Modified frequency modulation

The digital coding method "frequency modulation" (FM) as used in magnetic storage art has a variety of other names, including delay coding and differential Manchester encoding.[2]

Frequency modulation is the encoding of binary data to form a two-level signal where (a) a "0" causes no change of signal level unless it is followed by another "0" in which case a transition to the other level takes place at the end of the first bit period; and (b) a "1" causes a transition from one level to the other in the middle of the bit period.[3]

FM encoding is used primarily for encoding signals because the frequency spectrum of the encoded signal contains less low-frequency energy than a conventional non-return-to-zero (NRZ) signal and less high-frequency energy than a biphase signal.

FM encoding is an encoding using only half the bandwidth for biphase encoding but features all the advantages of biphase encoding: To be rewritten: It is guaranteed to have transitions every other bit, meaning that decoding systems can adjust their clock/DC threshold continuously. One drawback is that it lacks easy human readability (e.g. on an oscilloscope).

FM encoding is also known as Miller coding after Armin Miller, its inventor.[4]

A byte encoded using FM (above) and MFM (below). Dashed blue line denotes clock pulse (the signal level change in it is ignored), and dashed red line, data pulse (signal level change encodes 1, and absence thereof, 0).

As is standard when discussing hard drive encoding schemes, FM and MFM encodings produce a bit stream which is NRZI encoded when written to disk. A 1-bit represents a magnetic transition, and a 0-bit no transition. Data encoding has to balance two factors:

• there are limits on the minimum and maximum number of 0-bits that the hardware can detect between consecutive 1-bits, and the encoding must not exceed this limit;
• there are limits on the maximum number of 1-bits that the hardware can detect in a given amount of time. If a disk is encoded with a higher (average) number of magnetic transitions per bit, the bits will have to be "wider" and fewer sectors will fit each track;

Both FM and MFM encodings can also be thought of as having data bits separated by clock bits, but with different rules for encoding the bits. Still, both formats encode each data bit as two bits on disk (because of delimiters that are required at the beginning and end of a sequence, the actual density is slightly lower).

The basic encoding rule for FM is that all clock bits are 1: zeros are encoded as 10, ones are encoded as 11. The number of magnetic transitions per bit is on average 1.5(50% × 1 + 50% × 2).

The basic encoding rule for MFM is that (x, y, z, ...) encodes to (x, x NOR y, y, y NOR z, z, z NOR...). A zero is encoded as 10 if preceded by a zero, and 00 if preceded by a one (each of these cases occurs 25% of the time); a one is always encoded as 01 (which happens 50% of the time); thus the number of magnetic transitions is on average 0.75(25% 10 = yes + 25% 00 = no + 50% 01 = yes).

Note that the surrounding clock bits are sometimes known, but sometimes require knowledge of the adjacent data bits. A longer example:

Data:          0 0 0 1 1 0 1 1 ...
FM encoded:   10101011111011111...
MFM clock:    ? 1 1 0 0 0 0 0 0...
MFM encoded:  ?0101001010001010...

(The bold bits are the data bits, the others are the clock bits.)

In FM encoding, the number of 0-bits that may appear between consecutive 1-bits is either 0 or 1. In MFM encoding there is a minimum of 1 zero bit between adjacent ones (there are never two adjacent one bits), and the maximum number of zeros in a row is 3. Thus, FM is a (0,1) RLL code, while MFM is a (1,3) code.

A special “sync mark” is used to allow the disk controller to figure out where the data starts. This sync mark must follow the RLL code so that the controller can recognize it, but it does not follow the FM and MFM rules for clock bits. This way, it will never occur in any bit position in any encoded data stream. The shortest possible sync bit pattern, which follows the (1,3) RLL coding rules but cannot be produced by normal MFM coding, is 100010010001. In fact, the sync mark that is commonly used in MFM encoding starts with these twelve bits; it is called an “A1 sync” since the data bits form the start of the hexadecimal value A1 (10100001), but the fifth clock bit is different from the normal encoding of the A1 byte.

Data:      1 0 1 0 0 0 0 1
Clock:      0 0 0 1 1 1 0
Encoded:   100010010101001
Sync clock: 0 0 0 1 0 1 0
Sync Mark: 100010010001001
                    ^ Missing clock bit

MMFM, (Modified Modified Frequency Modulation), also abbreviated M²FM, or M2FM, is similar to MFM, but suppresses additional clock bits, producing a longer maximum run length (a (1,4) RLL code). In particular, a clock pulse is only inserted between a pair of adjacent 0-bits if the first bit of the pair did not have a clock pulse inserted before it.[5] In the example below, clock bits that would have been present in MFM are noted in bold:

Data:     1 1 0 1 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1
Clock:   0 0 0 0 0 1 0 0 1 0 0 0 1 0 1 0 0 1 0 1 0 0
Encoded: 01010001001001001000010010001001001000100001

In this system, sync marks are made by inserting additional clock pulses between adjacent zero bits (following the MFM rule) where they would normally be omitted. In particular, the data bit pattern "100001" has a clock pulse inserted in the middle, where it would normally be omitted:

Data:  1 0 0 0 0 1
Normal: 0 1 0 1 0
Sync:   0 1 1 1 0

• Group coded recording (GCR)

This article is based on material taken from the Free On-line Dictionary of Computing prior to 1 November 2008 and incorporated under the "relicensing" terms of the GFDL, version 1.3 or later.
 This article incorporates public domain material from the General Services Administration document: "Federal Standard 1037C".

• Savard, John J. G. (2018) [2006]. "Digital Magnetic Tape Recording". quadibloc. Archived from the original on 2018-07-02. Retrieved 2018-07-16.

• Johnson, Herbert R. (2016-07-06). "M2FM or MMFM diskette format". Archived from the original on 2017-06-18. Retrieved 2017-06-19.
• The PC Guide Frequency Modulation