Digital to Analog Encoding

Digital data converted to

Amplitude Shift Keying

Aka. ASK. Values are represented by amplitudes of the carrier signal. Usually 1 amplitude is 0. Easy to implement. Constant carrier frequency is used. Requires relatively low bandwidth.

ASK is relatively inefficient for several reasons:

• Poor noise immunity
  Amplitude variations can be easily corrupted by noise.
• Low power efficiency
  Varying amplitude requires linear amplifiers, which consume more power than non-linear ones.
• Limited data rate capability compared to other modulation techniques
• Reduced transmission range
  Due to signal degradation.
• Less reliable in environments with signal fading or interference

Not good for non-linear channels. Used over optical fiber.

Frequency Shift Keying

Aka. FSK. The frequency of the carrier signal is varied to represent binary data. In FSK, different digital values are represented by discrete frequency changes:

• Binary 1: Carrier signal transmitted at one frequency (f₁)
• Binary 0: Carrier signal transmitted at another frequency (f₀)

Characteristics:

• Better noise immunity
  Compared to ASK. Because noise typically affects amplitude more than frequency
• More reliable in noisy environments
• More power efficient than ASK
• Requires more bandwidth than ASK
  Because more frequency ranges including guard bands are required.

Commonly used in applications where reliability is more important than bandwidth efficiency. Widely used in modems, radio teletype, caller ID, and amateur radio.

BFSK

Short for Binary Frequency Shift Keying. Most common form of FSK. BFSK is a variant of FSK where only two frequencies are used to represent binary data.

Props:

• Simple
• Less susceptible to noise interference compared to ASK
• Allows high frequency

Multiple FSK

More than 2 frequencies are used. More bandwidth-efficient. More prone to errors. Each signal element represents more than 1 bit.

Phase Shift Keying

Aka. PSK or PK. The phase of the carrier signal is varied to represent binary data. Constant frequency and amplitude used. In its basic form, PSK uses different phase angles to represent different digital values:

Characteristics:

• More bandwidth-efficient than FSK
• Better noise immunity compared to FSK
• High power efficiency

Good for non-linear channels. Forms the basis for many advanced modulation schemes used in modern digital communications. In the presence of noise, bit error rate of PSK is about $3\,\text{dB}$ superior to ASK and FSK.

Widely used in wireless communications, satellite communications, and digital cellular systems.

Mathematical Representation

The PSK signal can be represented as:

$$s(t) = A × cos(2πft + θᵢ)$$

Here:

• $s(t)$ - modulated signal
• $A$ - amplitude
• $f$ - carrier frequency
• $θᵢ$ - phase angle that varies according to the digital input
• $t$ - time

Binary PSK

Two phases represent two binary digits. Typically 0° and 180° are used.

Differential PSK

Phase shifted relative to previous transmission rather than some reference signal.

Quadrature PSK

Each signal element represents 2 bits. Shifts phase by 90 degrees.

Can use even more phase shifts. Named as 8-PSK, 16-PSK, etc based on the number of phase shifts.

QAM

Short for Quadrature Amplitude Modulation. Combines ASK and PSK to transmit multiple bits per symbol. Logical extension of QPSK. Sends 2 different signals simultaneously on same carrier frequency, phase shifted. Each carrier is ASK modulated.

Used on Asymmetric Digital Subscriber Line (ADSL).

Comparison

For ASK and PSK, the bit rate is dependent on the bandwidth.

For FSK, bandwidth depends on both bit rate and separation $\Delta f$ between carriers.

• For low frequencies, the bit rate domniates the bandwidth
• For higher frequencies: total bandwidth is the sum of bit rate and $2\Delta f$.