In this blog, I am going to discuss a few basic things about the Bandwidth calculation of a signal.
A signal can be transmitted only when the bandwidth is finite i.e; band limited. How can we calculate the bandwidth of a signal? Consider a bandlimited signal in time-domain as well as in the frequency domain.
A signal can be transmitted only when the bandwidth is finite i.e; band limited. How can we calculate the bandwidth of a signal? Consider a bandlimited signal in time-domain as well as in the frequency domain.
Here in the frequency domain, the range of frequencies lies in
[-fm,fm]. As shown in the figure, the positive frequencies exist in the range [0,fm]. Hence the bandwidth is fm which is finite.
Therefore we can design a channel whose bandwidth is fm, the minimum value, can be transmitted.
The bandwidth of a few standard signals:
Can we transmit a delta signal?
Also, can we transmit a rectangular pulse signal?
Here also the bandwidth is infinite, makes it impossible for transmission. But the energy of the signal at [-2π/T,2π/T] contains 99% of the total signal. Hence it is bandlimited to [-2π/T,2π/T] and is recovered.
From these examples, we can conclude that we cannot judge whether the signal is bandlimited or band unlimited through time domain. It might have appeared that the signal is finite in the time but it does not mean it is suitable for transmission.
Here also the bandwidth is infinite, makes it impossible for transmission. But the energy of the signal at [-2π/T,2π/T] contains 99% of the total signal. Hence it is bandlimited to [-2π/T,2π/T] and is recovered.
From these examples, we can conclude that we cannot judge whether the signal is bandlimited or band unlimited through time domain. It might have appeared that the signal is finite in the time but it does not mean it is suitable for transmission.
