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Sound test. Signals and waveforms What is a signal? Need not be electrical Morse Speech Video Contains information.

Dec 16, 2015

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Page 1: Sound test. Signals and waveforms What is a signal? Need not be electrical Morse Speech Video Contains information.

Sound test

Page 2: Sound test. Signals and waveforms What is a signal? Need not be electrical Morse Speech Video Contains information.

Signals and waveforms

Page 3: Sound test. Signals and waveforms What is a signal? Need not be electrical Morse Speech Video Contains information.

What is a signal?

Need not be electrical

Morse

Speech

Video

Contains information

Page 4: Sound test. Signals and waveforms What is a signal? Need not be electrical Morse Speech Video Contains information.

Signals have shapes – waveforms

Water waves – height Audio – sound pressure

Audio – electrical voltage

Electrical waveforms are variations in voltage

AC mains has a waveform but is not a signal.

Page 5: Sound test. Signals and waveforms What is a signal? Need not be electrical Morse Speech Video Contains information.

BITX20 bidirectional SSB transceiver

Page 6: Sound test. Signals and waveforms What is a signal? Need not be electrical Morse Speech Video Contains information.

BITX20 bidirectional SSB transceiver

LO BFO

Mic

Mixer

MixerIF FilterRF Filter

Antenna

Transmit direction shown

Page 7: Sound test. Signals and waveforms What is a signal? Need not be electrical Morse Speech Video Contains information.

Summary of our radio waveforms

Audio Frequency (AF)

Beat Frequency Oscillator (BFO)

Intermediate Frequency stage (IF)

Local Oscillator (LO)

Radio Frequency stage (RF).

Page 8: Sound test. Signals and waveforms What is a signal? Need not be electrical Morse Speech Video Contains information.

Lets look at the waveforms

We start with the input Audio Frequency

Many of the waveforms are sine waves

Later we will look at why

Page 9: Sound test. Signals and waveforms What is a signal? Need not be electrical Morse Speech Video Contains information.

Why Sine waves are important

They are natural

They are as fundamental as the circle

All other waveforms can be broken down into sine waves (More on this later)

Page 10: Sound test. Signals and waveforms What is a signal? Need not be electrical Morse Speech Video Contains information.

A graph of a Sine Wave

Time ->

2 4 6 8 10 12

-1

-0.5

0.5

1

Page 11: Sound test. Signals and waveforms What is a signal? Need not be electrical Morse Speech Video Contains information.

Another natural Sine Wave generator

1 2 3 4 5 6

-1

-0.5

0.5

1

Page 12: Sound test. Signals and waveforms What is a signal? Need not be electrical Morse Speech Video Contains information.

Plotting waveforms

ScaleAxesOriginTime axis AmplitudeFrequencyNegative axesScope time base

-6 -4 -2 2 4 6

-1

-0.5

0.5

1

Page 13: Sound test. Signals and waveforms What is a signal? Need not be electrical Morse Speech Video Contains information.

The sound of waveforms

The note A above Middle C is defined to be 440 HzHere is a pure sine wave at 440Hz

0.001 0.002 0.003 0.004

-1

-0.5

0.5

1

Time in seconds->

Vol

ts->

Page 14: Sound test. Signals and waveforms What is a signal? Need not be electrical Morse Speech Video Contains information.

Other waveforms

Here is a Square wave at 440Hz (A above Middle C)

0.001 0.002 0.003 0.004

-1

-0.5

0.5

1

Time in seconds->

Vol

ts->

Page 15: Sound test. Signals and waveforms What is a signal? Need not be electrical Morse Speech Video Contains information.

Fundamentals and Harmonics

In general fundamental frequencies are sine waves.

Any waveform can be broken down into a fundamental sine wave and its harmonics.

Harmonics are 2,3,4 etc (i.e. integer) times the fundamental frequency.

A square wave can be shown to consist of a fundamental (of the same frequency) plus only odd harmonics.

Page 16: Sound test. Signals and waveforms What is a signal? Need not be electrical Morse Speech Video Contains information.

The harmonic content of a square wave

A square wave has a 3rd harmonic of amplitude 1/3 plus a fifth of amplitude 1/5 etc.

If it is a perfect square wave these go on forever.

(Being a symmetrical waveform it has no even harmonics)

We will add the harmonics one at a time and inspect them.

Page 17: Sound test. Signals and waveforms What is a signal? Need not be electrical Morse Speech Video Contains information.

3rd Harmonic

0.001 0.002 0.003 0.004

-1

-0.5

0.5

1

Playing just the harmonic

Time in seconds->

Vol

ts->

Page 18: Sound test. Signals and waveforms What is a signal? Need not be electrical Morse Speech Video Contains information.

3rd Harmonic added

0.001 0.002 0.003 0.004

-0.75

-0.5

-0.25

0.25

0.5

0.75

Page 19: Sound test. Signals and waveforms What is a signal? Need not be electrical Morse Speech Video Contains information.

5th Harmonic also added

0.001 0.002 0.003 0.004

-0.75

-0.5

-0.25

0.25

0.5

0.75

Page 20: Sound test. Signals and waveforms What is a signal? Need not be electrical Morse Speech Video Contains information.

7th Harmonic also added

0.001 0.002 0.003 0.004

-0.75

-0.5

-0.25

0.25

0.5

0.75

Page 21: Sound test. Signals and waveforms What is a signal? Need not be electrical Morse Speech Video Contains information.

Fundamental and odd harmonics up to 15

0.001 0.002 0.003 0.004

-0.75

-0.5

-0.25

0.25

0.5

0.75

There are a total of 7 notes playing

Page 22: Sound test. Signals and waveforms What is a signal? Need not be electrical Morse Speech Video Contains information.

Compare our original square wave

A Square wave at 440Hz (A above Middle C)

0.001 0.002 0.003 0.004

-1

-0.5

0.5

1

Page 23: Sound test. Signals and waveforms What is a signal? Need not be electrical Morse Speech Video Contains information.

And compare our original pure sine wave

Here is our pure sine wave at 440Hz again

0.001 0.002 0.003 0.004

-1

-0.5

0.5

1

Page 24: Sound test. Signals and waveforms What is a signal? Need not be electrical Morse Speech Video Contains information.

Linear and non linear systems

We have seen that waveforms can be broken down and rebuilt by adding sine waves.

This only works well for linear systems (i.e. if you can trust addition.)

For example if in your system doubling the input signal doesn’t double the output signal you have a non-linear system.

Page 25: Sound test. Signals and waveforms What is a signal? Need not be electrical Morse Speech Video Contains information.

Non linear systems

In a linear system when you apply a sine wave of frequency F you just get a sine wave of frequency F out.

In a nonlinear system you also get some harmonics at frequencies 2F, 3F etc. (only odd ones if its symmetrical)

E.g. if you seriously overdrive an amplifier with a sine wave you will get something like a square wave.

Page 26: Sound test. Signals and waveforms What is a signal? Need not be electrical Morse Speech Video Contains information.

Non linear systems

In a linear system when you apply two sine waves of frequency F and G you just get frequencies F and G

In a nonlinear system you also get sine waves at frequencies F+G and F-G.

(You also get all the harmonics and all the sums and differences of the harmonics)

Page 27: Sound test. Signals and waveforms What is a signal? Need not be electrical Morse Speech Video Contains information.

The ideal mixer

Another day we will look at the electronics of mixers.

An ideal mixer multiplies rather than adds waveforms.

If you feed two sine waves at frequencies F and G into a multiplier you just get sine waves at frequencies F+G and F-G and no harmonics.

Rather than prove this using maths this lets look and listen.

Page 28: Sound test. Signals and waveforms What is a signal? Need not be electrical Morse Speech Video Contains information.

The inputs to the ideal mixer

0.002 0.004 0.006 0.008 0.01

-1

-0.5

0.5

1

0.002 0.004 0.006 0.008 0.01

-1

-0.5

0.5

1

2000Hz

2200Hz

Page 29: Sound test. Signals and waveforms What is a signal? Need not be electrical Morse Speech Video Contains information.

The output from the ideal mixer

0.002 0.004 0.006 0.008 0.01

-1

-0.5

0.5

1

200Hz

4200Hz

and

Page 30: Sound test. Signals and waveforms What is a signal? Need not be electrical Morse Speech Video Contains information.

Comparison sounds to check the output

200Hz

4200Hz

0.002 0.004 0.006 0.008 0.01

-1

-0.5

0.5

1

0.002 0.004 0.006 0.008 0.01

-1

-0.5

0.5

1

Page 31: Sound test. Signals and waveforms What is a signal? Need not be electrical Morse Speech Video Contains information.

Some maths

Did you notice the output waveforms were 90 degree phase shifted sine waves of half the amplitude?

For many purposes this makes no difference

Sin(f)* Sin(g) = Cos(f-g)/2 – Cos(f+g)/2

My last graphs allow for the phase shift. A mathematician would call them cosines but they are still sine waves.

Page 32: Sound test. Signals and waveforms What is a signal? Need not be electrical Morse Speech Video Contains information.

BITX20 bidirectional SSB transceiver

LO BFO

Mic

Mixer

MixerIF FilterRF Filter

Antenna

Transmit direction shown

Page 33: Sound test. Signals and waveforms What is a signal? Need not be electrical Morse Speech Video Contains information.

Questions?