CORDIC function basics
This page covers CORDIC algorithm basics. It covers CORDIC function uses. It describes CORDIC Rotation mode and Vector Mode.
CORDIC stands for Co-ordiate Rotation Digital Computer. It is the concept or algorithm used to calculate trigonometric (sin, cos) and hyperbolic (tan-1) functions. It works based on look up table concept. For example, you would like to calculate sin(φ) for some angle φ In this method, all the values of sin(φ) for each and every φ is stored in a memory (RAM). Later based on φ, corresponding value is outputted.
The cordic is used when hardware multiplier is not available. As CORDIC is used in FPGA/DSP where subtraction, addition, table lookup and bitshift operations are only available to be used.
CORDIC is used for operations such as sine, cosine, polar to rectangle, general rotation, arctangent, vector magnitude, rectangular to polar, Arcsine, Arccosine etc. It is also used for Linear Functions, Hyperbolic Functions, Square Rooting, Logarithms, Exponentials etc.
|Sine, Cosine||Rotation||x = 1/An, y = 0, z = α||Reduce z to Zero|
|Polar to Rect.||Rotation||x = (1/An)Xmag , y = 0, z = Xphase||Reduce z to Zero|
|General Rotation||Rotation||x = (1/An)X0 , y = (1/An)y0, z = α||Reduce z to Zero|
|Arctangent||Vector||x = (1/An)X0 , y = (1/An)y0, z = 0||Reduce y to zero|
|Vector Magnitude||Vector||x = (1/An)X0 , y = (1/An)y0, z = 0||Reduce y to zero|
|Rect. to Polar||Vector||x = (1/An)X0 , y = (1/An)y0, z = 0||Reduce y to zero|
|Arcsine, Arccosine||Vector||x = (1/An), y = 0, arg = sin(α) or cos(α)||Reduce y to value in arg register|
CORDIC rotation mode and vector mode
Following two modes rotation mode and vector modes are used.
Following table of CORDIC rotation angles is very useful. This is stored in the form of look up table and is derived when needed.
Useful Links to MATLAB codes
Refer following as well as links mentioned on left side panel for useful MATLAB codes.
OFDM Preamble generation Time off estimation corr Freq off estimation corr channel estimation 11a WLAN channel PN sequence generation OFDMA Tx Rx AES DES carrier aggregation CCDF FIR Filter IIR Filter Low Pass FIR Viterbi decoder CRC8 CRC32