Bandwidth of a Digital Signal. Although the actual bandwidth of a digital signal is infinite, the effective bandwidth is finite. Solution A signal with L levels actually can carry log 2 L bits per level. A law of Fourier transformations says that if a signal is finite in time, its spectrum extends to infinite frequency, and if its bandwidth is finite, its duration is infinite in time. Now you have x[n] signal. Transmission of signals in binary form can require considerably more bandwidth than an equivalent analog signal. Note 7. The bandwidth of a channel is the frequency range over which it can transmit a signal with reasonable fidelity. Bandwidth is a scarce resource in wireless systems because: All technologies are sharing the transmission medium (the air), to be able to multiplex and demultiplex the signal we have to send every technology's signal on a different carrier frequency and with a limited BW to avoid interference between technologies. The maximum data rate of a channel (see Chapter 3) is N max = 2 × B × log 2 L (defined by the Nyquist formula). Bandwidth is the difference between the upper and lower frequencies in a continuous band of frequencies.It is typically measured in hertz, and depending on context, may specifically refer to passband bandwidth or baseband bandwidth.Passband bandwidth is the difference between the upper and lower cutoff frequencies of, for example, a band-pass filter, a communication channel, or a signal … Clearly we cannot have a time-domain signal of infinite duration, so we can never have a truly band-limited signal. For example, the transmission of 24 analog voice channels requires about 96KHz (24 x 4KHz). 3. Does this agree with the previous formula for N max ? Very simply, the bandwidth needed for an arbitrary digital signal is infinite. Though there is an infinite spectrum of frequencies available, it is not possible to use every frequency for communication purposes, except only those under a few hundred GHz. It would be erroneous to assume that fiber has infinite bandwidth for premises applications. While the telcos switched to single-mode fiber and fast laser sources, local area networks (LANs), closed-circuit television (CCTV) and other premises applications continued to use multimode fiber with light-emitting diode (LED) sources. This digital signal has 8 bits/sample x 8k sample/second = 64 kbits/second = 64 kpbs data rate. Digital Signals. Both V.90 and V.92 modems are discussed in Chapter 5, "Synchronous Modems, Digital Transmission, and Service Units." 54 Digital versus Analog Signal frequency 55 Using One Harmony and More Harmonies • To send n bps through an analog channel in the example, we need a bandwidth B such that – B = • Too add more harmonies – B = – B = • … An ideal op-amp requires infinite bandwidth because a) Signals can be amplified without attenuation b) Output common-mode noise voltage is zero c) Output voltage occurs simultaneously with input voltage changes d) Output can drive infinite number of device View Answer If you look at the power spectral density of a digital signal (including pseudorandom bitstreams of multilevel signals), the frequency content extends from DC to infinity. Bandwidth is a common frequency domain parameter used to describe the behavior of a circuit. For example, we usually consider a 3-dB bandwidth to describe the frequency response of a filter or communication channel. – digital signal, with all its sudden changes, is actually a composite signal having an infinite number of frequencies • a digital signal is a composite signal with an infinite bandwidth • if a medium has a wide bandwidth, a digital signal can be sent through it some frequencies will be weakened or blocked; still, enough frequencies will be A digital signal is a composite signal with an infinite bandwidth. Let's put solid examples: Consider an analog speech signal x(t) first it is lowpass filtered (by an analog RLC network) to 3khz, and then sampled at 8000 samples/second rate at 8-bits/sample resolution by a practical 8-bit ADC. Baseband transmission of a digital signal that preserves the shape of the digital signal is possible only if we have a low-pass channel with an infinite or very wide bandwidth. 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