Tech Tip:Digital Audio Basics, Part 2


Part 1

Part 2

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Part 2: Sample Rate / Bit Depth

 

Sample Rate
The sample rate determines how many samples or snapshots an A/D converter will take per second. For every second of incoming audio, the converter takes literally thousands of snapshots. Again, the more snapshots the converter takes, the more accurate the frequency response of the digital conversion. Faster sample rates allow the higher frequencies to be more accurately represented in the realm of digital audio.

 

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The relationship between sample rate and frequency might not be immediately apparent until you consider how the two are processed in relationship to time. To properly represent the two main aspects of a soundwave, frequency and amplitude, the A/D converter must take a snapshot at the most significant portions of the electronic signal, which are the highest and lowest points of each and every soundwave cycle. Therefore, the converter must take at least two snapshots for every cycle or Hz of an incoming frequency. A frequency of 1000 Hz would need to have at least 2000 snapshots taken per second to capture the peak high and low points of the wave. Taking this into account, a converter taking 44,100 snapshots per second won't be able to capture an accurate picture of any frequency above 22,000 Hz.

 

When a frequency is seen at the input of an A/D converter that is at a higher frequency than what the sample rate can capture, the high frequencies will "wrap around" in a phenomenom called aliasing. When this occurs, the high frequencies end up generating a distorted signal at a frequency of half the incoming one. To avoid this effect, many A/D converters have anti-aliasing filters, which literally cut off any frequencies above what the converter can handle.

 

Bit Depth (Sample Format)
The other aspect of digital audio converters which plays a large part in its accuracy is the bit depth, also sometimes referred to as sample format. The easiest way to understand bit depth and how it affects digital audio is to look at the actual binary numbers that are created when a sample or "snapshot" is taken. Each snapshot taken by the converter creates a series of binary digits (ones and zeroes) over time based on the incoming positive and negative electronic voltages. The number of different voltages that can be represented in digital form is determined by the number of digits available in the binary number created by the snapshot. The bit depth is what determines the size of the packets or the number of digits allowable for each snapshot. And the difference between a snapshot being represented by the 4-bit number "1011" or the 8-bit number "10110100" is enormous. Just compare the two pictures below to see what a difference a single bit makes to the represented.

 

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A simple mathematical example may also help to make it easier to understand how the bit depth affects the accuracy of a converter. Let's say that you feed three numbers - 1.56, 2.47, and 3.95 - into a calculator to be added together. If the calculator is accurate to two decimal places, the numbers will read exactly as they were entered and produce a sum of 7.98. If the calculator is accurate to only one decimal place, it would represent the sum as 8.1, since the last digit of each number entered would be rounded up. Now, if the calculator can add only integers (no decimal places), the sum would be 6, which isn't nearly as accurate. Obviously, the first calculator, which reads the most decimal places, provides the most accurate sum.

 

This is similar to how a converter's bit depth represents the sound being digitized. When the packet is larger - that is, when more digits are allowed to represent the incoming signal - the more accurately the signal is conveyed. When you're dealing with complex number such as those derived from sound waves, this is critical to the quality of the digital audio.

 

In the next installment, we'll look at the other side of the digital audio equation - the D/A converter - as well as a few other digital audio concepts you should know about.

 

Thanks to Barry Rudolph for his help in preparing this piece.

 

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