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Wave file: 44100 Hz, 16 bit, dual channel.

I use FFT to calculate magnitude at each frequency bins of output. But I don't know to scale it to draw (real-time) spectrum.

Anybody can help me ?

Paul R
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cobazet
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  • Many duplicates - see e.g. [Audio spectrum analysis using FFT algorithm in Java](http://stackoverflow.com/questions/6627288/audio-spectrum-analysis-using-fft-algorithm-in-java) – Paul R Jul 12 '11 at 15:40
  • Scale mothod on above link is only convert to db. Because I don't know max value of complex output after use FFT algorithm. I just only know max value of one instance output, but every N ms, i have an other output. Help me, please ! – cobazet Jul 12 '11 at 15:50
  • I can't calculate all output and find max value of them, it's too hard. – cobazet Jul 12 '11 at 15:53

2 Answers2

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well; there are a number of ways to do this...

for instance: if you want a dB scale, for each imaginary sample, compute

ymag = (x.real^2 + x.imag^2)

you'll only want to go through half the array because you want the positive frequencies; the second half will just be a repeat of the first with real data fed to the FFT.

search through the resulting values for the minimum and maximum values and store them. if your minimum value is zero, choose some very small value to instead be your minimum. (0.000001 or something). then, set your minimum dB value as mindB = 10 * log10(minimum).

now, the first value returned (sample[0]) will be your DC offset, which you will probably want to set to zero.

then, for each sample, compute: ydB = 10 * log10(ymag / maximum).

this should give you an array that represents the dB down from max of each sample bin. you can scale this to whatever you need; if your plot area goes from y=5 to y=200 you could use something like:

yscaled = ((ydB / -mindB) * (200 - 5) + 200)

i would also ensure that the scaled value fits in the bounds in case there were a FP roundoff error.

yscaled = min(max(yscaled, 5),200)

it's been a while since i did this so i apologize if there are any math errors. :)

shelleybutterfly
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    @cobazet i saw your comments above; i think this gives you what you want. as i recall it approximates scales from -inf dB to 0 dB... if this doesn't work for you, let me know and i will look into it further. – shelleybutterfly Jul 12 '11 at 16:20
  • yeah, it's really what i want. But I have a problem: my data is so large that i can't have enough memory to contain them, so that i can't find maximum or minimum to apply above formular. I think it have fixed min or max, then my work is more simple. – cobazet Jul 12 '11 at 16:32
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    you only have to find min and max of whatever you've just FFTed, not the whole set of data, in this case. (in other words: if you used a 32768 point FFT, you're only finding the max of the 16384 points you're working with...) – shelleybutterfly Jul 12 '11 at 16:36
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    although, yes, if it's necessary to have a 0 dB reference that represents the 0 dB of the absolute max of all the real-time FFTs for the whole chunk of data, then you would have to know that point in advance. if you need this your only choice would be to pick a value in advance to use as a max, probably from experimenting and finding an appropriate value. you could also choose the actual max possible value which would be related to your input data max possible value, but it's likely this would leave a lot of extra room at the top... – shelleybutterfly Jul 12 '11 at 16:42
  • if min ~ 0 => db result is < 0. If I choose min = 0.00001 or 0.0000001, mindb is too different (-50 and -60). Should I plus 1 to it, then db > 0 ? – cobazet Jul 12 '11 at 16:46
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    no; the result should be < 0; it computes dB down from the highest power bin, so everything will be less than or equal to zero; that's why the scaling uses "-mindB"... also i found some notes on what i used to use and we apparently used 0.000000001. – shelleybutterfly Jul 12 '11 at 16:50
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    so, in the example i gave with your plot area having a y=5 to y=200, you should get 5 on the scaled value at our attempted approximation to negative infinity dB, and you should get 200 for a scaled value that represents 0 dB. (i could have scaled something improperly somewhere, but that is the idea.) – shelleybutterfly Jul 12 '11 at 16:51
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Different FFT implementations have different scale factors, perhaps differing by N, 1/N, or 1/sqrt(N), where N is the length of the FFT. For at least one kind of signed integer input FFT, max scale is around sqrt(2) * N * 2^(b - 1), where b is the number of bits to the left of the decimal point (16 in your case, maybe 17 if you sum the channels into a larger data type before the FFT).

hotpaw2
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