Hi Guys,

i have a serious fft data normalization issue. i receive magnitude and phase data of different block sizes in a patch with a block size of 1024. this means e.g. i receive magnitudes with a block size of 128 (the bin numbers are interpolated so that it fits to the 1024) and i receive the corresponding phases in a block size of 8192 (also extrapolated to fit to 1024). now i have serious problems to normalize the data.

I've already read katjav's post here: http://puredata.hurleur.com/sujet-5266-fft-overlap-normalization-factor

this works fine when the magnitudes and phases are received by only one rfft~ object with one block size.

does anyone have an idea how to fix this?

I would think normalizing it before sending it to the interpolation would be enough, though I don't really know what you're doing.

i try to mix magnitudes and phases of different blocksizes.

okay. the idea of normalizing befor the interpolation is good. but there i'm still in the frequency domain and katjav's formula in the other thread only works right in time domain. so do you know the formula for normalization in the frequency domain?

Not really. The windowing itself is done in the time domain before sending it through [rfft~]. But the normalization factor is applied to the magnitudes after [rfft~]. So normalization is actually done in the frequency domain.

certainly? in katjav's example patch (http://puredata.hurleur.com/attachment.php?item=2639) is the normalization done in the time domain. or am i wrong? it happens right after the rifft~ an not between the rfft~ and rifft~

Okay, sorry. I thought you were trying to work with normalized magnitudes. I haven't actually done a lot of spectral processing in Pd. I usually use it for displaying the spectrum, in which case the normalization is best done after [rfft~].

Either way, though, the normalization factor should be block size independent. I suspect there's an issue in your patch with scaling your FFT data from different block sizes. It's possible that expanding the 128-bin FFT data to 1024 is creating more energy in the signal. Try dividing the magnitudes by 8 before the [rifft~] to reduce the energy and see if that helps.

FFT normalization factor depends on FFT frame size (which is equal to blocksize for fft~ & Co.), overlap, and window type.

In my experience you can normalize where ever you want: in time domain before FFT, in frequency domain, or in time domain after FFT. It is also possible to normalize in two steps, each of sqrt(normalization-factor), for example when you want the bin content normalized for certain processing or analysis jobs. Then you do one step before processing and the second after processing.

In frequency domain, you can either normalize amplitude of polar coefficients, or real and imaginary part of rectangular coefficients. This has no consequence for normalization factor.

If you would do normalization outside the reblocked subpatch, that is also possible, before or after FFT patch. But you must still consider blocksize and overlap.

You can verify all these possibilities by tweaking mentioned patch. The fact that normalization factor does not depend on the point in the process where you apply it, is convenient. However, for analysis or processing, that point of normalization does matter sometimes.

Consider for example a single-sample click: it's energy is spread over all frequency bins. With no normalization before spectral analysis, magnitude would be 1 for each bin. Next, consider a perfectly white noise, or a complex linear chirp over the full spectrum. With sqrt(normalization-factor) before analysis, the magnitude is 1 for each bin. Next, consider a pure sinusoid. With full normalization before analysis, the magnitude is 1 for a single bin, or the leaked equivalent of that.

You see, it depends on signal type how spectral magnitude can be shown independent of FFT size. Probably, the signals you want to process resemble a white noise rather than single pulses or full-scale pure sinusoids. So my guess is, that you would opt for the two-step normalization if you want to mix spectral data of different FFT sizes.

Good luck,

Katja

thanks for the sugestions. i tried both of it.
1. split the normalization process with sqrt(norm_factor) befor and after fft
2. just normalize the reblocked subpatches befor fft.

it works fine when i mix magnitudes and phases of the same block-size but when i mix magnitudes with 128 block-size and phases with 8192 block-size the output signal is to loud and vice versa the output is to quiet. humpf!

Did you try the dividing I suggested? Raising from 128 bins to 1024 means you have 8 times as many bins, and if you're interpolating, that energy is not being evenly spread out across the bins. Your just adding more energy to the new bins. I think that is the problem. You need to make up for that extra energy.

Same thing with the downsampled one that is two quiet. You're getting rid of energy there, so you need to make up for that lost energy.

the additional dividing and multiplying worked. Thanks alot. but i adjusted the factors slightly. a factor of 1/8 for the 128 to 1024 and 1/64 for 128 to 8192 is to much. but in the end it worked. thanks alot again!