Sound Basics #

    Dr Michael Towsey

    deployed sensor

    spectrogram

    Five Key Concepts #

    1. Decibels
    2. Clipping & gain
    3. ADC: Sample rate & bit depth
    4. Fast Fourier Transform (FFT)
    5. Spectrograms: time/frequency trade-off

    1: Decibels #

    Sound pressure level (spl) (Pascals)

    Volts
    (V)

    Signed 16 bit integer
    (-32768 to +32767)

     

    Real value
    (-1.00 to +1.00)

     

    $ dB(spl) = 30 dB$

    $ db(V) = 35 dB$

    $ db = -70dB $

    Decibels #

    Decibels are always the log of a ratio

    $$ 10 \log_{10}{\left( \frac{\text{Power}}{\text{Reference Power}} \right)} $$

    $$ 20 \log_{10}{\left( \frac{\text{Amplitude}}{\text{Reference Amplitude}} \right)} $$

    dB(spl) dB
    reference = 0.00002 Pa = 0 dB reference = 1.00 = 0 dB
    quiet room = 30 dB bird call ≈ -50 dB
    conversation = 60 dB cold morning ≈ -80 dB
    long-term damage = 85 dB least sound = 1/32767 = -90 dB

    2: Clipping and Gain #

    • Rule 1: Do not increase gain if it clips sounds of interest!
    • Rule 2: Use the factory settings!!

    3: Analogue to digital conversion #

    3: Analogue to digital conversion #

    diagram of sampling and quantization

    4: Fourier transform #

    • An FFT converts a waveform into a spectrogram
    • A sound wave can be represented as the sum of a series of sine waves
    • We can convert from time domain to frequency domain

    fourier transform

    4: Fourier transform #

    maximum frequency in spectrograms

    Maximum frequency in spectrograms = sample rate / 2 = Nyquist

    4: Fourier transform # 

    Function FFT($array){
    $Len = $array.Count
    If($Len -le 1){Return $array} 
    $Len_Over_2 = [Math]::Floor(($Len/2))
    $Output = New-Object Complex[] $Len

    $EvenArray = @()
    $OddArray  = @()

    For($i = 0; $i -lt $Len; $i++){
        If($i % 2){ $OddArray  += $array[$i] }
        Else      { $EvenArray += $array[$i] }
    }

    $Even = FFT($EvenArray)
    $Odd  = FFT($OddArray)

    For($i = 0; $i -lt $Len_Over_2; $i++){
        $Twiddle = [Complex]::Exp(
            [Complex]::ImaginaryOne*[Math]::Pi*($i*-2/$Len)
        ) * $Odd[$i]
        $Output[$i]             = $Even[$i] + $Twiddle
        $Output[$i+$Len_Over_2] = $Even[$i] - $Twiddle
    }

    Return $Output
}
    • 20 lines of code that changed human civilization
    • Thanks to Cooley and Tukey in 1965 (or Gauss 1805)

    5: Spectrograms: time/frequency trade-off #

    Waveform

    Spectrogram

    waveform

    spectrogram

    STFT
    ➡️

    audacity settings

    5: Spectrograms: time/frequency trade-off #

    Finished. Next up: recording and labelling.