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4 thoughts on “The FFT Algorithm | The Secrets of the FFT | Part 4”
Hi Mark,
Thanks for this series it is very informative. I have tried following along in Python and comparing my outputs with Numpy’s FFT. I think there is a mistake in your ‘twiddle factor’ calculations. My outputs are off by a factor of -j when compared to numpy.
I get the correct answer if I calculate the twiddle factor as W = exp(-j * 2*pi*I/O) = cos(-2*pi*I/O) + j * sin(-2*pi*I/O); rather than W = exp(j * 2*pi*I/O).
I see where you are coming from. However, the meaning of the -j in exp(-j * 2*pi*I/O) does not mean that the 2pi is negative, rather, if you were to express the twiddle factor in polar form, you get cos(2*pi*I/O) – j * sin(2*pi*I/O) instead of cos(2*pi*I/O) + j * sin(2*pi*I/O). In other words, the sign between the cosine and sine terms is minus rather than plus. I do indeed have an error in the equation. Thank you for pointing it out I’ve corrected the equations in the 2 posts referring to the twiddle factors and in the JavaScript library which I wrote.
Hi therе would you mind sharing whіch blog platform you’re using?
I’m going to start my own blog in the near future but I’m having a hard time choosing between BlogEngine/Wordpress/B2evolution and Drupal.
The reason Ӏ ask is because your design seems different then most blogs and I’m loօking
for ѕomething completely unique.
P.S Sorry for ƅeing off-topic but I had to ask!
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Hi Mark,
Thanks for this series it is very informative. I have tried following along in Python and comparing my outputs with Numpy’s FFT. I think there is a mistake in your ‘twiddle factor’ calculations. My outputs are off by a factor of -j when compared to numpy.
I get the correct answer if I calculate the twiddle factor as W = exp(-j * 2*pi*I/O) = cos(-2*pi*I/O) + j * sin(-2*pi*I/O); rather than W = exp(j * 2*pi*I/O).
Regards,
Neil
I see where you are coming from. However, the meaning of the -j in exp(-j * 2*pi*I/O) does not mean that the 2pi is negative, rather, if you were to express the twiddle factor in polar form, you get cos(2*pi*I/O) – j * sin(2*pi*I/O) instead of cos(2*pi*I/O) + j * sin(2*pi*I/O). In other words, the sign between the cosine and sine terms is minus rather than plus. I do indeed have an error in the equation. Thank you for pointing it out I’ve corrected the equations in the 2 posts referring to the twiddle factors and in the JavaScript library which I wrote.
Hi therе would you mind sharing whіch blog platform you’re using?
I’m going to start my own blog in the near future but I’m having a hard time choosing between BlogEngine/Wordpress/B2evolution and Drupal.
The reason Ӏ ask is because your design seems different then most blogs and I’m loօking
for ѕomething completely unique.
P.S Sorry for ƅeing off-topic but I had to ask!
I use WordPress