246

Fast Fourier Transform

A Fourier transform is computationally intensive and for this reason it is common to use a technique called a Fast Fourier Transform (FFT) to perform spectral analysis. The FFT utilizes mathematical shortcuts to reduce the processing time at the expense of putting limitations on the analysis size.

The analysis size, also referred to as the FFT size, indicates the number of samples from the audio signal used in analysis and also determines the number of discrete frequency bands. When a large number of frequency bands are used, the bands have a smaller bandwidth and this provides for more accurate frequency readings.

However, since complex sounds have a rapidly changing spectrum, a large analysis size can blur the time- changing frequencies of a sound. For example, when performing FFT analysis of an audio file sampled at 44,100 Hz using an analysis size of 4096, almost 100 milliseconds (44,100/4096) of sound are analyzed. If the sound is not constant for those 100 milliseconds, it is impossible to focus on the instantaneous spectrum at smaller time intervals. This is the trade-off between time resolution and frequency resolution encountered when analyzing audio signals.

Spectrum Analysis allows you to perform precise FFT analysis and displays the resulting data in two graphical formats: the Spectrum Graph allows real-time monitoring of playback or input, while the Sonogram displays a playback cursor for real-time preview. Both formats make it easy to navigate data and read audio frequency and position.

Using a spectrum graph

In the spectrum graph, the horizontal axis represents frequency in Hertz (Hz), while the vertical axis represents amplitude in decibels (dB).

Displaying a spectrum graph

1.Open an audio file.

2.Select the portion of the waveform you want to analyze. The sound or note you want to analyze should be in the center of the highlighted area.

3.From the View menu, choose Spectrum Analysis. The Spectrum Analysis window displays.

Spectrum graph

USING SPECTRUM ANALYSIS

CHP. 17