12-09-2018, 02:54 AM

I hope you can help me. I am trying to understand how the fast Fourier transform is calculated (FFT).

Sample problem:

n_0 = 0.54

n_1 = 0.66

n_2 = 0.52

where N = 3

The formula to the FFT (I think) is:

X_k = Σ( x_n * e^(-i * 2 * π * k * n / N) ) for n = 0 to N-1

Using the formula above I get:

X_0 = 1.62

X_1 = 0

X_2 = 0

But the fft function on the HP Prime returns:

1.72

-0.05 - 0.12124355653i

-0.05 + 0.12124355653i

However Wolfram Alpha returns:

0.993042

-0.0288675 + 0.07i

-0.0288675 - 0.07i

I am confused. Are there different fast Fourier transforms or am I missing something obvious? I want to understand the basic calculation before I attempt to understand the Tukey and Cooley algorithm. Any help and insight is appreciated. Thanks!

Sample problem:

n_0 = 0.54

n_1 = 0.66

n_2 = 0.52

where N = 3

The formula to the FFT (I think) is:

X_k = Σ( x_n * e^(-i * 2 * π * k * n / N) ) for n = 0 to N-1

Using the formula above I get:

X_0 = 1.62

X_1 = 0

X_2 = 0

But the fft function on the HP Prime returns:

1.72

-0.05 - 0.12124355653i

-0.05 + 0.12124355653i

However Wolfram Alpha returns:

0.993042

-0.0288675 + 0.07i

-0.0288675 - 0.07i

I am confused. Are there different fast Fourier transforms or am I missing something obvious? I want to understand the basic calculation before I attempt to understand the Tukey and Cooley algorithm. Any help and insight is appreciated. Thanks!