Joseph Fourier who discovered these techniques. The modern way of analyzing a signal in terms of its frequency components (sinewaves) is by using the Fast Fourier Transform (FFT) which is a digital implementation of the Fourier Transform but can be implemented extremely efficiently either in hardware or software.  Analogue bandwidth is measured in Hertz (Hz) which means cycles per second. Signals are either periodic which means that they repeat after a certain time duration and every period is the same as all previous periods, or a signal is aperiodic or non-periodic (same thing) meaning that it doesn’t repeat. Most real signals are aperiodic, and in fact periodic signals carry no information apart from the amplitude, phase, and the time period at which it repeats. Once you know these you can define the signal for all time in the future or in the past and no information apart from this can be carried. So all signals that carry *any* information are aperiodic. So the only sinusoids that are of any interest are the frequency components that go to make up the signals and also the sinewave that carries the information, which is called the carrier. The carrier is important because it defines where in the spectrum the signal will be transmitted over the air waves. More of that later and back to bandwidth. So you can analyze a signal as a bunch of sinewaves with different frequencies and amplitudes that when added together would reconstruct the original signal. The analysis of a signal in terms of its frequency components is analyzing in the frequency domain and you a suitable display would be of a graph with frequency on the horizontal axis and amplitude on the vertical axis and there would be a graph which showed where the signal contains frequencies and what their amplitude is.  So, finally, the bandwidth of an analogue signal is the difference in frequency between the highest and lowest frequencies contained in the signal. A signal might contain frequencies outside of a band that it is supposed to use, so the signal is passed through a filter which removes the frequency components outside of what is called the filter’s passband. For example, the difference between the highest and lowest frequencies of the passband will be the bandwidth of the filter. Usually, the bandwidth of a filter will be defined as the difference between the higher and lower frequencies at which the power is half that in its passband. A signal on the other hand might be defined by its bandwidth between the frequencies at which its power is far lower than half that of its passband. This is because the frequency components at the edge of a band have to be very small (attenuated) so that they don’t interfere with the frequency components of a signal that is transmitted in an adjacent band.  An example of analogue bandwidth of a signal would be the range of frequencies that contain 95% of all the power in the signal or possibly 99% of the power of the signal.

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