10 - 10: FOURIER ANALYSIS OF COMPLEX SOUNDS Amplitude,...

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10: Fourier Analysis- 1 10: F OURIER A NALYSIS OF C OMPLEX S OUNDS Amplitude, loudness, and decibels Several weeks ago we found that we could synthesize complex sounds with a particular frequency, f, by adding together sine waves from the harmonic series with a fundamental equal to the frequency ( f, 2f, 3f, 4f,…). We can reverse the process: a complex sound with particular frequency can be analyzed and quantified by the amplitude spectrum: the relative amplitudes of the harmonics. Our goal today is to understand how the pitch, loudness, and timbre of a sound are represented in a spectrum. However, rather than use analog Band Filter, like last week, we will use the P RAAT program, which has powerful analysis software built in to calculate and graph the spectrum of a recorded sound. For the last couple of weeks we have used the amplitudes to represent the different waves. We can represent these in a table (the choice for the amplitude of the fundamental wave to be 2V is completely arbitrary): Another way to represent the relative amplitudes, which is used by P RAAT , is to graph the power for each harmonic. Since the sound power is proportional to the square of the amplitude for each harmonic, these numbers often get quite small for the higher harmonics. For this reason, the power is often expressed as a decibel. The power for each harmonic in decibels (dB) is: Relative Power (dB) = P n = 10 log 10 [ ( A n /A 1 ) 2 ] = 20 log 10 [ ( A n /A 1 ) ] Since the logarithm of zero is negative infinity, the Relative Power (dB) for the even harmonics is "Error".
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10: Fourier Analysis- 2 We can display the harmonic power spectrum as a bar graph: Note that the bars for the even harmonics are missing since these harmonic are "missing" from a square wave. Analysis of a Triangle Wave A. Predictions based on known relative amplitudes Try to make a table similar to Table 1 for the triangle wave you synthesized several weeks ago. Assume the amplitude of the fundamental wave to be 2V. Remember that the even harmonics had zero amplitude and the amplitudes for the odd harmonics were given by: A n = A 1 /n 2 .
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10: Fourier Analysis- 3 Now graph your results for the relative power in dB for each harmonic. Note that the fundamental is 0 dB by definition: B. "Warm up": Analysis of a measured sine wave Before using P RAAT to analyze a more complex wave, first analyze a simple sine wave to better understand frequency spectra. Take the output from the frequency synthesizer ground (black socket) to the headphone box ground input (also black socket). Use another banana plug cable from the top red 8 Ω output socket of the synthesizer to the other input on the
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10: Fourier Analysis- 4 headphone box. Use the synthesizer to generate a sine wave (use oscillator 1-Left, change the
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This note was uploaded on 01/20/2012 for the course P 109 taught by Professor Staff during the Fall '08 term at Indiana.

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10 - 10: FOURIER ANALYSIS OF COMPLEX SOUNDS Amplitude,...

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