Sample Frequency

At least as important as the sample size is the sample frequency. This characteristic refers to the number of samples taken per second. Audio CDs are recorded at 44,100Hz—that is, 44,100 samples per second. Most sound cards sold today can record at up to that rate, if not higher. Some can go to 48,000Hz, which is the sample rate used by digital audio tape (DAT) recorders.

If you want to manipulate sound files that originated on, or will be transferred to, DAT, be sure your sound card can handle 48,000Hz sample frequency. This advice doesn't apply if you're using a DAT drive only for backup purposes. It only applies if you intend to use DAT as an audio platform.

Sample frequency affects how high a tone can be recorded. As a general rule, you need a sample rate of at least twice the frequency of the tone you want to record. For instance, consider Figure 10.2, which shows a pure tone of 20,000Hz. This means that a peak or valley occurs 20,000 times a second, or once every 0.00005s. Now, consider a digital sample frequency of

Chapter 10

0.00005s (20,000Hz). The result might be Samples 1 and 3 shown in Figure 10.2. Because these samples occur at two peaks of the same height, the result would be interpreted by a sound card as a flat line—the sound card wouldn't know that a valley existed between the two samples. To reproduce the 20,000Hz tone with any accuracy, it's necessary to double the sample frequency to 40,000Hz, which adds Sample 2 to the mix. Now the sound card can reproduce a reasonable facsimile of the waveform, with both peaks and valleys intact.

Figure 10.2

To reproduce a sound, a digital reproduction method must sample the signal frequently enough to detect both the peaks and the valleys of the original signal.

Figure 10.2

To reproduce a sound, a digital reproduction method must sample the signal frequently enough to detect both the peaks and the valleys of the original signal.

Note that I said you need to sample a sound using a sample rate of at least twice the sample frequency, in order to reproduce the sound. Consider what would happen if Figure 10.2's samples occurred at points slightly offset from the peaks and valleys, as shown in Figure 10.3. The result is a greatly attenuated sound—the volume will be reduced. In a worst-case scenario, the volume will be so low that the sound will be inaudible.

Matters are complicated still further by real-life sounds, which usually don't consist of the pure tones depicted in Figures 10.2 and 10.3. Real-life sounds consist of several different frequencies overlaid upon one another, which creates complex waveforms, such as those shown in Figure 10.1. Fortunately, it's the highest-frequency tones that are most important in determining the requirements for digital audio sample rates. For instance, if a 20Hz tone were overlaid upon the waveform shown in Figures 10.2 and 10.3, these figures would barely need to be modified, because 1000 of the 20,000Hz waves would fit within a single 20Hz wave. On the scale used in Figures 10.2 and 10.3 (just three 20,000Hz waves), the shifts associated with the 20Hz tone would be minor.

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Part III

Sample Sample Sample 1 2 3

Figure 10.3

If a digital sample at twice a pure tone's frequency is offset from the sound's peaks and valleys, its apparent volume will be reduced in the reproduction.

As a result of these considerations, you can see that the maximum 44,100Hz sample rate produces a maximum best-case accurate reproduction for most sound cards of about 22,050Hz, with the potential for some attenuation of volume at more than 11,025Hz. It's no coincidence that the range for adult human hearing is approximately 20-20,000Hz. (Children can often hear somewhat higher than this, and some animals, such as dogs and dolphins, can hear much higher tones.)

Many of the sounds we hear in everyday life contain little in the way of high-frequency components, however. For recording a person speaking normally, a much lower sample rate might suffice. You should have no trouble understanding speech recorded at 8000Hz, for instance. If you want to accurately reproduce most music, though, a 44,100Hz recording rate is an absolute must.

All sound cards support setting a variety of recording and playback sample rates, and most sound software offers you a choice of several standard rates—generally power-of-2 fractions of 44,100Hz or multiples of 8,000Hz. You can therefore adjust your recording sample rate to fit the type of audio you're recording.

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