## What Can a System do to a Signal?

All systems can be simplified to the following block diagram structure:

The stuff inside the system block may be a whole bunch of subsystems, or it may be simply one block performing one function. Regardless, the system block will have some sort of effect on the signal and that effect will be seen at the output signal. The following subsections describe the different effects that a system may have.

### Gain and Loss

We have already studied gain and loss in systems and know that when a system adds a gain or a loss to a signal, the signal either increases in power and/or amplitude (gain) or decreases in power and/or amplitude (loss).

Practically speaking, this gain or loss results in a multiplication of the input signal by the gain/loss of the system to give the output signal. Or if values are given in dB, then the gain in dB is added to the signal. Mathematically, the relationship between input and output can be expressed as

Output = Gain \times Input

or as:

Output = Gain(dB) + Input

For the first equation, the input and output signals would typically be in Watts of Volts. For the second equation, the input and output signals should be in dBm, dBW, or dBV (or some other type of power or amplitude measurement expressed in dB).

System gain is usually the result of an active process. In other words it is the purposeful adding of energy to the system to increase the signal amplitude and power. System loss, may be purposeful attenuation of a signal that is too strong, but it is more often simply the result of natural signal attenuation. For example, as signals propagate through the air, they lose strength due to traveling away from the transmission point. Similarly, as signals travel down a wire, they can lose strength due to the resistance/impedance of the wire.

### Filtering and Bandlimiting

We have also already studied filtering and bandlimiting (which are more or less interchangeable terms). They both refer to removing a range of frequencies from the signal. For now, it is sufficient to understand that when you filter a signal, there will be a lower cutoff frequency and an upper cutoff frequency and only frequencies between those two limits will be allowed through. Low pass filters are filters that have a lower cutoff frequency of 0 Hertz and all frequencies below the upper limit are allowed through. High pass filters are filters that have an upper cutoff approaching infinity and all frequencies above the lower cutoff are allowed through.

### Noise

All systems are going to add noise, and we have seen one method of quantifying the amount of noise added – the noise factor and noise figure. Noise is any unwanted signal and will obscure the signal, making it more difficult to discern.

In order to include noise when we are talking about a signal, we need to talk about the signal to noise ratio. Noise is never gong to be zero so there will always be a noise component passing through the system along with the signal. To include the noise added by the system, add the noise power of the system to the noise power of the signal going through. It is important that these powers be in watts; it is not possible to add together power values when they are in dBm.

Example:

An input signal has a power of 100mW, and the noise on the signal is 3 \times 10^{-5} Watts. If a system adds 5 \times 10^{-6} Watts of noise, what is the output SNR?

Signal Power Out = Signal Power In = 100mW

Noise Power Out = Noise Power In + System Noise Power = 3.5 \times 10^{-5} W

SNR_{out} = \frac{0.1W}{3 \times 10^{-5}} + 5 \times 10^{-6} = 2857

### Changing the Signal Type

Changing the signal type is a system function that we have not yet encountered. This system function involves changing a signal from one of the types covered here into another signal type. The following are examples of these conversions:

- analog ↔ digital
- continuous ↔ discrete
- deterministic ↔ random

Analog to digital converters (or ADCs) are systems that convert analog signals into digital ones. They do this by periodically sampling the analog signal, and converting that signal into a digital number representing the signals analog values. We will look at ADCs in more detail later in the course.

Digital to analog converters (or DACs – pronounced “dac”) are systems that convert digital signals into analog ones. These systems convert the digital number representing the signal’s value and output it on a continuous scale. We will look at DACs in more detail later in the course and will examine such things as how does the converter fill in all of the values between the digital values to make the signal have continuous values.

Most of the time, ADCs also convert the signal from a continuous one into a discrete one. Similarly, DACs also usually convert the signal from discrete into continuous. We will study all of these cases in a later chapter.

### Modulation/Demodulation

**Modulation** involves taking a carrier signal, which is a single frequency and modifying it somehow (modulating it) to add information to that signal. By changing one or more of frequency, amplitude or phase of the carrier information from a second signal can be added to the carrier. This information carrying signal can be an analog signal (such as audio), or a digital signal.

Simple examples of analog modulators are AM and FM radio transmitters:

- AM transmission systems add information to the single frequency carrier by modulating the amplitude using the information signal.
- FM transmission systems add information to the single frequency carrier by modulating the frequency using the information signal.

Digital modulators put the data bits on to the carrier by either

- changing the amplitude of the carrier to one of two or more discrete values. This is called
*amplitude shift keying*(ASK) - changing the frequency of the carrier to one of two or more discrete values. This is called
*frequency shift keying*(FSK) - changing the phase of the carrier to one of two or more discrete values. This is called
*phase shift keying*(PSK) - changing the amplitude and phase of the carrier to one of two or more discrete values). This is called
*quadrature amplitude modulation*(QAM)

**Demodulation** is the process of extracting the original information from the modulated carrier. Modems are devices that can do both MODulation and DEModulation.