# Bandwidth-Limited Signals

## Bandwidth

The range of frequencies that are used for transmitting a signal without being substantially attenuated is called the bandwidth. It is calculated as the difference between the highest and the lowest frequencies. It is expressed in Hertz (Hz).

For example, if the minimum frequency is 100 Hz and the maximum frequency is 1000 Hz, the bandwidth will be 900 Hz.

The bandwidth of a transmission medium is the frequency width of the medium and is dependent upon its physical characteristics like thickness, material, length etc. For example, the bandwidth of a coaxial cable is 750 MHz ( MegaHertz).

## Baseband

Baseband transmissions are those requiring low – pass channels, i.e. the frequency range starts from 0. The bandwidth of a baseband channel is simply its maximum frequency.

## Bandpass and Passband

Bandpass is an electronic filter that allows frequencies within a particular range to pass through it, while screening out other frequencies. The output of a bandpass filter is a passband signal.

## Bandwidth – Limited Signal

A signal is called bandwidth – limited or simply band-limited when the amplitude of the spectrum goes to zero whenever its frequency crosses the allowable limits. Thus, its Fourier transform is non-zero only for a finite frequency interval. A band-limited signal is represented by a finite number of harmonics.

In most applications, an analog signal is sampled, converted to digital form on which operations are performed, which is finally reconstructed to analog form. For data communications, a signal, which is to be transmitted, has an infinite number of terms in its Fourier transform. However, when this signal needs to be transmitted through a channel of fixed bandwidth, band-limiting is required. It can be observed that among the infinite Fourier components, only the first few terms (harmonics) suffice to reconstruct the signal. So, if the bandwidth of the channel permits these harmonics to be transmitted, then the original signal can be reconstructed with sufficient accuracy.

Limiting the bandwidth of a signal will limit the data rate, even if the channel is perfect with very less noise. A solution is to use coding schemes with different voltage levels.

Samual Sam

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