How to implement sine wave using Taylors series?

applied numerical methods by carnahan ebook

Hi,

i need design for FPGA implementation of sine wave using Taylor's series .
Can any one guide me .

Thanks In Advance.

USMAN HAI

sinus as taylor series

For any given precision (16bit, 32, 64FP, etc) there will be an optimised finite Taylor series, sometimes with only 4 to 6 terms. A good source of the coefficients is the source code of the maths library of open source compilers.

Git

carnahan luther wilkes

the Taylor series is easy to derive but not a very good method of calculating sines, Taylor series being expanded about a single point. if you have a choice of methods, you might want to look at Chebyshev polynomials, "Applied Numerical Methods" - Carnahan, Luther, Wilkes, is a painless introduction

Re: Taylor's series

if you have the right to choose any method I recommend CORDIC algorithm. It is easy and precise

Re: Taylor's series

Let me distinguish two different cases:

1) it is required to calculate the sinus of an arbitrary argument at any time
2) it is required an oscillator

In the first case, polynomial approximation is good. It has the form of a power series, but the coefficients are not exactly the same as in the Taylor series because they are optimized for some objective (minimum peak error, minimum rms error) over the interval of interest.
For the sin() function, a polynomial in the interval [0,pi/2] is needed.

In the second case, the values are calculated sequentially, not in a random order. This allows a simpler implementation. One of the simplest is a coupled oscillator, that has the form of a second order IIR filter with a pole pair on the unit circle and can produce sinus and cosinus outputs. Look for coupled oscillator in some book on Digital Signal Processing. (Means have to be provided for controlling the amplitude of the oscillation).

Regards

Z

Re: Taylor's series

Hi Usman Hai,

Why do you need to perform Tailor series in FPGA instead of in uC?
How ar you going to use the sine wave?
Can you describe your project?

ragards
dora

Re: Taylor's series

cherrytart said:

the Taylor series is easy to derive but not a very good method of calculating sines, Taylor series being expanded about a single point. if you have a choice of methods, you might want to look at Chebyshev polynomials, "Applied Numerical Methods" - Carnahan, Luther, Wilkes, is a painless introduction

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hi, is there ebook version for the book?