[pd] FFT sine to saw oscilator (was:[pd] hanning window + fft)

[mami music]

Chuck! thanks a lot for your explanation, and yes, your solution of mixing
is definitely easier. I wanted to take another look at the same issue to
begin studying the fft functions.
Ill take a deep look into your explanation of fft and ifft. It gives me the
complete picture.

dan

2006/9/5, Charles Henry <czhenry at gmail.com>:
>
> to use the ifft for synthesis, you need to know the amplitude and
> phase for each frequency, and you need to express it as a complex
> number.
>
> z=a+b*i, a=Amp*cos(phase)  and b=Amp*sin(phase)
>
> fft~ gives two outlets, the left is the real part of the fourier
> transform, the right is the imaginary part.
> next thing is, the second half of your fourier coefficients are
> complex conjugates of your first half (when dealing with real-valued
> signals) according to the following pattern
>
> F(0) is real (the imaginary part is zero) and so is F(N/2)
> F(1)=F(N-1)*   where * denotes conjugate
> F(2)=F(N-2)*
> ...
> F(N/2-1)=F(N/2+1)*
>
> for a block size of 64,
> you've got 33 distinct real values (0 to N/2)
> and 31 distinct imaginary values (1 to N/2-1)
> to calculate before packing them all up into signals
>
> and there's some limitations.  To do things cleanly all of your
> frequencies need to be ingeter multiples of (sampling freq. fs/ N),
> the lowest frequency you can achieve with Fourier series on N points
>
> Luckily, your sawtooth and square waves are made up of frequencies in
> just this way.  But you're still limited to JUST the frequencies in
> your fourier transform (fs/N, 2*fs/N, 3*fs/N, ..., N/2 * fs/N)
>
> It's probably not the best way to do it, for what you're describing.
> You want to be able to continuously mix different levels of your saw,
> sine and squares as a function of time, right?
> I think you'll have better luck by just sync'ing up a phasor~ and an
> osc~, and creating your square wave (in phase) by using >~ and <~ on
> osc~ and summing the outputs together like
> [osc~]
> |     \
> [>~][<~]
> |      |
> |      [*~] [sig~ -1]
> |      |
> [+~]
> output square wave
>
> then just mix your signals together.
>
> Chuck
>
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