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Sound in Time and Frequency Sound in Time and Frequency Telecommunications 1 Telecommunications 1 P. Mathys P. Mathys Types of Sound Signals Types of Sound Signals Sound Signals Deterministic (predictable) Random (unpredictable) periodic aperiodic stationary non-stationary sine sawtooth rectangular talking clock (date/time) white noise speech music sine_sig.wav wnoise_sig.wav speech_sig.wav 201pm.wav sine_sig.wav 201pm.wav speech_sig.wav wnoise_sig.wav
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Sound in Time and Frequency - University of …mathys/ecen1200/sound/... · Sound in Time and Frequency Telecommunications 1 P. Mathys Types of Sound Signals Sound Signals Deterministic

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Page 1: Sound in Time and Frequency - University of …mathys/ecen1200/sound/... · Sound in Time and Frequency Telecommunications 1 P. Mathys Types of Sound Signals Sound Signals Deterministic

Sound in Time and FrequencySound in Time and Frequency

Telecommunications 1Telecommunications 1P. MathysP. Mathys

Types of Sound SignalsTypes of Sound Signals

Sound Signals

Deterministic(predictable)

Random(unpredictable)

periodic aperiodic stationary non-stationary

sinesawtooth

rectangular

talking clock(date/time)

white noise speechmusic

sine_sig.wav wnoise_sig.wav speech_sig.wav201pm.wav

sine_sig.wav 201pm.wav speech_sig.wavwnoise_sig.wav

Page 2: Sound in Time and Frequency - University of …mathys/ecen1200/sound/... · Sound in Time and Frequency Telecommunications 1 P. Mathys Types of Sound Signals Sound Signals Deterministic

Characterization of TonesCharacterization of Tones

Sounds (digital and analog) are made Sounds (digital and analog) are made up from combinations of tones, e.g.,up from combinations of tones, e.g.,

Pure tones are also called sinusoids.Pure tones are also called sinusoids.

A sinusoidal tone is characterized by its A sinusoidal tone is characterized by its amplitude, frequency and phase.amplitude, frequency and phase.

Pure Tone Chord Musicnote_c5.wav chor_c5.wav beeth1.wav

Sinusoidal ToneSinusoidal Tone

Graph versus time for 10 ms:Graph versus time for 10 ms:

Formula: A*sin(2*pi*f*t+phi)Formula: A*sin(2*pi*f*t+phi)

note_c5.wav

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Sinusoidal Tone: ParametersSinusoidal Tone: Parameters

In A*sin(2*pi*f*t+phi),In A*sin(2*pi*f*t+phi),AA is the is the amplitudeamplitude of the sinewave. A loud of the sinewave. A loud tone has a high amplitude.tone has a high amplitude.ff is the is the frequencyfrequency, i.e., the number of , i.e., the number of periodic repetitions per second. A low tone periodic repetitions per second. A low tone has low frequency, a high tone has high has low frequency, a high tone has high frequency. Note: pi = 3.14159265359...frequency. Note: pi = 3.14159265359...phiphi is the is the phasephase, i.e., the time shift of the , i.e., the time shift of the sinewave along the horizontal axis.sinewave along the horizontal axis.

Sinusoidal Tone: ParametersSinusoidal Tone: Parameters

The human ear is insensitive to the The human ear is insensitive to the phasephase of individual tones. Modems use of individual tones. Modems use their own reference signal to transmit or their own reference signal to transmit or receive data via phase changes.receive data via phase changes.AmplitudeAmplitude or loudness is straightforward.or loudness is straightforward.FrequencyFrequency is the most important is the most important parameter for us to characterize tones.parameter for us to characterize tones.

Page 4: Sound in Time and Frequency - University of …mathys/ecen1200/sound/... · Sound in Time and Frequency Telecommunications 1 P. Mathys Types of Sound Signals Sound Signals Deterministic

Sinusoidal Tone: ParametersSinusoidal Tone: Parameters

To understand more intuitively what To understand more intuitively what amplitude and frequency mean, let’s amplitude and frequency mean, let’s listen to an listen to an amplitude modulated (AM)amplitude modulated (AM)signal and to a signal and to a frequency modulated frequency modulated (FM)(FM) signal.signal.

No modulation AM FMnomodx.wav amx.wav fmx.wav

Sinusoidal Tone: FrequencySinusoidal Tone: Frequency

Example: Listen to this simple tune: Example: Listen to this simple tune: We recognize the melody because of We recognize the melody because of the specific changes in tone frequency.the specific changes in tone frequency.The sine function is periodic, i.e.,The sine function is periodic, i.e.,sin(x+2*pi) = sin(x)sin(x+2*pi) = sin(x), (2*pi is 360 degrees)., (2*pi is 360 degrees).

Frequency is defined as the number of Frequency is defined as the number of periods per second or, equivalently, as periods per second or, equivalently, as “one over the period length in seconds.”“one over the period length in seconds.”

twink.wav

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Frequency: ExampleFrequency: ExampleThis graph shows 10 ms of a tone:This graph shows 10 ms of a tone:

What is the frequency of this tone?What is the frequency of this tone?

note_c5.wav

Frequency: ExampleFrequency: ExampleThis graph shows 10 ms of a tone:This graph shows 10 ms of a tone:

There are 5.25 periods. Thus, the There are 5.25 periods. Thus, the frequency is: frequency is: f = 100*5.25 = 525 Hzf = 100*5.25 = 525 Hz..

note_c5.wav

Page 6: Sound in Time and Frequency - University of …mathys/ecen1200/sound/... · Sound in Time and Frequency Telecommunications 1 P. Mathys Types of Sound Signals Sound Signals Deterministic

Frequency of TonesFrequency of Tones

Note that frequency is usually measured Note that frequency is usually measured in in HertzHertz (in honor of Heinrich Hertz, (in honor of Heinrich Hertz, 18571857--1894, German physicist who 1894, German physicist who discovered radio waves).discovered radio waves).Note:Note:

1,000 Hz = 1 kHz (kilo Hertz),1,000 Hz = 1 kHz (kilo Hertz),1,000,000 Hz = 1 MHz (mega Hertz),1,000,000 Hz = 1 MHz (mega Hertz),

1,000,000,000 Hz = 1 GHz (giga Hertz).1,000,000,000 Hz = 1 GHz (giga Hertz).

FrequenciesFrequencies

We can hear tones in the range from We can hear tones in the range from about 50 Hz to 16 kHz.about 50 Hz to 16 kHz.

AM radio uses 540 kHz … 1.6 MHz.AM radio uses 540 kHz … 1.6 MHz.FM radio uses 88 MHz … 108 MHz.FM radio uses 88 MHz … 108 MHz.Microwave ovens use 2 … 3 GHz.Microwave ovens use 2 … 3 GHz.

400 Hz 1000 Hz 4000 Hzsine_400.wav sin_1000.wav sin_4000.wav

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Frequency DomainFrequency Domain

When we look at a plot of sound intensity When we look at a plot of sound intensity versus time, we say that we look at a versus time, we say that we look at a waveform in the waveform in the time domaintime domain..We can look at the same waveform We can look at the same waveform through filters which pass only certain through filters which pass only certain frequency bands, and plot intensity frequency bands, and plot intensity versus frequency. In this case we look at versus frequency. In this case we look at the waveform in the the waveform in the frequency domain.frequency domain.

Frequency Domain: ExampleFrequency Domain: Example

Spectrogram of 3 sequential tones:Spectrogram of 3 sequential tones:

sin_up.wav

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Frequency Domain: ExampleFrequency Domain: Example

Spectrogram of chirp: 100 Hz … 20 kHzSpectrogram of chirp: 100 Hz … 20 kHz

chirp.wav

Frequency Domain: ExampleFrequency Domain: Example

Spectrogram of musical tune:Spectrogram of musical tune:

twink.wav

Page 9: Sound in Time and Frequency - University of …mathys/ecen1200/sound/... · Sound in Time and Frequency Telecommunications 1 P. Mathys Types of Sound Signals Sound Signals Deterministic

HarmonicsHarmonics

Let f1 be the fundamental frequency of Let f1 be the fundamental frequency of a sound, e.g., from a music instrument.a sound, e.g., from a music instrument.Then f2=2*f1, f3=3*f1, f4=4*f1, etc, are Then f2=2*f1, f3=3*f1, f4=4*f1, etc, are called the 2’nd, 3’rd, 4’th, etc, called the 2’nd, 3’rd, 4’th, etc, harmonicsharmonics..The presence (or absence) of The presence (or absence) of harmonics changes the “quality”, but not harmonics changes the “quality”, but not the “pitch” of the sound.the “pitch” of the sound.

Rectangular WaveformRectangular WaveformHas 1’st, 3’rd, 5’th, 7’th, etc, harmonics.Has 1’st, 3’rd, 5’th, 7’th, etc, harmonics.

4 periods in 10 ms => f1 = 400 Hz

rect_400

sin_400sin400_sig.wav

rect_sig.wav

Page 10: Sound in Time and Frequency - University of …mathys/ecen1200/sound/... · Sound in Time and Frequency Telecommunications 1 P. Mathys Types of Sound Signals Sound Signals Deterministic

Rectangular WaveformRectangular Waveform

400 Hz

1200 Hz

2000 Hz2800 Hz

3600 Hz

4400 Hz

5200 Hz

Sawtooth Sawtooth WaveformWaveformHas 1’st, 2’nd, 3’rd, 4’th, etc, harmonics.Has 1’st, 2’nd, 3’rd, 4’th, etc, harmonics.

4 periods in 10 ms => f1 = 400 Hz

saw_400

sin_400

rect_400

sin400_sig.wav

rect_sig.wav

saw_sig.wav

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Sawtooth Sawtooth WaveformWaveform

400 Hz

1200 Hz

2000 Hz

2800 Hz2400 Hz

1600 Hz

800 Hz

Human VoiceHuman Voice

Most energy is concentrated in the band Most energy is concentrated in the band from about 500 to 2000 Hz.from about 500 to 2000 Hz.The telephone transmits frequencies in The telephone transmits frequencies in the range from 300 to 3000 Hz.the range from 300 to 3000 Hz.This is adequate for understanding This is adequate for understanding speech, but not for Hispeech, but not for Hi--Fi reproduction.Fi reproduction.

Hi-Fi Telephone(low pass)

High pass

infa_tel.wavinfa_ori.wav infa_hpf.wav

Page 12: Sound in Time and Frequency - University of …mathys/ecen1200/sound/... · Sound in Time and Frequency Telecommunications 1 P. Mathys Types of Sound Signals Sound Signals Deterministic

Human Voice: Time DomainHuman Voice: Time Domain

The HiThe Hi--Fi version versus time:Fi version versus time:

Speech is easily identified by the Speech is easily identified by the pauses between words and sentences.pauses between words and sentences.

infa_ori.wav

Human Voice: Frequency DomainHuman Voice: Frequency Domain

Spectrogram of HiSpectrogram of Hi--Fi version:Fi version:

Note: Most energy is below 4000 Hz.Note: Most energy is below 4000 Hz.

4 kHz

10 kHzinfa_ori.wav

Page 13: Sound in Time and Frequency - University of …mathys/ecen1200/sound/... · Sound in Time and Frequency Telecommunications 1 P. Mathys Types of Sound Signals Sound Signals Deterministic

Human Voice: Frequency DomainHuman Voice: Frequency Domain

Spectrogram of telephone version:Spectrogram of telephone version:

Now frequencies above 2.5 kHz and Now frequencies above 2.5 kHz and below 250 Hz are cut off.below 250 Hz are cut off.

4 kHz

infa_tel.wav

MusicMusicMusic typically covers a larger Music typically covers a larger frequency range than human voice.frequency range than human voice.More energy at lower frequencies, but More energy at lower frequencies, but higher frequencies are needed to higher frequencies are needed to distinguish different instruments.distinguish different instruments.For HiFor Hi--Fi quality, 50…16000 Hz range is Fi quality, 50…16000 Hz range is needed.needed.

50..20000 Hz 50..10000 Hz 50..5000 Hz

muss44.wav muss22.wav muss11.wav

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Music: Time DomainMusic: Time DomainThe 50..20000 Hz version versus time:The 50..20000 Hz version versus time:

Intensity fluctuates in time, but pauses Intensity fluctuates in time, but pauses are much rarer than with speech.are much rarer than with speech.

muss44.wav

Music: Frequency DomainMusic: Frequency Domain

Spectrogram of 50..20000 Hz version:Spectrogram of 50..20000 Hz version:

High frequency content substantial.High frequency content substantial.

10 kHz

20 kHzmuss44.wav

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Music: Frequency DomainMusic: Frequency Domain

Spectrogram of 50..5000 Hz version:Spectrogram of 50..5000 Hz version:

Same tune, but “less HiSame tune, but “less Hi--Fi” sound.Fi” sound.

10 kHz

20 kHzmuss11.wav

DTMF SignalsDTMF Signals

Dual Tone MultiDual Tone Multi--Frequency signals are Frequency signals are used extensively in telephony.used extensively in telephony.

1209 Hz 1336 Hz 1477 Hz

697 Hz 1 2 3

770 Hz 4 5 6

852 Hz 7 8 9

941 Hz * 0 #

Example

dtmf_x.wav

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DTMF Signal: Time DomainDTMF Signal: Time Domain

How do we know frequencies?How do we know frequencies?

Do we even know there are two?Do we even know there are two?

dtmf_x.wav

DTMF Signal: SpectrogramDTMF Signal: Spectrogram

Use filters (frequency domain).Use filters (frequency domain).

We see that there are 2 frequencies.We see that there are 2 frequencies.

dtmf_x.wav

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Different Types of FiltersDifferent Types of Filters

LPF:LPF: Lowpass Lowpass filter, passes all filter, passes all frequencies below a cutoff frequency.frequencies below a cutoff frequency.BPF:BPF: Bandpass Bandpass filter, passes all filter, passes all frequencies from a lower to an upper frequencies from a lower to an upper cutoff frequency.cutoff frequency.HPF:HPF: Highpass Highpass filter, passes all filter, passes all frequencies above a cutoff frequency.frequencies above a cutoff frequency.

DTMF Signal: After LPFDTMF Signal: After LPF

After lowAfter low--pass filter (LPF) at 1000 Hz:pass filter (LPF) at 1000 Hz:

7.75 periods in 10 ms ==> f=775 Hz

dtmf_x_lpf.wav

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DTMF Signal: After HPFDTMF Signal: After HPF

After highAfter high--pass filter (HPF) at 1000 Hz:pass filter (HPF) at 1000 Hz:

14.75 periods in 10 ms ==> f=1475 Hz

dtmf_x_hpf.wav

White NoiseWhite Noise

Contains all frequencies with equal power.Contains all frequencies with equal power.

Random signal, no visible regularity

wnoise_sig.wav

Page 19: Sound in Time and Frequency - University of …mathys/ecen1200/sound/... · Sound in Time and Frequency Telecommunications 1 P. Mathys Types of Sound Signals Sound Signals Deterministic

Spectrogram of White NoiseSpectrogram of White Noise

PSD of White NoisePSD of White Noise

Page 20: Sound in Time and Frequency - University of …mathys/ecen1200/sound/... · Sound in Time and Frequency Telecommunications 1 P. Mathys Types of Sound Signals Sound Signals Deterministic

Pink NoisePink Noise

Equal power per octave.Equal power per octave.

pink

whitewnoise_sig.wav

pink1.wav

Spectrogram of Pink NoiseSpectrogram of Pink Noise

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PSD of Pink NoisePSD of Pink Noise