Audio Sampling Laboratory

This is a Java application that lets you see the effects of sampling rate and bits-per-sample on the shape of an analog waveform when it is digitized. Here is a screen shot. (You can increase your browser’s text size to zoom in.):

When sound is recorded digitally, a microphone transforms changes in sound pressure level to voltages that are a direct analog of the sound pressure level as it varies in time. To digitize the voltage, an analog to digital converter (ADC) samples the voltage at a certain rate, converting each voltage sample into a binary number. To reconstruct the sound later, the binary numbers are fed into a digital to analog converter (DAC) at the same rate at which they were recorded. The DAC outputs a fixed voltage for each binary number it receives; a loudspeaker or headphone causes sound pressure level changes in proportion to the voltages it receives from the DAC.

When you run the program, you will see three main panels:

• The left panel is labelled “Sampled Voltages.” The upper part represents the points at which an analog sine wave would be sampled, with the frequency of the sine wave and the sampling rate being controlled by the sliders below it. The horizontal (time) axis is scaled so that exactly one cyle of the sine wave fits onto it.
  There is a “Show Samples” button in the lower right part of the application that will display the numerical values of each of the sample points: the time of the sample in microseconds, the amplitude of the sample in volts, and the binary encoded representation of that amplitude. The time is relative to the beginning of a cycle; the amplitude assumes the signal has a peak-to-peak voltage ranging from -1.0 to +1.0; the binary value is an unsigned integer (see below).
• The center panel shows how voltage ranges would be digitized into unsigned binary numbers, given the number of bits per sample set by the slider below it. This table can be used to see how the third column of the “Show Samples” display was derived from the second column of that display.
  The slider below the table controls the number of bits per sample. If you try to set this value too high, (a) the program can take a very long time to respond to inputs because it has so many sample values to compute, and (b) the pixel height of the Generated Waveforms panel limits how many different intensity values can be represented.
• The right panel shows the output waveform that would be generated if each sample value is converted to a voltage for the duration of one sampling interval.

Downloading

The application consists of a Java jar file, so you need to have the Java runtime environment installed on your computer to run it. Download the jar file: AudioSampling.jar. Save it to a convenient spot, such as your desktop. You can then run the application by double-clicking on it (Windows, OS X) or using the command, "java -jar AudioSampling.jar" (all systems). Note: if your browser downloads the file as AudioSampling.jar.zip, just rename it to AudioSampling.jar; don’t unzip it.

Start-up and run-time options.

If you run the program from the command line, you can specify initial values for the signal frequency, sampling rate, and bits per sample on the command line. Use name=value pairs, where name is “frequency”, “rate”, “bitspersample”, or “bits” (the last two are equivalent). Also, the program’s audio playback feature can be disabled by specifying the “disableAudio” option on the command line.

Using either command line arguments or the controls in the application, the signal frequency may be set to a value between 0.1 and 25 KHz. (The upper limit of human hearing under ideal circumstances is about 20 KHz.) Sampling rate values may be set to any value in the range of 0.1 to 50 KHz, but cannot be set any higher than your computer’s audio system will support, normally 44.1 KHz. Bits per sample can range from 1 to 20, but values large values will produce no visible effect in the generated waveform, and might slow the program down considerably. Like the sampling rate, this parameter cannot be set higher than the maximum value supported by your computer’s audio system.

Audio Playback

The program can generate a tone based on the signal frequency, sampling rate, and bits per sample. There are a few thing to note about this feature:

• The program has been tested successfully on a number of computers, both Windows and Macintosh. But on the computers in the “TREE” domain at Queens College (and presumably other computers as well), the program’s audio output is interrupted by short drop-outs, leading to a strong buzzing sound, making this feature virtually useless on those computers. (Fix the problem and win a prize!)
• The tone you hear is not the displayed waveform repeated over and over because doing that would produce an intensity discontinuity at the end of each cycle whenever the tone’s frequency is not an exact multiple of the sampling rate. Rather, the program generates a continuous stream of output intensity samples from a continuous sine wave. When the tone’s frequency is not an exact multiple of the sampling rate, this means that the sampled values will drift throughout the waveform from cycle to cycle, and as a result you might hear a tone where the waveform on the screen appears to be too degraded to produce one.
• The program produces lower sampling rates by a process called “downsampling.” That is, each sample’s intensity is sent to the computer’s audio system a number of times based on the ratio between the computer’s sampling rate and the rate you select. The control for selecting the sampling frequency limits you to selecting integer divisors of the computer’s sampling rate instead of arbitrary values.
  In addition, lower bits per sample are produced by masking off low order bits in the samples, not by actually changing the audio system. That is, the program never actually modifies the computer’s audio sampling rate and bits per sample.
• Note that sub-optimal parameter values will often produce “wrong” tones, not just lower quality ones. These sounds are generally the natural result of a digital sampling artifact called “aliasing.”

Source Code

The source code for the application, along with some classes for experimenting with the Java Sampled Audio package, are embedded in the jar file. You can import the jar file as an Eclipse project if you want to work on the source code instead of just running it.