GFSK

GFSK is an acronym for Gaussian frequency-shift keying.  It's a type of frequency shift keying (FSK) modulation that uses a Gaussian filter to smooth positive/negative frequency deviations. Gaussian filtering is a common way to reduce spectral width. It's also used in GMSK. I got into some of this in my posts on Digital modes here.

Gaussian filtering, like Gaussian elimination and Gaussian functions come from linear algebra. In 1810,  Johann Carl Friedrich Gauss invented a lot of what we now call linear algebra. I won't get into this in too much detail.  The Gausian filters in GFSK have more to do with Gaussian functions, it's more related to geometry than algebra. A function reveals the probability that any real measurement will fall between any two real limits (a low and high value) and the probability curve approaches zero on either side of those limits. a comparison of probability density functions allows us to assign values within that rage with confidence. Here it's used outbound to shape the pulses to reduce spectral width.

In the case of GFSK the Gaussian filter is used to smooth positive and negative frequency deviations, which represent a binary 1 or 0. remember the amplitude is not varying (much), the frequency is shifting, just over a relatively narrow frequency band, the minimum deviation is only 115 kHz. In a technology like Bluetooth, where the frequency hops 1600 times a second, the pulses might be a bit messy. So GFSK has the advantage of reducing out-of-band spectrum.

The Modem (Part 2)

Let's discuss SYN-ACK. I really breezed past it yesterday and it was actually important to understanding how the modem came to be. Below is a simplified summary of the TCP 3-way handshake: (SYN, SYN-ACK, ACK) More here.

• Host A sends a TCP synchronize packet (SYN) to Host B 
• Host B receives A's synchronize packet (SYN)
• Host B sends a synchronize-acknowledgement (SYN-ACK)
• Host A receives B's synchronized-acknowledgement (SYN-ACK)
• Host A sends acknowledge (ACK)
• Host B receives acknowledgement (ACK). 
• the TCP socket connection is now established!

This whole sequence comes from the modem. That is if you tend to agree that the modem descended from the work of Jean Maurice Émile Baudot. He patented a 5-bit telegraph code in 1870. In 1874 he invented a telegraphic system of TDM (Time-Division Multiplexing.) He used synchronized clockwork-powered switches at the transmitting and receiving ends, and was able to transmit five messages simultaneously. But because the timing was controlled mechanically the telegraph operator had to enter characters at a steady 30 wpm. The receiving end was a bit more forgiving, as those signals were temporarily stored on a set of five electromagnets, before being decoded to print the corresponding character on paper tape.

If not, then for you the first modem was probably a crude device that transmitted data as audio via a loudspeaker into the earpiece of the phone. This wooden box with a speaker and a mic were formally known as an acoustic coupler. They were sensitive to external noise, and variances in the shape and size of handsets. The dialing done by modern modems now was done then by human fingers on a rotary dial. They were also wholly technologically unnecessary. But directly connecting the the phone network was illegal. Inexplicably such systems were still in use well into the 1990s for mobile use such as in Telecommunications device for the deaf (TDDs.)

It was 50 years after Baudot's work that George Stibitz invented the first relay computer in 1937. AT&T put a full scale model into production in 1940. This relay computer connected Computer in New York to a teletype at Dartmouth College in New Hampshire over a phone line. It was the first remotely accessed computer.  The computer was a "complex number computer" an early digital computer. This required an A-to-D conversion.

AT&T built five of these complex number computers for the military. A total of 7 existed. They were used by the military to interpolate linear sequences for aiming anti-aircraft guns. It had no electronic memory, not even Baudot's simple magnets, but instead used his five-channel paper tape in a loop. Tapes had to be swapped to allow the computer to employ different mathematical functions. Post war yet different tapes allowed them to be re-purposed. (In this sense it was reprogrammable)

In 1949 Dr. George Valley of M.I.T.'s Lincoln Laboratory had recommended computerized networking  to operate our radar stations guarding the northern air approaches to the United States. Manual (i.e. human) identification, warning and control was slow compared to computers. This project was farmed out to IBM. An experimental subsector in Massachusetts was online in 1955. The SAGE (Semi-Automatic Ground Environment ) air-defense system used modems to connect their sites.  They combined analog radar signals so they could be sent from one computer to another. (Ken Olsen from MIT designed a series of transistorized computers to run the system.) It's modems were used to communicate data over the public switched telephone network or PSTN. The groundbreaking for the SAGE System was held at McChord AFB in 1957. By December of 1961 they had networked 78 SAGE radar stations and DEW Line sites.

In 1960 the Federal Communications Commission issued the Carterphone decision causing an explosion of private development.  The commercial potential was clear, by 1962, the first commercial modem was being manufactured by AT&T the Bell 103. It was the first modem with full-duplex transmission, frequency-shift keying or FSK, and had a speed of 300 bits per second or 300 bauds. in 1972, Vadic introduced the VA3400 which was capable of full duplex operation at 1200 bit per second. In 1976 AT&T came out with their own model capable of the same. Then in 1977 the Hayes modems debuted on the market and the modern era had begun...

The Modem (Part 1)

Older readers might associate the word "modem" with the dial-up noise. That noise is the sound of the modem, communicating with another modem. The first tones set a speed they can communicate at. Then the SYN-ACK sets other parameters like the bit number and parity. Then they check the rate, set up duplex for simultaneous communication and viola! throughput. For younger readers it may mean nothing at all. It's just a very annoying noise. A modem is a device that modulates an analog carrier signal to encode digital information and demodulates the signal to decode the transmitted information. The word is a Portmanteau of Modulate and Demodulate.

modem (ˈməʊdɛm) — n computing a device for connecting two computers by a telephone line, consisting of a modulator that converts computer signals into audio signals and a corresponding demodulator

Most sources cite the first modems as being invented in "the 1950s" a reference to the DEWline (Distant Early Waming) or sometimes specifically will refer to the PC modem which was invented in 1977 by Dennis C. Hayes and Dale Heatherington. Neither of these were the first modem. There were modems long before there were computers and even long before there was a cold war.

The modem evolved from news wire services in the 1920s. In order to transmit data over a phone line it had to be converted (modulated) into an analog signal so it could be multiplexed on the telegraph wire. To receive it, the same analog signal had to be converted (demodulated) back into signals the telegraph could receive.  This allowed a much more efficient use of the available spectrum. While the goal as multiplexing, those modulate/demodulate processes are comparable to those of later modems. Note how much that sounds like the A-to-D and D-to-A conversions you do in digital audio.

DIGITAL MODES: Part 2 (FSK)

Let me stop and explain "symbols" for a moment. In ASK a symbol might just be a dot or dash in Morse code. Other digital modes use multiple audio tones for each symbol being transmitted. This is usually explained in documentation by appending a number to the mode acronym. MFSK16 for example uses 16 tones for each symbol.   Not that's the only implementation of MFSK, there is also MFSK8 and so on. 

So if ASK is Amplitude Shift Keying you probably already guessed that FSK is Frequency Shift Keying. In FSK, the center frequency of the carrier wave alternates between multiple values. A common application of this would be BFSK (Binary Frequency Shift Keying.) In BFSK only two frequencies are used. In this scheme, the 0 and the 1 are called the space frequency and the mark frequency respectively. More here.

AFSK (Audio Frequency Shift Keying) is another early FSK-type digital mode. In this scheme the data is represented by changes in the frequency of an audio tone. AFSK differs from regular frequency-shift keying in performing the modulation at baseband frequencies. In radio applications, the AFSK-modulated signal normally is being used to modulate an RF carrier (using a conventional technique, such as AM or FM) for transmission.AFSK differs from BFSK in that AFSK is modulating baseband frequencies, BFSK is modulating a carrier wave. It can send and receive data up to1,200 baud.  It is also used in the the Emergency Alert System and by NOAA

The problem with MFSK is that the acronym stands for two different types of MFSK, Minimum Frequency Shift Keying and Multiple Frequency Shift Keying. Multiple Frequency Shift Keying is just FSK using more than two frequencies. The most common application of it is Dual-Tone Multi-Frequency (DTMF) also known as touch tone™ dialing. The other MFSK, (Minimum Frequency Shift Keying) is also known asMSK is (Minimum Shift Keying) yet another application of FSK. MSK is a more efficient form of FSK. MSK encodes each bit as a half sinusoid and thus the waveforms used to represent a 0 and a 1 bit differ by exactly half a carrier period. More here.

GMSK (Gaussian Minimum Shift Keying) is based on MSK.Thsi is a form of continuous-phase frequency-shift keying modulation. the data stream is first shaped with a Gaussian Filter.  A Gaussian filter modifies an input signal by convolution with a Gaussian function (named after Carl Friedrich Gauss) these apply an exponential function to a general quadratic function, in this application the result looks like a bellcurve because it reduces sideband power. More here.   If you think that's complicated try wrapping your head around PDGMSK (Pulse Driven Gaussian Minimum Shift Keying) More here.  This modification to GMSK sort of hurts my brain.

Even more complex is CPFSK, Continuous Phase Frequency Shift Keying.  In this application of FSK the carrier phase abruptly resets to zero at the start of every "symbol." In normal FSK at the end of each "symbol" the phase of the carrier wave changes because it's signals are generated by separate oscillators that aren't phase-synchronized. CPFSK changes its frequency continuously but the phase is a constant. It maintains a constant amplitude signal and has very narrow bandwidth requirements. DCPFSK stands for Differential Continuous Phase Frequency Shift Keying and please don't ask me to explain it. I stopped reading when I encountered the word "phase trellis." More here and here. I'll get into more phase related shifting in part 3.

VOCABULARY TERMS

• FSK - Frequency Shift Keying
• BFSK- Binary Frequency Shift Keying
• DTMF - Dual-Tone Multi-Frequency
• AFSK - Audio Frequency Shift Keying
• MSK - Minimum Shift Keying
• MFSK - Multiple Frequency Shift Keying
• PDGMSK - Pulse Driven Gaussian Minimum Shift Keying
• DCPFSK -  Differential Continuous Phase Frequency Shift Keying
• GMSK - Gaussian Minimum Shift Keying
• CPFSK- Continuous-phase frequency-shift keying