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Digital Audio - Creating a Sine Wave
Abstract:
This tutorial covers the creation of a sine wave and outputting the
sine wave to a PCM file.
Why would you want to create a sine wave?
Creating a sine wave is useful for a number of things. The most common
usage is for testing SPL, where low-frequency sine waves would be created.
Sine waves are also useful for creating frequency sweeps, where you move
from frequency a to frequency b over a series of steps.
How hard is it?
Sine waves are about the easiest waveform to create other than square waves.
What are the steps?
There are really only three things you need to know in order to create a
sine wave: The frequency, the sample rate and the level. For our example,
let's create a 100Hz sine wave using CD quality encoding (16 bit, 44.1kHz
sampling rate).
A sine wave use the Sin() function to determine the frequency. From
trigonometry, we know that the period of a sine wave is 360 degress. That
is, a sine wave completes an entire revolution in 360 degrees. In radians,
that's 2 * Pi. Sin() varies from -1 to 1. We also know that the maximum
value of a 16 bit recording is 32,767 and the minimum value is -32,768.
So, basically, we simply follow a sine wave, pull out the relevant values
and multiple them by our level to come up with the proper values to place
in the PCM data file.
How do we determine the relevant values?
The relevant values are the ones that convert the sine wave into the time
domain. If we have a sine wave that has a frequency of 80Hz, that means
that 80 times a second it makes a complete (360 degree) revolution.
So, given the frequency and the sample rate, we can determine the relevant
values as a series of angles. Using radians, where 360 degrees = 2 * Pi,
we can do something like the following:
increment = (2* Pi) / (SampleRate / Frequency)
Increment now specifies the distance in radians that each sample is separated
by. Take a look at how this works, just so it is clear.
If you divide SampleRate by Frequency, you end up with the number of samples
in a specific time period. So, if the SampleRate = 44,100Hz and the frequency
you want is 100Hz, then 441 samples are used to create 1 period of 100Hz
musical energy. So, then you divide 2*Pi by 441 to determine the differnce
in the angles for each increment.
So, with this information, what do you do?
Basically, the samples are created in a loop. Amplitude is going to be
your maximum amplitude (so, say 32,767 for 16 bit).
You'd use the following code to get your sample:
' Loop to create the proper number of sine waves.
For sineCount = 1 To (seconds * frequency)
' Loop inside the sine wave (360 degrees)
For inputValue = 0 To (2 * Pi) Step increment
Sample = Int(amplitude * Sin(inputValue))
' Extract your data and write it to a file.
Next inputValue
Next sineCount
That's pretty much it. Remember that when you write your data, you are going
to write it as 16 bit integers. Since you are storing in 32 bit, you'll need
to extract the bytes one by one, including grabbing the sign bit.
Conclusion
This tutorial should have covered the basics of creating a sine wave signal for
a PCM file.
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