# Wave Modulation – analog and digital

This article touches upon wave modulation techniques used in physical layer that allows one or multiple low bandwidth signals to use or share a high frequency bandwidth. Note that post only covered the lowest layer of OSI model ie physical layer and not the data link layer which actually provides access technologies liek FDMA , TDMA , CDMA etc.

## Analog Modulation

Modulating a wave means changing one or more of its fundamental characteristics to encode information. The unmodulated wave used for this is called a carrier wave. There are three basic ways to modulate a carrier wave:

• Amplitude Modulation works with the height (intensity) of the wave
• Frequency Modulation works with number of waves that pass in a single second and is measured in Hertz (cycles/second)
• Phase Modulation that works with point in the wave’s cycle at which a wave begins and is measured in degrees. For example, changing a wave’s cycle from crest to trough corresponds to a 180 degree phase shift.

The general function for a sinusoid is

or

#### f(t) = A sin(omega t + phi)

we can see that this has 3 parameters that can be altered .

• A – called the magnitude, or amplitude of the sinusoid.
• omega – known as the frequency
• phi – known as the phase angle.

Therefore there are three basic ways to modulate a carrier wave ( which is the modulated unaltered wave carrying some information) :

### 1. Amplitude Modulation

Amplitude Modulation (AM), also called Amplitude Shift Keying (ASK), means changing the height of the wave to encode data. Shown below amplitude modulation in which one bit is encoded for each carrier wave change.
A high amplitude means a bit value of 1
Zero amplitude means a bit value of 0

The amplitude of the carrier signal is modulated (changed) in proportion to the message signal while the frequency and phase are kept constant.

### 2. Frequency Modulation

Frequency Modulation (FM), also called Frequency Shift Keying (FSK), means changing the frequency of the carrier wave to encode data. Shown below is frequency modulation in which one bit is encoded for each carrier wave change.
Changing the carrier wave to a higher frequency encodes a bit value of 1
No change in the carrier wave frequency means a bit value of 0

The frequency of the carrier signal is modulated (changed) in proportion to the message signal while the amplitude and phase are kept constant.

### 3. Phase Modulation

Phase refers to the point in each wave cycle at which the wave begins. Phase Modulation (PM) or Phase Shift Keying (PSK) means changing the carrier wave’s phase to carry data.
Shown is phase modulation in which one bit is encoded for each carrier wave change.
180o phase shift corresponds to a bit value of 1
No phase shift means a bit value of 0
Two bits per symbol could be encoded using phase modulation using 4 phase shifts such as 0o, 90o, 180o and 270o.

This encodes information as variations in the instantaneous phase of a carrier wave.It changes the phase angle of wave in direct proportion to the message signal.

The above discussed techniques are only applicable for analog modulation . For digital modulation got the next blog : Wave Modulation – digital.

### Need for Analog modulation

Pulse Code Modulation (PCM) samples the incoming analog signal 8000 samples/second using 8 bit samples.The resulting 64,000 bits per second signal, called a DS-0, that is used throughout the telephone network to send digital transmissions of voice transmissions.

1. Transmitting medium is acts like a bandpass filter

The transmitting channel ( air / wire o/ fibre ) is like a bandpass filter ie both the lowest frequency components and the highest frequency components are cut off beyond a range with transmission only being practical over some intermediate frequency range . In such a case our orignal wave is unusuable unless we shift our frequency up wthout changing the information contained . Thus modulation is the only solution for transmission.

2. Limits the size of Antenna from huge to small

A baseband (low frequency) signal has a long wavelength thus an anteena of the size of about 1/10 of wavelength is required to listen to it .This results in really large antenna sizes. However since modulation shifts the baseband signal up to a much higher frequency, which has much smaller wavelengths it allows the use of a much smaller antenna.

## Digital Modulation

Information can be sent from A to B as an electromagnetic signal, in either an analog or digital form. The difference between the two is that :

Data is typically sent as a packet that contains one or more bytes.
The “time to send” Ts= bits in packet / bits sent per packet .
The propagation delay or Tp = distance in metre / velocity in metre per second .

The most fundamental digital modulation techniques are based on keying:

### PSK (phase-shift keying)

a finite number of phases are used.

#### FSK (frequency-shift keying)

a finite number of frequencies are used.

a finite number of amplitudes are used.

widely used encoding schemes that encodes multiple bits per symbol by combining amplitude and phase modulation. A finite number of at least two phases and at least two amplitudes are used. An inphase signal (or I, with one example being a cosine waveform) and a quadrature phase signal (or Q, with an example being a sine wave) are amplitude modulated with a finite number of amplitudes, and then summed. It can be seen as a two-channel system, each channel using ASK. The resulting signal is equivalent to a combination of PSK and ASK.

#### Constellation Diagram

Representation of a signal modulated by a digital modulation scheme such as quadrature amplitude modulation or phase-shift keying. It displays the signal as a two-dimensional scatter diagram in the complex plane at symbol sampling instants.

### Trellis Coded Modulation

Sources :

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