sine function on 16-bit microcontroller

Question

I need to generate a sine wave to fill a char table of size 1024. The word size on the microcontroller is 16-bit and floating-point operations are not available.

The sine wave itself will oscillate between the value of 0 to 255, with 127 being the center point.

Any ideas?

Answer 1

You only actually need to store one quarter of the sine wave -- you can lookup the other three quarters from the first quadrant. So you only need 256 bytes.

To generate the values on the micro controller, implement CORDIC. You can store one value, and generate the whole sine wave from that.

Answer 2

Create a precomputed array on your PC. You only have to create a fourth of the array if ROM (or equivalent, such as flash or code segment) space is at a premium, then mirror this part out to the other 768 bytes of the array.

Answer 3

Write a sin table generator in your favorite language using float.
Scale and round the results to desired ranges 1024/-127..+128 (you may do that right away). From the table, generate a source file in ASM or C, what ever works better for you.
Make sure the generated table in marked "const" in C or make go to a approbiate section in ASM so it goes to FLASH rather than RAM.
Include the file in your project.

Now intsin(x)1 is:

int intsin(int x)
limit x // 0..360° or 2PI
scale to 1024
read table at x
return x

You can improve resolution by using the table for the first quadrant only. You can than use positive values only, too (0..255). Then your intsin(x) would need to determine the quadrant and mirror the first quadrant results.

Answer 4

You just generate table on your PC and use it on your MCU. As somebody said you just need a quater period, but to answer your question fully, here are all 1024 chars:

  for k := 0 to 1023 do
      buffer[k] := (round(128+127*sin(2*pi*k/1024)));


128, 129, 130, 130, 131, 132, 133, 133, 134, 135, 136, 137, 137, 138, 139, 140, 140, 
141, 142, 143, 144, 144, 145, 146, 147, 147, 148, 149, 150, 150, 151, 152, 153, 
154, 154, 155, 156, 157, 157, 158, 159, 160, 160, 161, 162, 163, 163, 164, 165, 
166, 166, 167, 168, 169, 169, 170, 171, 172, 172, 173, 174, 174, 175, 176, 177, 
177, 178, 179, 179, 180, 181, 182, 182, 183, 184, 184, 185, 186, 186, 187, 188, 
189, 189, 190, 191, 191, 192, 193, 193, 194, 195, 195, 196, 197, 197, 198, 199, 
199, 200, 200, 201, 202, 202, 203, 204, 204, 205, 206, 206, 207, 207, 208, 209, 
209, 210, 210, 211, 212, 212, 213, 213, 214, 214, 215, 216, 216, 217, 217, 218, 
218, 219, 219, 220, 221, 221, 222, 222, 223, 223, 224, 224, 225, 225, 226, 226, 
227, 227, 228, 228, 229, 229, 230, 230, 230, 231, 231, 232, 232, 233, 233, 234, 
234, 234, 235, 235, 236, 236, 237, 237, 237, 238, 238, 239, 239, 239, 240, 240, 
240, 241, 241, 241, 242, 242, 242, 243, 243, 243, 244, 244, 244, 245, 245, 245, 
246, 246, 246, 246, 247, 247, 247, 248, 248, 248, 248, 249, 249, 249, 249, 250, 
250, 250, 250, 250, 251, 251, 251, 251, 251, 252, 252, 252, 252, 252, 252, 253, 
253, 253, 253, 253, 253, 253, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254, 
254, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 
255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 254, 254, 
254, 254, 254, 254, 254, 254, 254, 254, 254, 253, 253, 253, 253, 253, 253, 253, 
252, 252, 252, 252, 252, 252, 251, 251, 251, 251, 251, 250, 250, 250, 250, 250, 
249, 249, 249, 249, 248, 248, 248, 248, 247, 247, 247, 246, 246, 246, 246, 245, 
245, 245, 244, 244, 244, 243, 243, 243, 242, 242, 242, 241, 241, 241, 240, 240, 
240, 239, 239, 239, 238, 238, 237, 237, 237, 236, 236, 235, 235, 234, 234, 234, 
233, 233, 232, 232, 231, 231, 230, 230, 230, 229, 229, 228, 228, 227, 227, 226, 
226, 225, 225, 224, 224, 223, 223, 222, 222, 221, 221, 220, 219, 219, 218, 218, 
217, 217, 216, 216, 215, 214, 214, 213, 213, 212, 212, 211, 210, 210, 209, 209, 
208, 207, 207, 206, 206, 205, 204, 204, 203, 202, 202, 201, 200, 200, 199, 199, 
198, 197, 197, 196, 195, 195, 194, 193, 193, 192, 191, 191, 190, 189, 189, 188, 
187, 186, 186, 185, 184, 184, 183, 182, 182, 181, 180, 179, 179, 178, 177, 177, 
176, 175, 174, 174, 173, 172, 172, 171, 170, 169, 169, 168, 167, 166, 166, 165, 
164, 163, 163, 162, 161, 160, 160, 159, 158, 157, 157, 156, 155, 154, 154, 153, 
152, 151, 150, 150, 149, 148, 147, 147, 146, 145, 144, 144, 143, 142, 141, 140, 
140, 139, 138, 137, 137, 136, 135, 134, 133, 133, 132, 131, 130, 130, 129, 128, 
127, 126, 126, 125, 124, 123, 123, 122, 121, 120, 119, 119, 118, 117, 116, 116, 
115, 114, 113, 112, 112, 111, 110, 109, 109, 108, 107, 106, 106, 105, 104, 103, 
102, 102, 101, 100, 99, 99, 98, 97, 96, 96, 95, 94, 93, 93, 92, 91, 
90, 90, 89, 88, 87, 87, 86, 85, 84, 84, 83, 82, 82, 81, 80, 79, 
79, 78, 77, 77, 76, 75, 74, 74, 73, 72, 72, 71, 70, 70, 69, 68, 
67, 67, 66, 65, 65, 64, 63, 63, 62, 61, 61, 60, 59, 59, 58, 57, 
57, 56, 56, 55, 54, 54, 53, 52, 52, 51, 50, 50, 49, 49, 48, 47, 
47, 46, 46, 45, 44, 44, 43, 43, 42, 42, 41, 40, 40, 39, 39, 38, 
38, 37, 37, 36, 35, 35, 34, 34, 33, 33, 32, 32, 31, 31, 30, 30, 
29, 29, 28, 28, 27, 27, 26, 26, 26, 25, 25, 24, 24, 23, 23, 22, 
22, 22, 21, 21, 20, 20, 19, 19, 19, 18, 18, 17, 17, 17, 16, 16, 
16, 15, 15, 15, 14, 14, 14, 13, 13, 13, 12, 12, 12, 11, 11, 11, 
10, 10, 10, 10, 9, 9, 9, 8, 8, 8, 8, 7, 7, 7, 7, 6, 
6, 6, 6, 6, 5, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 3, 
3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 
2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 
2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 
4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 
7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 10, 10, 10, 10, 11, 
11, 11, 12, 12, 12, 13, 13, 13, 14, 14, 14, 15, 15, 15, 16, 16, 
16, 17, 17, 17, 18, 18, 19, 19, 19, 20, 20, 21, 21, 22, 22, 22, 
23, 23, 24, 24, 25, 25, 26, 26, 26, 27, 27, 28, 28, 29, 29, 30, 
30, 31, 31, 32, 32, 33, 33, 34, 34, 35, 35, 36, 37, 37, 38, 38, 
39, 39, 40, 40, 41, 42, 42, 43, 43, 44, 44, 45, 46, 46, 47, 47, 
48, 49, 49, 50, 50, 51, 52, 52, 53, 54, 54, 55, 56, 56, 57, 57, 
58, 59, 59, 60, 61, 61, 62, 63, 63, 64, 65, 65, 66, 67, 67, 68, 
69, 70, 70, 71, 72, 72, 73, 74, 74, 75, 76, 77, 77, 78, 79, 79, 
80, 81, 82, 82, 83, 84, 84, 85, 86, 87, 87, 88, 89, 90, 90, 91, 
92, 93, 93, 94, 95, 96, 96, 97, 98, 99, 99, 100, 101, 102, 102, 103, 
104, 105, 106, 106, 107, 108, 109, 109, 110, 111, 112, 112, 113, 114, 115, 116, 
116, 117, 118, 119, 119, 120, 121, 122, 123, 123, 124, 125, 126, 126, 127