of Microprocessors

426
MUSICAL ApPLICATIONS OF MICROPROCESSORS
AOORESS OF TABLE ENTRY
,
3 BYTES IN
MEMORY
PAGE NUMBER
Fig. 13-4. Table scanning in an a-bit microprocessor
entries skipped is less than one-half the period of the highest significant
harmonic in the tabulated waveform, nothing is lost and no audible noise is
added. If the number of entries skipped becomes larger than this, alias
distortion occurS. Also, the fact that each trip around the table is likely to be
different is of no significance, since the effect would be the same as sampling
a waveform at a rate that is not an exact multiple of its frequency.
As before, only a very few frequencies can be generated with integer
increments, so it will be necessary to extend the precision of the increment by
adding afractional part. Now, the pointer increment and the table pointer are
mixed numbers having an integer part and a fractional part. Note that the
fractional part of the pointer implies some kind of interpolation between
adjacent table entries. For maximum speed, however, the fractional part of
the pointer can be ignored and the integer part used to select the table entry
as before.
A simple example should clarify this some. Let us assume a moderateperformance
direct synthesis sytem with a sample rate of 15 ks/s and
waveform tables having 256 entries of 8 bits each. If a tone frequency of 220
Hz (A below middle C) is desired, the pointer increment should be 3.75466
according to the formula: I = NFIFs, where I is the increment, N is the
number of table entries, F is the tone frequency, and Fs is the sample rate. In
an 8-bit machine, it is convenient to make the pointer and the increment
double-byte mixed numbers with the upper byte being the integer part and
the lower byte being the fractional part. Thus, the decimal mixed number,
3.75466 would have an integer part of 3 and a fractional part of 193, the
latter being 0.75466 multiplied by 256.
To get the next sample from the table, the increment would be
double-precision added to the pointer with overflow from the integer parts
ignored. Then the integer part of the pointer would be used to access the
table. If the microprocessor has an indirect addressing mode through memory
like the 6502, then Fig. 13-4 illustrates how utterly simple these
operations are. A three-byte vector in memory is used for each tone. The
most significant byte gives the page address of the waveform table, while the
remaining two bytes are the pointer. An indirect load through the leftmost
two bytes of the vector are all that is necessary for the table lookup! In the
6502, the entire operation of adding the increment and getting the next