These technique it helps us to make pure sine inverters or to generate sine signals with different frequencyes. As we know from previous posts some pins of arduino can generate PWM signals at high frequencies, so we will utilize this and adapt for sine equation.

So 10ms is half cycle period. To generate a sine wave we will use two pins one for positive half cycle and one for negative half cycle. For a smooth signal we choose phase correct pwm at a frequency Hz -see previous post.

One of the biggest problem is that how we calculate the necessary duty cycle for each pulse. That means for every pulse we move forward with 0. But we want to alternate pins for each half cycle and make a variable duty cycle for each pulse. For this thing we use another timer Timer 1 in CTC mode with interrupts. To change the duty cycle at every pulse on pins 5 and 6 we must generate interrupts with a Hz to enable one interrupt at the same time with an pulse on pins 5 and 6.

## How to generate a sine wave from arduino or atmega 328

At interrupts when timer hits the compare match value the interrupt is generate, so number 2 dissapear. To be sure there is no problem with interrupts we will use cli stop interrupts and sei enable interrupts. As you can see we have in vector elements and the program only because at last we have the transition between pins, and on the oscilloscope we have a better frequency.

Another thing we can see here is time between switching pins. In the image below is represented the output signal from the two pins:. At last the frequency on this application is between In this picture is presented only a half cycle because i have used only one low pass filter i had only one capacitor and you can see that the resulting frequency is Because someone ask me how to generate such a signal on pins 9 and 10 next is a program that generate a sine wave at 50Hz on pins 9 and 10 :.

Hithank you for this very very good tutorialif I want to put the frequency of 60 Hz which should be the value of OCR2A?? Thank you in advance. For 60 Hz the period of this signal is In the vector you should have elements with different values from the our example and in the ISR where appear you must have or if give you an more precise frequency.

Thank you sir for your reply, is what it is inside of these braces I have to put the Elements?? Yes but i repead with your values. Yes you must have the same specification as the machines you want to power or the grid. Try to understand all the aspects of the project. Hello sir, please can you make a tutorial where the frequency is 60 Hz?

For weeks I try to do it but I can not. Glad i could help! Yes Sir, i will share my projet when i finishâ€¦Sir what is the value of the film capacitor you use for the low-pass filter still 22 uf?? Around 1uF i have had three in paralel with small capacities total 1.

Be aware that for transistors you should use the pwm signal not filtered!If you like the article click the follow button from social media to stay in touch with us! The default frequency of arduino PWM pins is around Hz for 9, 10, 3,11 and around HZ for 5, 6, but for many applications we need some higher frequencies.

The arduino uno can generate frequencies for PWM pins up to 8Mhz.

To modify these values we need to work with timers which contains registers. For PWM, arduino has three timers one for two pins like:. This mode has half of fast pwm mode frequency. It is preferred in motors control picture from atmega datasheet. CTC mode -in this mode timer count to a TOP value and when it reach that value clear the timer and execute something.

This mode let us to make very precise operation picture from atmega datasheet. Timer 0 manage pins 5 and 6, so next in a couple of examples we will show you how to manage the pwm frequencies. In the image below we have such a signal This mode has advantage that can reach very high frequencies but the disavantage is that you have a fix duty cycle. If OCR0A is 50 and no prescaler the frequency from formula is The prescaler is used to control the frequency from formules and is managed in the TCCR0B register like in the images from atmega datasheet.

Which of programs you have try because each of them i have analized on the oscilloscope and work well??? Is this code just used on a standard arduino uno and could it possibly be modified to work on a standalone atmega to produce a 40kHz pwm signal?

Sorry for late response! Hi, very nice Tutorial! Is that possible?

### C++ Fast Trigonometric Functions

Currently you have JavaScript disabled. In order to post comments, please make sure JavaScript and Cookies are enabled, and reload the page. Click here for instructions on how to enable JavaScript in your browser. Please let us in the comment zone any suggestions that you think will improve the article! But first bit and the third why are they 1??? The prescaler is used to control the frequency from formules and is managed in the TCCR0B register like in the images from atmega datasheet It is controlled by CS00, CS01 and CS02 bits with different combinations as you can see in the image above.

How to control arduino pins from registers without digitalWrite and digitalRead. December 30, admin 0. November 27, admin 0. November 26, admin 0.By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. The dark mode beta is finally here. Change your preferences any time. Stack Overflow for Teams is a private, secure spot for you and your coworkers to find and share information.

I am googling the question for past hour, but there are only points to Taylor Series or some sample code that is either too slow or does not compile at all. Well, most answer I've found over Google is "Google it, it's already asked", but sadly it's not I cannot optimize this three functions out, nor calculate both sine and cosine in one pass there interdependentbut I don't need too accurate results for my simulation, so I can live with faster approximation.

The CPUs are just so fast these days, and cache is not. I made a mistake, I though that I need to calculate several factorials for Taylor Series, and I see now they can be implemented as constants. BUT if you insist upon computing at runtime you can use the Taylor series expansion of sine or cosine For more on the Taylor series One of the keys to getting this to work well is pre-computing the factorials and truncating at a sensible number of terms.

The factorials grow in the denominator very quickly, so you don't need to carry more than a few terms. It is also not the way professional libraries implement these trigonometric functions, and knowing the best numerical implementation allows you to tweak the accuracy to get speed more efficiently.

In addition, this problem has already been extensively discussed in StackOverflow. Here is just one example. It is quite hard to beat them on execution speed. Finally, let's talk about the code on your old PC.

Check gsl gnu scientific library or numerical recipes implementation, and you will see that they basically use Chebyshev Approximation Formula.

## Arduino Is Slow - and How to Fix It!

Chebyshev approximation converges faster, so you need to evaluate fewer terms. I won't write implementation details here because there are already very nice answers posted on StackOverflow. Check this one for example. This will decrease the precision, but it seems that is exactly what you want. Oh, you wanted better accuracy than 1. Well, here is a sine function that is similarly fast:. This answer actually does not suckwhen x is close to zero.

For small x, sin x is approximately equal to x. Engineers in the s made some fantastic discoveries in this field, but new programmers are simply unaware that these methods exist, because they're not taught as part of standard computer science curricula.

You need to start by understanding that there is no "perfect" implementation of these functions for all applications.Post a Comment. To improve algorithm performance, one direct way is to shorten calculation time. The part that consumes the most computation power would be the trig functions. The built-in trig functions are generally very good in terms of accuracy. But we don't need that level of precision, so we can sacrifice accuracy to achieve faster speed.

Firstly I generated a list of input from 0 towith equal intervals, and get a list of results for each input. The reason that I use 1 degree instead of smaller interval, is that not only it saves spaces, but also I won't need that kind of precision.

Actually, we don't need the full cycle of SIN, we just need the first quarter cycle, because the whole cycle can be replicated by the first quarter, so we save a lot of memory! The difference is just on the indexing. Also the table need to be huge because we can't reduce table size like what we did in the SIN function. So might be better to use infinite series stated here. It should be noted that the more accurate, the higher power term needs to be computed.

Power is a terrible performance killer, so I will only keep the first 4 terms. To verify the accuracy, we can compare the built-in method with the 'polynomial' method in Excel. Email This BlogThis! No comments:. Post a Comment Note: only a member of this blog may post a comment. Newer Post Older Post Home. Subscribe to: Post Comments Atom.By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service.

Arduino Stack Exchange is a question and answer site for developers of open-source hardware and software that is compatible with Arduino. It only takes a minute to sign up. I am using an Arduino Uno board to compute the angles of my system robotic arm. I am only going to be operating in the 1st quadrant 0 to 90 degwhere both sines and cosines are positive, so there is no problem with negative numbers. My doubts can be expressed in 3 questions:. There are the sin and cos functions in the Arduino IDE, but how does the Arduino actually calculate them as in do they use look-up tables, or approximations etc.

They seem like an obvious solution, but I would like to know their actual implementation before I try them out. PS: I am open to both standard coding on the Arduino IDE and assembly coding, as well as any other options not mentioned. Also I have no problems with errors and approximations, which are inevitable for a digital system; however if possible it would be good to mention the extent of possible errors.

The Arduino's math library libm, part of avr-libc uses the former. Rest assured though it will be the most optimised pure-float implementation brains far superior to ours could come up with. However the key there is float.

Anything on the Arduino involving floating point is going to be heavyweight by comparison to pure integer, and since you are only requesting integers between 0 and 90 degrees a simple lookup table is by far the simplest and most efficient method. A table of 91 values will give you everything from 0 to 90 inclusive. However if you make that a table of floating point values between 0. That may be as simple as storing the value multiplied byso you have between 0 and instead of between 0.

These Q16 values and the related Q15, Q1. Don't forget as well that the sin function expects radians, so you first have to convert your integer degrees into a floating point radians value, making the use of sin even more inefficient compared to a lookup table that can work directly with the integer degrees value. A combination of the two scenarios, though, is possible. Linear interpolation will allow you to get an approximation of a floating point angle between two integers. It's as simple as working out how far between two points in the lookup table you are and creating a weighted average based on that distance of the two values.

For instance if you are at Basically your sine wave becomes a series of discrete points joined together by straight lines. You trade accuracy for speed. There are some good answers here but I wanted to add a method which hasn't been mentioned yet, one very well suited to computing trigonometric functions on embedded systems, and that's the CORDIC technique Wiki Entry Here It can compute trig functions using only shifts and adds and a small look-up table.

Here's a crude example in C. It uses floating point, but can be adapted for use with fixed-point arithmetic. I have been playing a bit with computing sines and cosines on the Arduino using fixed-point polynomial approximations. Here are my measurements of average execution time and worst case error, compared with the standard cos and sin from avr-libc:.

The multiplications themselves are done in assembly, as I found that gcc implemented them inefficiently. If you think this can suit your bill, here is the code: Fixed-point trigonometry.By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. The dark mode beta is finally here. Change your preferences any time.

Stack Overflow for Teams is a private, secure spot for you and your coworkers to find and share information. I am rendering x points in real-time.

**Stepper motors with arduino, Finding the maximum speed / acceleration curves**

I have to compute the position of points using atan and sin functions. By using atan and sin I am getting 24 fps frames per second. So, the big problem is with sin.

How can I use Fast Sin version. Can I create a Look Up Table for that? I don't have any specific values to create LUT. It depends on the accuracy that you need. The maximum derivative of sin is 1, so if if x1 and x2 are within epsilon of one another, then sin x1 and sin x2 are also within epsilon. If you just need accuracy to within, say 0.

This can be faster than what the native code does, since the native code probably uses a lookup table for polynomial coefficients, and then interpolates, and since this table can be small enough to stay in cache easily. If you need complete accuracy over the whole range, then there's probably nothing better that you can do. Defining your error tolerance is important for figuring out what shortcuts you can take. You have a triangle, you're computing the hypoteneuse.

First, you're taking atan value to get the angle, and then using value again with sin to compute h. So we have the scenario where one side of the triangle is But then, sqrt isn't the fastest function around either. Perhaps I've missed the point or you've left something out.

I've always used lookup tables for sin and cosand found them to be fast. If you don't know the values ahead of time then you need to approximate, but this means a multiplication, truncation to integer and possibly sign conversion in order to get the array index.This is a custom math library for Arduinowhich should be more efficient than the standard C math library.

At the moment I have come up with functions: sincosacosatan2which has proven to be faster. Part of the implementation is at the end of this post. They are not necessary better than the old ways, so I will be comparing them in the next section. The performance really depends on the hareware architecture and varies from platform to platform.

All results were measured in micro seconds us. Both functions were run 2 million times with a random input between 0 to degree, for built-in way and new way. I am not testing the old way because the new way is almost the same as the old way except the look-up table size is now doubled.

The acos functions were run times with a random input between 0 and 1. This function were runtimes with two random float numbers between I lost the exact result data to this one, but the outcome clearly shown the built-in way is still far better than the new implementation. This one is a interesting one. In theory, arithmetical operations should be faster with long and integer data than float generally.

When this scaled number is multiplied or divided by another scaled number with the same precision for example 1. And that introduces overhead to the computation, we could just have this:. The long data type performed quite well with low number of arithmetical operations and higher number of additions. But as expected, the more multiplications and divisions, the closer it gets to performance of the float type. It even became worse than float when there are more divisions involved. Obviously the more operations we do, the more computationally expensive it gets, which will not do us any good.

Besides, in the Arduino Architecture, float and long both take up 32 bits, so there is no advantage of replacing float with long data type memory wise. Therefore we will stick to float when needed. The same applies to the look-up table. Some might suggest to use Integer type data for it, which is 16 bits Verse 32 bits for float currently using. But if the output of the trigonometry functions are float, that means we will have to do conversions probably with divisions involved before output.

This will kill the performance. So whenever is possible, I should stick to float type in the look-up table so I can use the data directly. One thing we should not do is to use other platforms other than Arduino itself for performance testings. Because it varies from architectures to architectures.

You can now find the library in GitHub not my account. Hi Oscar, you made a good work. I was thinking to reimplement them as you made, but fortunately, before I made a search on the web. Could you provide the sources of the lib? Thanks Francesco.

Really struggling with the math. Would love it if you could share your library with me This sounds great, can I be emailed the library please?

And what licensing will be needed if I use this in a commercial project?