Signals

Used to transmit data via a medium, such as cables and air. Generated by changing strength of a form of energy. Here frequency of a signal is also measured in cycles per second.

Attenuation

Signal strength loss over distance.

Types

Analog

Continuously varying.

Digital

Discrete. Can take any number of discrete values, not to be confused with binary.

Terminology

Bandwidth

For analog signals, the range of frequencies that a medium is capable of handling.

For digital signals, the maximum number of bits that can be transmitted over a medium in a given period of time.

Baud rate

Number of signal changes per second.

Data rate

Number of bits tranmitted per second. Measured in bits per second.

$$\text{Data rate} = \text{Baud rate} \times \text{Bits per symbol}$$

Data rate can be increased by increasing the number of signal components, to some extent.

As the number of signal variations increases, the difference between each symbol becomes smaller and makes it hard to distinguish them at the receiver, especially in noisy environments.

Sampling

Converting an analog signal to digital by observing the signal at regular intervals.

Sampling rate

Number of samples taken per second. Must be equal to or higher than baud rate.

Signal to Noise Ratio

Aka. SNR. Ratio between signal power and the noise power. Measured in decibels ($\text{dB}$). $$

$$\text{SNR} = 10 \log_{10} \left(\frac{P_\text{signal}}{P_\text{noise}}\right)$$

High SNR is desirable.

Theorems

Nyquist theorem

If the highest frequency a medium can transmit is $f$, then a receiver is able to completely reconstruct the signal by sampling it at $2f$, assuming the channel is noiseless.

Aliasing

Occurs when the sampling rate is less than $2f$. High-frequency components of a signal are misinterpreted as lower frequencies, leading to distortion.

Shanon’s theorem

Maximum data rate of a medium is related to both the maximum frequency the medium can handle and SNR.

$$\text{data rate} = \text{bandwidth} \times \log_2 \left( 1 + \frac{S}{N} \right)$$