infinity-project.org Engineering education for today’s classroom 53 Design Problem - Digital Band...

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Engineering education

for today’s classroom

Design Problem - Digital Band

• Build a digital system that can create music of any style, with any performers, whenever we want to hear it

User controls

Music source

Outline

• Music, Sound, and Signals

• Making Music from Sines and Cosines

• Improving the Design - Making Different Instruments

2.1 Introduction

Ways to Make Music

• All systems that make music Have a musical source Have a way to read

music information Convert musical

information to sound Create sound waves in

air• The result: A sound

signal - but what is it?

Signals are Everywhere

• Signal: A pattern or variation that contains information

2.2 Music, Sound and Signals

Sound Signals

• Sound Signal: A pattern or variation in molecules that a sound makes

• Sound has a speed that is different for different materials

Making Sounds Using Signals

• Amazing Fact: Any sound can be created, stored, and played using signals!

• Microphones and loudspeakers enable us to record and play sounds

• We only need one signal to represent any one sound

Exercise: Plotting Signals

• Plot the signals s(t) = 2 t + 3

s(t) = 0.3 cos(3 t)

s(t) = 6 t2 - 4

time (sec)

• Which one of these looks like a musical signal?

Manipulating Signals

Three musically-useful ways:1. Amplitude scaling: Changing its height

x(t) = A • s(t) 2. Time shifting: Moving left or right

y(t) = s(t + d)3. Time scaling: Stretching or shrinking

the time axisz(t) = s(c • t)

Plots of Real Instrument Signals

Plots of Notes on a Piano Keyboard

Musical Signals and Period

• Observation: The simplest musical signals are periodic; they have shapes that repeat

• Period: The repeating interval T of a periodic signal in units of time (seconds, milliseconds.)

• For any periodic signal p(t), p(t) = p(t + T).

time (sec)

p(t)Example: T = 0.0038 sec = 3.8 msecp(t+T)

Pitch and Fundamental Frequency

• Pitch: how high or low a periodic signal sounds. Can we be more precise?

• Yes! Use fundamental frequency, given by

f = 1/T • Units of frequency: cycles

per second or Hertz (Hz)

Problem: Fundamental Frequency and Period

• Determine the fundamental frequencies of the sounds shown

Sinusoidal Signal

Saxophone SignalSolution: Both haveperiods of

0.0038 sec. Therefore, f=1/0.0038f = 263Hz(middle C)

A Little Musical Notation

• Each note on a page of sheet music corresponds to a signal with a particular frequency and duration…

The x-axis is time

The y-axisis frequency

The Key to Reading Music

• When a musical score is played, each note becomes a signal with a fundamental frequency

• The type of note determines its duration

Making Musical Sounds

• Signals that have a pitch are periodic• A periodic signal repeats over and over• Therefore, to make a single note from a musical

instrument, we need to create one period of its sound and play it over and over.

Our First Digital Band Design

Loudspeaker

Sound Waves

Single period of instrument signal

Translate notes to fundamental frequenciesand durations

Infinity Project Experiment - 2.1

Plots of Speech

Plots of Speech - Block Diagram

2.3 Making Music from Sines and Cosines

Refining the Design

• How do we get the musical information to our digital band?

• How do we specify each instrument’s signal shape?

• How do we make several instrument sounds and play them simultaneously?

Specifying the Musical Score

• Traditionally, music has been written on paperPortable and easy for humans to readDestructible and a little hard for digital

devices to read

• Is there a more convenient format for our musical information?

Musical Instrument Digital Interface (MIDI)

• MIDI specifies (a) note on/off time stamps and (b) note frequencies

• Convenient digital format

• A standard in widespread use

Translate notes to fundamental frequenciesand time stamps

Specifying the Shape of the Musical Instrument Sound

• Most musical instrument signals have complicated shapes

• We shall start with simple periodic signals - the sine and cosine functions

Turning a Sine or Cosine into a Sinusoid

• To make a sound from a sine or cosine function, make the angle a function of time

s(t) = A cos(2 π t / T) [angle units: radians] A = {Amplitude} , T = {Period}

• Can show: s(t) = s(t + T) is periodic

Example:A = 3.1

T = 2.5 msec

People can’t hear the

difference between sinesand cosines!

Making Simple Melodies

time (sec) time (sec)

Saxophone Sinusoid

Our Second Digital Band Design

Translate notes to fundamental frequenciesand time stamps

Cosine generator

This system allows us to play simple single-notemelodies with a simple (sinusoidal) instrument sound.

How do we extend thissystem to play(a) Different

instruments?(b) Multiple notes

simultaneously?

Making More than One Note at a Time

• To play two notes simultaneously, add their signals together

MIDI Information:

Translate notes to period valuesand time stamps

Cosine generator

Block Diagram:

Example Problem: Adding Two Signals Together

time (sec)

Example Problem: Solution

Example: Adding Two Sinusoids Together

• This problem is hard to do by hand…

• …but easy to do digitally!

Reverse-Engineering the Musical Score

• Spectrum: A plot of a signal’s frequency content over a specified window

• “Spikes” in the spectrum correspond to sinusoids

• Spectrum Analysis: A procedure for computing the spectrum

Spectrum Analysis is also easy to do digitally!

Spectrogram

Generating Sine and Cosine Signals

Infinity Project Experiment-2.3

Listening to Sines and Cosines

Infinity Project Experiment-2.4

Measuring a Tuning Fork

Building the Sinusoidal MIDI Player

The Spectrogram File Read

The Spectrogram Microphone

2.4 Improving the Design—Making Different Instruments

Improving the Design - Making Better Instrument Sounds

• Synthesis: The creation of useful and interesting sounds from more basic signals

• Three types:Waveform SynthesisAdditive Synthesis(Physical Modeling Synthesis)

Waveform Synthesis

• Method: Using a single period from a real instrument sound, make period signals at different frequencies

• Procedure: Copy, Time Warp, and Repeat

Time Warping

• Goal: “Stretch” or “squeeze” a periodic signal to change its period

• Formula:pnew(t) = p((Tnew / T) t) pnew(t) = p((f / fnew ) t)

• Result: pnew(t) = pnew(t + Tnew)

Example Problem: Time Warping

Original Signal Time Warped Signal #1

Time Warped Signal #2

What are the fundamental frequencies of these signals?

Additive Synthesis

• Fact: Any signal can be approximated to arbitrary accuracy by adding the right sinusoids together.

• Example: Saxophone sound

Giving a Sound its Character: The Envelope

• Most musical sounds don’t have a constant volume Piano and guitar: Decay away Flute and trumpet: Always changing

• Envelope: The (changing) amplitude of a sound over time, denoted as e(t).

Example: Piano e(t)

Using the Envelope for Sound Synthesis

• Formula: s(t) = e(t) x p(t)

• Can use with p(t) from either waveform or additive synthesis

e(t) x p(t) = s(t)

Making Music Using Envelope and Periodic Signals

Plots of Clarinet Note

SketchWave with MIDI

SketchWave with Envelope Functions

Sketch-Wave with Envelope Functions

Echo Generator

Interesting Application - 2.10

Sound Effects: Reverberation

Sound Effects -Flanging

Sound Effects Flanging

Master Design Problem

Master Design Problem: Ultimate Karaoke Machine

• Design a system that would make any singer sound like a music superstar!

• Goals Pitch correction - “Fix” any wrong notes

while the singer is singing?Music creation - Background tracks?Special effects - An “Elvis” preset? Practice - Can it teach the singer to sing

better?

Steps in the Design

• ConstraintsLow cost, portable, wireless…?

• Research and Gather InformationHas this been done before?

• Create and AnalyzeBlock diagram? Functions of each block?

• Choose, Build, and TestHow well does it work?

End of Chapter 2

infinity-project.org Engineering education for today’s classroom 53 Design Problem - Digital Band...

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