Band Limited Signal

_{Band Limited Signal}
 

_{A signal is said to be a band limited signal if all of its frequency components are zero above a certain finite frequency. i.e it's power spectral density should be zero above the finite frequency.}

_{Figure 1 shows a signal g(t) that is band limited.}

Bandwidth requirements (communications)

The channel bandwidths needed to transmit various types of signals, using various processing schemes. Every signal observed in practice can be expressed as a sum (discrete or over a frequency continuum) of sinusoidal components of various frequencies. The plot of the amplitude versus frequency constitutes one feature of the frequency spectrum (the other being the phase versus frequency). The difference between the highest and the lowest frequencies of the frequency components of significant amplitudes in the spectrum is called the bandwidth of the signal, expressed in the unit of frequency, hertz. Every communication medium (also called channel) is capable of transmitting a frequency band (spectrum of frequencies) with reasonable fidelity. Qualitatively speaking, the difference between the highest and the lowest frequencies of components in the band over which the channel gain remains reasonably constant (or within a specified variation) is called the channel bandwidth.

Clearly, to transmit a signal with reasonable fidelity over a communication channel, the channel bandwidth must match and be at least equal to the signal bandwidth. Proper conditioning of a signal, such as modulation or coding, however, can increase or decrease the bandwidth of the processed signal. Thus, it is possible to transmit the information of a signal over a channel of bandwidth larger or smaller than that of the original signal.

Amplitude modulation (AM) with double sidebands (DSB), for example, doubles the signal bandwidth. If the audio signal to be transmitted has a bandwidth of 5 kHz, the resulting AM signal bandwidth using DSB is 10 kHz. Amplitude modulation with a single sideband (SSB), on the other hand, requires exactly the same bandwidth as that of the original signal. In broadcast frequency modulation (FM), on the other hand, audio signal bandwidth is 15 kHz (for high fidelity), but the corresponding frequency-modulated signal bandwidth is 200 kHz.

C. E. Shannon proved that over a channel of bandwith B the rate of information transmission, C, in bits/s (binary digits per second) is given by the

equation below, where SNR is the signal-to-noise power ratio. This result assumes a white Gaussian noise, which is the worst kind of noise from the point of view of interference.

It follows from Shannon's equation that a given information transmission rate C can be achieved by various combinations of B and SNR. It is thus possible to trade B for SNR, and vice versa.

A corollary of Shannon's equation is that, if a signal is properly processed to increase its bandwidth, the processed signal becomes more immune to interference or noise over the channel. This means that an increase in transmission bandwidth (broadbanding) can suppress the noise in the received signal, resulting in a better-quality signal (increased SNR) at the receiver. Frequency modulation and pulse-code modulation are two examples of broadband schemes where the transmission bandwidth can be increased as desired to suppress noise.

Broadbanding is also used to make communication less vulnerable to jamming and illicit reception by using the so-called spread spectrum signal.

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