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I was baffled by FFT, too, when I first encountered in math class. It seemed useless. It's not until I started working with sound that it really dawned on me

by ww520 10y ago

I was baffled by FFT, too, when I first encountered in math class. It seemed useless. It's not until I started working with sound that it really dawned on me how it's being used. I think the best illustrated usage of DFT (FFT is just the fast algorithm of DFT) is the sound equalizer. Sound comes in. DFT converts it into the strength over frequency on the equalizer. You can visually see the strength bars on each frequency slots (from the high, the mid range, to low frequency slots). This let you adjust the frequency strength in each frequency slot individually. You can bump up the high frequency slot or depress the mid range slot. The adjusted frequencies are combined to produce the new distorted sound. When a sound comes in straight, you can only adjust its amplitude (volume). Now with DFT, you can adjust the decomposed frequency components of the sound individually, giving you finer control over the sound's pitch and quality. You can amplify the high frequencies to make it higher pitch. Or amplify the lower frequencies to give more booming bass. You can chop off the low frequency completely to remove background noise. You can chop off both the low and high frequencies to make the sound "clearer." DFT/FFT basically let you control the different dimension of the sound (or any time-based sine wave data).

edblarney 10y ago
That I get. But the FFT results show all sorts of harmonics and results that effectively need to be further decomposed. It does not produce a the results as you described, in reality. Using FFT to decompose someones speech, I'm getting peaks at 300Hz, 600Hz, 900Hz etc.. My crude understanding is that those are all related to one another, though I can't quite fathom why. I fully grasp the example you give ... but the actual results are something bewildering altogether ...
- ww520 10y ago
  I'm afraid the interpretation of the output of FFT really has to go into some theory and the text book version of it. Here're some good description on the time-domain and frequency-domain of the FFT. http://www.dspguide.com/ch8/2.htm http://www.dspguide.com/ch8/2.htm, http://www.dspguide.com/ch8/3.htm http://www.dspguide.com/ch8/3.htm. As for the output you got, the peaks at 300Hz, 600Hz, 900Hz, etc are the signal strength level at those frequencies of the speech. A voice is made up of many different frequencies at various strength levels. Most frequencies of a voice have nearly 0 energy. Some have more energy, with varying levels of strength. DFT breaks the voice down and figures out the strength levels for all the frequencies. The frequency range in human voice is from about 70Hz to 10KHz. That's why you see some strength at 300Hz, 600Hz, and 900Hz. Instead of just describing a voice as volume over time, DFT decomposes it into an array of frequency strengths, giving you the frequency characteristic of the voice. The index into the FFT output array identifies the frequency. Let's say you sample the signal at 10000Hz (10000 samples per second). And you pass only 1000 samples into FFT. FFT always spits out an array F with half of the input size, i.e. 500 elements. Each element represents a frequency fraction with respect to the input size. So F[0] is at 1/1000 fraction, F[1] at 2/1000 fraction, etc, upto F[499] at 500/1000 fraction. To convert back to the real frequency, just multiply the fraction to the sampling rate. F[0] with 1/1000 * 10000Hz = at 10Hz. F[1] with 2/1000 * 10000Hz = at 20Hz, F[499] at 500Hz. The values at F[0], F[1], etc are the signal strength at those frequencies.
- qb45 10y ago
  > Using FFT to decompose someones speech, I'm getting peaks at 300Hz, 600Hz, 900Hz etc.. My crude understanding is that those are all related to one another, though I can't quite fathom why. This is not a quirk of FT but a result of the way physical things actually vibrate. You get this output from FT because your input consists of 300/600/900/...Hz sinewaves superimposed on each other. https://en.wikipedia.org/wiki/Harmonics https://en.wikipedia.org/wiki/Harmonics
  - edblarney 10y ago
    There is a person talking - that's it. The peaks at 600Hz and 900Hz are higher than 300Hz. Humans can't make speech at 600 and 900Hz, is my understanding. Listening to it, I don't hear those frequencies. So it's hard for me to understand how they are there.
    - ww520 10y ago
      Where do you get your information about human voice frequency range? 600Hz and 900Hz are certainly within the frequency range of human voice.
      - nkurz 10y ago
        I would have all these frequencies were in range, but when I search I find several sources suggesting that 600 and 900 Hz are indeed greater than the fundamental frequencies of human voices: Baby cries have a fundamental frequency (hereafter referred to as Fo) of around 500 Hz (roughly corresponding to the note B4). Child speech ranges from 250-400 Hz (notes B3 to G4, adult females tend to speak at around 200 Hz on average (about G3), and adult males around 125 Hz (or, B2). http://www.ncvs.org/ncvs/tutorials/voiceprod/tutorial/influence.html http://www.ncvs.org/ncvs/tutorials/voiceprod/tutorial/influe... My guess at this point would be that while the "fundamental frequencies" are lower for vowels, higher frequencies are still required for the consonants?
        ww520 10y ago
        Fundamental frequency is the lower bound of the frequency range. That's the floor.

by ww520 10y ago

edblarney 10y ago

That I get. But the FFT results show all sorts of harmonics and results that effectively need to be further decomposed. It does not produce a the results as you described, in reality. Using FFT to decompose someones speech, I'm getting peaks at 300Hz, 600Hz, 900Hz etc.. My crude understanding is that those are all related to one another, though I can't quite fathom why. I fully grasp the example you give ... but the actual results are something bewildering altogether ...

ww520 10y ago
I'm afraid the interpretation of the output of FFT really has to go into some theory and the text book version of it. Here're some good description on the time-domain and frequency-domain of the FFT. http://www.dspguide.com/ch8/2.htm http://www.dspguide.com/ch8/2.htm, http://www.dspguide.com/ch8/3.htm http://www.dspguide.com/ch8/3.htm. As for the output you got, the peaks at 300Hz, 600Hz, 900Hz, etc are the signal strength level at those frequencies of the speech. A voice is made up of many different frequencies at various strength levels. Most frequencies of a voice have nearly 0 energy. Some have more energy, with varying levels of strength. DFT breaks the voice down and figures out the strength levels for all the frequencies. The frequency range in human voice is from about 70Hz to 10KHz. That's why you see some strength at 300Hz, 600Hz, and 900Hz. Instead of just describing a voice as volume over time, DFT decomposes it into an array of frequency strengths, giving you the frequency characteristic of the voice. The index into the FFT output array identifies the frequency. Let's say you sample the signal at 10000Hz (10000 samples per second). And you pass only 1000 samples into FFT. FFT always spits out an array F with half of the input size, i.e. 500 elements. Each element represents a frequency fraction with respect to the input size. So F[0] is at 1/1000 fraction, F[1] at 2/1000 fraction, etc, upto F[499] at 500/1000 fraction. To convert back to the real frequency, just multiply the fraction to the sampling rate. F[0] with 1/1000 * 10000Hz = at 10Hz. F[1] with 2/1000 * 10000Hz = at 20Hz, F[499] at 500Hz. The values at F[0], F[1], etc are the signal strength at those frequencies.
qb45 10y ago
> Using FFT to decompose someones speech, I'm getting peaks at 300Hz, 600Hz, 900Hz etc.. My crude understanding is that those are all related to one another, though I can't quite fathom why. This is not a quirk of FT but a result of the way physical things actually vibrate. You get this output from FT because your input consists of 300/600/900/...Hz sinewaves superimposed on each other. https://en.wikipedia.org/wiki/Harmonics https://en.wikipedia.org/wiki/Harmonics
- edblarney 10y ago
  There is a person talking - that's it. The peaks at 600Hz and 900Hz are higher than 300Hz. Humans can't make speech at 600 and 900Hz, is my understanding. Listening to it, I don't hear those frequencies. So it's hard for me to understand how they are there.
  - ww520 10y ago
    Where do you get your information about human voice frequency range? 600Hz and 900Hz are certainly within the frequency range of human voice.
    - nkurz 10y ago
      I would have all these frequencies were in range, but when I search I find several sources suggesting that 600 and 900 Hz are indeed greater than the fundamental frequencies of human voices: Baby cries have a fundamental frequency (hereafter referred to as Fo) of around 500 Hz (roughly corresponding to the note B4). Child speech ranges from 250-400 Hz (notes B3 to G4, adult females tend to speak at around 200 Hz on average (about G3), and adult males around 125 Hz (or, B2). http://www.ncvs.org/ncvs/tutorials/voiceprod/tutorial/influence.html http://www.ncvs.org/ncvs/tutorials/voiceprod/tutorial/influe... My guess at this point would be that while the "fundamental frequencies" are lower for vowels, higher frequencies are still required for the consonants?
      - ww520 10y ago
        Fundamental frequency is the lower bound of the frequency range. That's the floor.