WaveForms is Digilent’s free USB Test and Measurement software application compatible with all our Discovery family devices. WaveForms takes just under 60 seconds to download and install and provides the user interface for 12 instruments. A waveform is a representation of how alternating current (AC) varies with time. The most familiar AC waveform is the sine wave, which derives its name from the fact that the current or voltage varies with the sine of the elapsed time. Other common AC waveforms are the square wave, the ramp, the sawtooth wave, and the triangular wave.
What is an Audio Waveform?
As a matter of fact, a waveform is merely a graph that displays amplitude or level changes over time. Amplitude is measured in a bipolar manner, with positive and negative values; not to be confused with level, which can be the absolute value of amplitude changes or an average.
What makes this concept abstract is that waveforms typically contain tens of thousands of discrete changes within an unimaginably short period, crammed into a short block in a sequencer. As you probably already know, as you zoom in on a waveform, its contour becomes more and more visible.
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PCM and NYQUIST FREQUENCY
A waveform is a digitized recreation of very dynamic voltage changes over time. Here is how they are typically generated….
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The discrete changes in an input signal are rectified in an instant through a process called “Pulse Code Modulation” (PCM). Simply put, PCM assigns a bit value to each sample at whatever sampling rate you’re running. Furthermore, the higher the bit depth, the more values the computer has to choose from and the more accurate the rectification is. Sampling Rate for recording purposes is pretty standard – 44100 Hz, the Nyquist Frequency for audio. Here is why it is standard…
- The highest audible frequency for humans is 20,000 Hz.
- Every frequency has a positive half and a negative half (compression and rarefaction).
- So, as long as we sample (analyze and generate) rapidly enough to catch both the positive and negative portions of the highest (most rapidly oscillating) audible frequency – we can confidently rectify just about every audible frequency.
- This means at a sampling rate of 40000 Hz, we will catch both the positive and negative portions 20,000 Hz. However, since sine waves are infinitely smooth and gradual, just one sample of each portion will not produce a very accurate waveform at very high and very low frequencies – but this gets pretty close. This is why the extra 4100 Hz in Nyquist Frequency exists. It accounts for any aliasing that may occur when sampling very low and very high frequencies.
Of course at this point you may be asking yourself “Why not just sample as frequently as possible? Why not just go to 50,000 Hz or 100,000 Hz?” The answer is negligence. We cannot hear the improvement past 44100 Hz. BUT THIS DOES NOT MEAN OTHER SAMPLE RATES ARE NOT USED. For example, when producing sound or music for film, the sample rate of the audio should match the video resolution rate – which is often over 90,000 Hz.
SYNTHETIC WAVEFORMS
Synthetic waveforms are MILES less complex than audio recorded from an acoustic or electrical source. This, frankly, is the beauty of them – they allow us tocreate sounds from scratch without getting ahead of ourselves. After all, every frequency part of a sound – harmonic or not – has the potential to send you down a path of unintentional, unfocused ideas that will do more harm than good in context. These are the four basic synthetic waveforms.
Sine
One harmonic, one frequency. So perfectly simple that it cannot technically exist acoustically or electrically. On the whole, even the purest sounding oscillators and self-resonating filters have a little bit of noise in their output. Y= Asinx describes it mathematically.
Square
Contains odd harmonics (odd whole number multiples of the fundamental). This means that if the fundamental frequency of a square wave is 200 Hz, it will also generate 600 Hz (3rd harmonic), 1000 Hz (5th harmonic), 1400 Hz (7th harmonic) and so on…..
Triangle
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In short, Triangle is like a square wave in that it contains odd harmonics, except the harmonic content, is lower in amplitude than in a square wave. Meaning, the harmonics have less influence on the overall shape of the wave.
Sawtooth
Contains all harmonics. This means that this is the most complex of the four basic synthetic waveforms – but still nowhere close to as complex as real sound. In addition, ff the fundamental of a sawtooth is 100 Hz, that means it also contains 200 Hz, 300 Hz, 400 Hz ….etc. Each harmonic is a little lower in amplitude in comparison to the previous one.
To conclude, IT IS IMPORTANT TO REALIZE that triangle, square, and sawtooth waves ARE MADE UP OF SINE WAVES – AS IS EVERY SOUND IN THE UNIVERSE. In essence, one can synthesize a somewhat accurate square wave by adding odd multiples of the fundamental frequency to a sine wave. In the audio below, I have done just that! Listen to the sine wave gradually form into a square wave as I sweep in odd harmonics. The synthesized square wave plays in isolation at the end. I have isolated each partial on a different track and, in doing so, created a crude “spectrum” analysis of the sound.
https://soundbridge.io/wp-content/uploads/2015/09/WF.-Sin-to-Sq.mp3aboutnewordercatalogstarstreams | |||
Since 1994, here at Waveform we've remained on our unhurried but deliberate path of establishing, exposing and defining this sensual and stimulating genre of chill and ambient music we call 'exotic electronica' - whirly, swirly, sometimes dubby, sometimes dreamy soundscapes by artists from around the planet. It's positive, timeless music for intellectual stimulation. Waveform titles released over two decades ago still sound as relevant, fresh and dynamic today as when they originally appeared. We strive for consistent quality throughout, listen, you'll come away feeling that every track is good. You've probably already experienced our music! Waveform tracks have been heard on HBO's 'True Blood,' 'Six Feet Under,' 'Sex & the City' and network TV's 'CSI:Miami,' as well as many movies, television commercials and public performances. We're also heard every day on the radio and online. Visit our catalog page for links to pages for each of our titles and then buy them at direct from the source prices, on our secure order form. We offer track info, descriptions, reviews, and audio samples of every track on every album, plus links to instantly download, stream or buy CD copies (where offered) of our titles including our two most recent - the seventh Waveform release from zerO One - octOgon and our latest various artist compilation - Maui Chill - Vol Two (Sunset at the Kihei Cafe). Learn more about each title by clicking on its cover image on our catalog page. Listen to our Starstreams program at Mixcloud while you're here. Click label info to learn our history. Visit our facebook page. Make contact. Get comfortable and enjoy your visit! Attention Artists: Want us to listen? Send us links to your mid to downtempo exotic electronica submissions by email. another important transmission from: Waveform. |