Re: [music-dsp] Fast convolution with synthesis window

On 10/4/15 12:36 PM, Earl Vickers wrote: rbj wrote: why would you *want* to use a synthesis window if you're doing OLA fast-convolution? Good question. [ ] it might be a very nice way to have a changing filter kernel and have it sound nice in the transitions. Good answer! Yes, I’m doing ti

Re: [music-dsp] Fourier and its negative exponent

>the reason why it's merely convention is that if the minus sign was swapped >between the forward and inverse Fourier transform in all of the literature and >practice, all of the theorems would work the same as they do now. Note that in some other areas they do actually use other conventions. It's

Re: [music-dsp] test (sorry)

On 10/5/15 5:58 PM, Stijn Frishert wrote: > Your mail (the first copy) was well received and is still ringing through my > mind. Especially the part about -j and +j having equal claim to square to -1 > is an eye opener. check out "Imaginary unit" at Wikipedia. > I'm still thinking about the con

Re: [music-dsp] test (sorry)

Hi Robert, Your mail (the first copy) was well received and is still ringing through my mind. Especially the part about -j and +j having equal claim to square to -1 is an eye opener. I'm still thinking about the consequences and need to write some stuff out on paper, but I'll get back to it. Th

Re: [music-dsp] Fourier and its negative exponent

On 10/5/15 5:40 PM, robert bristow-johnson wrote: about an hour ago i posted to this list and it hasn't shown up on my end. okay, something got lost in the aether. i am reposting this: On 10/5/15 9:28 AM, Stijn Frishert wrote: In trying to get to grips with the discrete Fourier transform, I

[music-dsp] test (sorry)

about an hour ago i posted to this list and it hasn't shown up on my end. -- r b-j r...@audioimagination.com "Imagination is more important than knowledge." ___ dupswapdrop: music-dsp mailing list music-dsp@music.columbia.edu ht

Re: [music-dsp] Fourier and its negative exponent

On 10/5/15 9:28 AM, Stijn Frishert wrote: In trying to get to grips with the discrete Fourier transform, I have a question about the minus sign in the exponent of the complex sinusoids you correlate with doing the transform. The inverse transform doesn’t contain this negation and a quick searc

Re: [music-dsp] Fourier and its negative exponent

"does not mean" > "does mean" Esteban On 10/5/2015 8:47 PM, Esteban Maestre wrote: By the way: complex-conjugate does not mean it rotates in opposite direction; check out this picture: http://www.eetasia.com/STATIC/ARTICLE_IMAGES/200902/EEOL_2009FEB04_DSP_RFD_NT_01c.gif Rotation in opposite

Re: [music-dsp] Fourier and its negative exponent

By the way: complex-conjugate does not mean it rotates in opposite direction; check out this picture: http://www.eetasia.com/STATIC/ARTICLE_IMAGES/200902/EEOL_2009FEB04_DSP_RFD_NT_01c.gif Rotation in opposite direction happens with negative frequencies. Cheers, Esteban On 10/5/2015 8:06 PM, S

Re: [music-dsp] Fourier and its negative exponent

Think of the Fast Fourier Transform as computing the inner product of a piece of signal (the length of the transform) with all kinds of basis functions: the various frequencies that can "fit" in the interval. Without going into engineering basics, you can take a sine and a cosine as a basis func

Re: [music-dsp] Fourier and its negative exponent

Hi again, You can see the Fourier Transform as a projection. Finding projections can be seen as computing inner products. Inner products of complex numbers (or functions) involve complex-conjugating one of the numbers (functions). Here's an alternative read: https://sites.google.com/site/bu

Re: [music-dsp] Fourier and its negative exponent

Thanks Allen, Esteban and Sebastian. My main thought error was thinking that negating the exponent was the complex equivalent of flipping the sign of a non-complex sinusoid (sin and -sin). Of course it isn’t. e^-a isn’t the same as -e^a. The real part of a complex sinusoid and its complex conju

Re: [music-dsp] Fourier and its negative exponent

Since e^(-jw) equals 1/(e^(jw)), the same sinusoids are used, just reverting what the other transformation did. No phase shift involved. Sebastian Stijn Frishert wrote: Hey all, In trying to get to grips with the discrete Fourier transform, I have a question about the minus sign in the expo

Re: [music-dsp] Fourier and its negative exponent

On 10/5/2015 6:15 PM, Esteban Maestre wrote: the complex sinusoid you are "testing", and its complex-conjugate Sorry: I mean "your signal and the complex sinusoid your are testing". Esteban -- Esteban Maestre CIRMMT/CAML - McGill Univ MTG - Univ Pompeu Fabra http://ccrma.stanford.edu/~este

Re: [music-dsp] Fourier and its negative exponent

HI Stijn, That "minus" comes from complex-conjugate (of Euler's formula). To find the projection coefficients (Fourier Transform), in each of the terms in the summation one computes the inner product of two complex vectors: the complex sinusoid you are "testing", and its complex-conjugate. The

Re: [music-dsp] Fourier and its negative exponent

In Chapter 7 of Think DSP, I develop the DFT in a way that might help with this: http://greenteapress.com/thinkdsp/html/thinkdsp008.html If you think of the inverse DFT as matrix multiplication where the matrix, M, contains complex exponentials as basis vectors, the (forward) DFT is the multiplic

[music-dsp] Fourier and its negative exponent

Hey all, In trying to get to grips with the discrete Fourier transform, I have a question about the minus sign in the exponent of the complex sinusoids you correlate with doing the transform. The inverse transform doesn’t contain this negation and a quick search on the internet tells me Fourie

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Re: [music-dsp] Fast convolution with synthesis window

rbj wrote: > why would you *want* to use a synthesis window if you're doing OLA > fast-convolution? Good question. > [ ] it might be a very nice way to have a changing filter kernel and > have it sound nice in the transitions. Good answer! Yes, I’m doing time-varying filtering. Just wonder