# Introduction to Digital Signal Processing

### Realtime processing vs. offline processing

Does the processing happen instantaneous or not?
Where does the signal originate and end?

### Frequency

Hz, pitch
Human hearing range
Bit-depth
Sample Rate
App Recording 20211107 1704.aiff
3.7 MB

### Amplitude

Loudness, dB
- 1 phon = 1dB at 1.000 Hz

### Waveform

Simple Single Cycle Waveform - The Sonic Hieroglyphs
Frequency content of waveforms - harmonics ()
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 to create 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= A * sin (x) describes it mathematically.
Saw - 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.
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 - 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.
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.

## Envelopes & Glissandi

### Recap

1) What is the difference between realtime sound synthesis and realtime signal processing?
2) What is the difference between realtime sound synthesis and offline soundsynthesis?
3) What type of conversion should be used if you want to digitally sample a sound?
4) What perceptual sensation corresponds to frequency?
5) What musical parameter corresponds to amplitude?
6) What are the minimum and maximum frequencies that can be heard by humans?
7) How do you measure amplitude?
8) What is the difference between peak amplitude and instantaneous amplitude?
9) What is a continuous variation of the pitch of a sound called?
10) What do you call a variation of the amplitude of a sound over time?
11) What is the name of the transition that goes from initial silence to the maximal amplitude of a sound?
12) What does the term "release" mean?
13) What happens during the sustain phase of an envelope?
14) After what stage of the envelope does decay take place?
15) Name four types of waveform.