Basics

We will try to write this section as simple as possible to introduce the novice to the basic concepts of digital and analog communications. If the reader finds that we omitted something or something is incorrect please feel free to contact us.

In this section we will cover the following topics:
• Analog and digital transmission.
• Bandwidth.
• Noise.
• Attenuation.
• Cumulative effect.
• Carrying capacity of a communications channel.
Analog and digital transmission.
• Analog data, analog transmission.
• Digital data, analog transmission.
• Digital data, digital transmission.
• Analog data, digital transmission.
Our analog world.

Analog signals characterize themselves as having a continuous nature rather than a pulsed or discrete nature. In electrical or physical terms a continuous signal is one that varies in some direct correlation with another signal. This variation can be in phase, voltage or frequency in response to changes in physical phenomena, such as sound, light, heat, position, or pressure.

 Analog Signal Digital Signal
Table 1.

Devices that convert signals from one form to another are called converters. The device needed to convert from a an analog to a digital signal is called an Analog to Digital converter or ADC. The device needed to convert from a digital to an analog signal is called an Digital to Analog converter or DAC.

Bandwidth.
• The range of frequencies present in a signal is known as the bandwidth of the signal.
 Start Frequency Stop Frequency Sweep
Table 2.
• A signal’s energy or power is distributed among all its spectral components.
• The frequency domain representation of a signal is called the spectrum.
• To reproduce a signal at the receiver, the communication system must carry all spectral components of the signal. The Fourier series is a method of expressing an arbitrary periodic function as a sum of sine and cosine terms. In the following example a square wave can be defined a a sum of cosines using odd harmonics (1,3,5,7,9 .. ∞) The amplitude and phase values representing a signal are called the Fourier coefficients.

Figure 1. Square wave represented by the fundamental.

Figure 2. Square wave represented with one harmonic.

Figure 3. Square wave represented with two harmonics.

Figure 4. Square wave represented with five harmonics.

Figure 5. Square wave represented with ten harmonics.

Figure 6. Square wave represented with twenty five harmonics.

 Spectrum of a sine wave(narrow view) Spectrum of a square wave(narrow view) Spectrum of a square wave(wide view)
Table 3.
• Table 3 picture 1 shows the spectrum of a pure 1 MHz sine wave. Sine waves have only one component the fundamental frequency. Picture 2 shows a symmetric 1 MHz square (50% duty cycle) wave with two of it's odd harmonics, one at 3 Mhz and the other at 5 MHz. Picture 3 is the same 1 Mhz square wave shown in a wide view (50 Mhz span). The Fourier series of a square wave is given by the following formula:

• To represent a signal exactly at the receiving end the system must carry all the spectral components of the signal.
• Since some signals may have an infinite bandwidth no practical communications channel will have an infinite bandwidth.
• The bandwidth of the channel must be sufficient to carry the signal bandwidth but the signal bandwidth can be limited by the channel to some extent without causing undue distortion.
Noise
• Unwanted electrical energy.
• Most commonly modeled as Additive White Gaussian Noise.
• Thermal noise, crosstalk, electromagnetic interference, electrostatic interference.
• AWGN noise have an infinite bandwidth but the communications channel have a defined finite bandwidth therefore the noise corrupting the signal is limited by the communications channel.
 Clean Spectrum0 ~ 50MHz Noisy Spectrum0 ~ 50MHz Noise Envelope0 ~ 50MHz
Table 4.

Attenuation.
• Received signal power = Transmitted signal power + loss in the communications channel.
• Signal power is lost as it travels along the channel.
• Attenuation increases with frequency and with distance.
• Attenuation is due to heat dissipation, spreading of the signal in space.
Cumulative Effect of noise bandwidth and attenuation.
• The S/R signal to noise ratio.
• The communications channel must be optimized to maximize the S/R.
• As the S/R increases the probability of error decreases.
• The communications channel must not be designed to maximize power or minimize noise power levels.
Carying capacity of a Communications Channel.
Nyquist’s theorem implies that a channel having bandwidth B can carry multilevel data at a rate of 2B baud.
• Nyquist showed that in the absence of noise, a channel having bandwidth B can carry binary data at a rate of 2B bits/second.
• Multi-level signals can encode several bits into one level.
Shannon showed that a channel in the presence of noise can carry no more information than C = B log2 (1 + S/N) where C = channel capacity in bits/sec, B = channel bandwidth in Hz and S/N = Signal to noise ratio at the receiving end.

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