Slider instead Play button to allow for real playing with visualization
vertical guiding lines like in Fig.2 in CORRELATION chapter to emphasize that sampling points stay at the same position
THE FOURIER TRANSFORM: interactive animation with sliders
This chapter requires quiet long "mental jump"
Personally, I would preset sliders setting to leave non zero for two of them to leave only 2 spinning circles.
(1: max and 3: 1/3 max for example to show something people are familiar one)
GEOMETRIC INTERPRETATION OF THE DFT: last equation
Maybe it is possible to recall definition of alpha like in the first equation in the chapter A WALKTHROUGH OF THE DFT
At first look there ere 3 free variables in the equation (k, n and alpha)
SINE WAVE ORTHOGONALITY
There two statement which seems to "interfere"
"any two sine waves whose frequencies are multiples of one another are also orthogonal"
"dot product is always zero unless the two waves are at the exact same frequency"
so taking into account that sliders positions are multiple of one can say that:
"a dot product of any integer frequencies are zero excluding the same frequency"
(examples: 2,3; 5,6)
Missing Prev button by the Next button.
PASSING THE NYQUIST LIMIT
vertical guiding lines like in Fig.2 in CORRELATION chapter to emphasize that sampling points stay at the same position
THE FOURIER TRANSFORM: interactive animation with sliders This chapter requires quiet long "mental jump" Personally, I would preset sliders setting to leave non zero for two of them to leave only 2 spinning circles. (1: max and 3: 1/3 max for example to show something people are familiar one)
GEOMETRIC INTERPRETATION OF THE DFT: last equation Maybe it is possible to recall definition of alpha like in the first equation in the chapter A WALKTHROUGH OF THE DFT At first look there ere 3 free variables in the equation (k, n and alpha)
SINE WAVE ORTHOGONALITY There two statement which seems to "interfere" "any two sine waves whose frequencies are multiples of one another are also orthogonal" "dot product is always zero unless the two waves are at the exact same frequency" so taking into account that sliders positions are multiple of one can say that: "a dot product of any integer frequencies are zero excluding the same frequency" (examples: 2,3; 5,6)