Sinusoidal function on a 16-bit microcontroller

Question

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

The sine wave itself will fluctuate between a value from 0 to 255, and 127 will be a center point.

Any ideas?

Answer 1

In fact, you only need to save one quarter of the sine wave - you can find the other three quarters from the first quadrant. Therefore you only need 256 bytes.

To generate values ​​on the microcontroller, run CORDIC . You can save one value and deduce from it the entire sine wave.

Answer 2

Create a pre-computed array on your PC. You only need to create the fourth part of the array if the ROM (or the equivalent, for example, a flash or code segment) is at a height, and then separate this part from the remaining 768 bytes of the array.

Answer 3

Write a sin table generator in your favorite language using float.
Scale and round the results to the desired ranges of 1024 / -127 .. + 128 (you can do it right away). From the table, create the source file in ASM or C, which will one day be better for you.
Make sure that the generated table with the marked “constant” in C or make goes to the allowed partition in ASM, so it goes to FLASH, not RAM.
Include the file in your project.

Now intsin (x) 1:

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

You can improve resolution using only the table for the first quadrant. You can use only positive values ​​(0..255). Then your intsin (x) will need to determine the quadrant and display the results of the first quadrant.

Answer 4

You simply create a table on your PC and use it on your MCU. Since someone said that you only need a quater period, but to fully answer your question, here are all 1,024 characters:

  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