Real FFT Tables

const q15_t __ALIGNED (4)

const float32_t realCoefA[8192]

const float32_t realCoefB[8192]

const q31_t realCoefAQ31[8192]

const q31_t realCoefBQ31[8192]

group Real FFT Tables

Functions

const q15_t __ALIGNED (4)

Weights Table.

Q15 table for reciprocal.

end of DCT4_IDCT4_Table group

Generation fixed-point realCoefAQ15 array in Q15 format:

n = 4096

for (i = 0; i < n; i++)
{
   pATable[2 * i]     = 0.5 * ( 1.0 - sin (2 * PI / (double) (2 * n) * (double) i));
   pATable[2 * i + 1] = 0.5 * (-1.0 * cos (2 * PI / (double) (2 * n) * (double) i));
}

Convert to fixed point Q15 format round(pATable[i] * pow(2, 15))

Generation of real_CoefB array:

n = 4096

for (i = 0; i < n; i++)
{
   pBTable[2 * i]     = 0.5 * (1.0 + sin (2 * PI / (double) (2 * n) * (double) i));
   pBTable[2 * i + 1] = 0.5 * (1.0 * cos (2 * PI / (double) (2 * n) * (double) i));
}

Convert to fixed point Q15 format round(pBTable[i] * pow(2, 15))

Weights tables are generated using the formula :

weights[n] = e^(-j*n*pi/(2*N))

C command to generate the table

for(i = 0; i< N; i++)
{ 
  weights[(2*i)]   =  cos(i*c);
  weights[(2*i)+1] = -sin(i*c);
} 

where N is the Number of weights to be calculated and c is pi/(2*N)

Converted the output to q15 format by multiplying with 2^31 and saturated if required.

In the tables below the real and imaginary values are placed alternatively, hence the array length is 2*N.

cosFactor tables are generated using the formula :

cos_factors[n] = 2 * cos((2n+1)*pi/(4*N)) 

C command to generate the table

for (i = 0; i< N; i++)
{
  cos_factors[i] = 2 * cos((2*i+1)*c/2);
} 

where N is the number of factors to generate and c is pi/(2*N)

Then converted to q15 format by multiplying with 2^31 and saturated if required.

Variables

const float32_t realCoefA[8192]

Generation of realCoefA array:

n = 4096

for (i = 0; i < n; i++)
{
   pATable[2 * i]     = 0.5 * ( 1.0 - sin (2 * PI / (double) (2 * n) * (double) i));
   pATable[2 * i + 1] = 0.5 * (-1.0 * cos (2 * PI / (double) (2 * n) * (double) i));
}

const float32_t realCoefB[8192]

Generation of realCoefB array:

n = 4096

for (i = 0; i < n; i++)
{
   pBTable[2 * i]     = 0.5 * (1.0 + sin (2 * PI / (double) (2 * n) * (double) i));
   pBTable[2 * i + 1] = 0.5 * (1.0 * cos (2 * PI / (double) (2 * n) * (double) i));
}

const q31_t realCoefAQ31[8192]

Generation fixed-point realCoefAQ31 array in Q31 format:

n = 4096

for (i = 0; i < n; i++)
{
   pATable[2 * i]     = 0.5 * ( 1.0 - sin (2 * PI / (double) (2 * n) * (double) i));
   pATable[2 * i + 1] = 0.5 * (-1.0 * cos (2 * PI / (double) (2 * n) * (double) i));
}

Convert to fixed point Q31 format round(pATable[i] * pow(2, 31))

const q31_t realCoefBQ31[8192]

Generation of realCoefBQ31 array:

n = 4096

for (i = 0; i < n; i++)
{
   pBTable[2 * i]     = 0.5 * (1.0 + sin (2 * PI / (double) (2 * n) * (double) i));
   pBTable[2 * i + 1] = 0.5 * (1.0 * cos (2 * PI / (double) (2 * n) * (double) i));
} 

Convert to fixed point Q31 format round(pBTable[i] * pow(2, 31))