CM · Digital modulation

Digital Modulation: ASK, FSK, PSK

A sinusoidal carrier has only three knobs to vary: amplitude, frequency, phase. Switch one of them with the bits and you get ASK, FSK or PSK. See the same bit stream through all three and learn which resists noise.

Same bits, three knobs

Tap ASK, FSK, PSK in turn. The same bit stream 1 0 1 1 0 appears as three waveforms — switching amplitude on and off, swapping between two frequencies, or flipping the phase.

The knob being switched

ASK : A → {0, 1}

Amplitude · noise-prone

Three knobs of the carrier

Write one sinusoid and it reads s(t) = A cos(2π f t + φ). The only quantities you can touch are the amplitude A, the frequency f and the phase φ — three of them. Digital modulation pairs the bits 0 and 1 with two values of one of these three, clicking that knob each time a bit changes. Which knob you pick names the scheme.

ASK, FSK, PSK

ASK turns the amplitude on and off — send the carrier for a 1, kill it for a 0 — the simplest scheme, but with the information in the amplitude it is jostled directly by amplitude noise. FSK keeps the amplitude constant and swaps between two frequencies, so it is less swayed by amplitude noise. PSK fixes amplitude and frequency and flips the phase between 0 and π. At the same signal power, 0 and π are the two farthest-apart points in the constellation, which makes PSK the most noise-resistant of the three.

Observes(t) = A cos(2π f t + φ)

Three knobs — amplitude A, frequency f, phase φ.

ChooseΔφ → ?

Switching the phase is PSK.

Grouping bits into symbols

Raise the number of phases from two to four or eight and a single symbol carries more bits. With M phases, each symbol holds n = log₂ M bits: 4-PSK carries 2 bits per symbol, 8-PSK 3, and so on. But the more points crowd onto the same circle, the closer they sit and the more fragile they are to noise. This bargain between the greed to send faster and the safety to survive noise leads into the next unit on bandwidth and symbol rate.

Fill inn = log₂ ?

M phases carry log₂ M bits per symbol.

On your ownRb = n · ?

Bit rate = bits per symbol × symbol rate.

Back to the first screen

In ASK the carrier switched on for each 1 and off for each 0; in FSK the amplitude held while only the frequency split in two; in PSK the phase flipped whenever a 0 arrived. All three put the same bit stream on the same carrier — they differed only in which knob, amplitude, frequency or phase, was turned. And PSK, using the phase, was the most noise-resistant at equal power. That is the one thing to hear in digital modulation.

Digital modulation puts the bits on one knob of the carrier. ASK switches the amplitude, FSK the frequency, PSK the phase, between two values according to the bits. PSK is the most noise-resistant at equal power because phases 0 and π are the farthest apart. The M-ary version, with M phases, carries n = log₂ M bits per symbol, and the bit rate is Rb = n Rs.

In the next unit

Sending symbols faster, or packing more bits per symbol, is quick — but both have limits. Next we look at how fast symbols can go in a given bandwidth, how symbol rate and bandwidth are tied together. The Nyquist signaling rate and the bits-per-second-per-hertz efficiency are the starting point.