1 Introduction to Information Technology LECTURE 6 AUDIO AS INFORMATION IT 101 – Section 3 Spring, 2005

2 Audio as Information What, physically, is an audio signal? What are the characteristics of audio signals? Period, Frequency, Amplitude How can audio signals be captured and represented using electrical waveforms? How can audio signals be converted to digital information? Sampling and Quantization Systems for capturing, transmitting, and recreating audio signals have been around since 1876 (e.g. phonograph and telephone). Examples of modern digital audio systems include CD players and digital telephone transmission systems.

3 Sound is Analog Sound is created by the motion of air particles in space. E.g., speech causes air to vibrate with varying amplitude (volume) and frequency (pitch).

4 A continuous acoustic waveform can be detected by a device and converted into an analogous electrical waveform for transmission over a circuit. For example, a microphone converts the sound motion through air into an electrical signal. Sound is Measurable and Quantifiable

5 Qualities of Human Hearing What is the range of pitch or frequencies humans can hear? Lowest frequency: 20 Hz Low, rumbling bass note Highest frequency: 20 KHz = 20,000 Hz Those of us who have listened to too much loud music probably can’t hear this. What is the dynamic response of human hearing? Recall that the EYE can only detect image changes per second. In contrast, the EAR can respond to a stimulus that changes 20,000 times per second. Therefore, we will need to use far more samples per second of information to represent audio than we needed for video. Fortunately, audio signals take far less bandwidth than video images. Audio technology is constrained by limitations in human hearing.

6 Properties of Audio Signals Audio signals have frequency components that are complex. In other words, most audio signals are made up of many different frequencies, combining to make the sound we recognize. Human voice varies from about 100 Hz to 4000 Hz. Piano: Concert A above Middle C is 440 Hz. Hertz (Hz) means cycles per second. Sound follows a pattern similar to a sine wave. Concert A cycles 440 times per second. What would a “pure tone” look like? Hertz (Hz) = cycles per second

7 Pure Tone t (ms) 0 V 1 V 2 V 3 V -1 V -2 V -3 V -4 V 4 V Regular, sinusoidal peaks and valleys. Single sinusoidal.

8 Characteristics of Signals Frequency (f) refers to the rate of repetition of the signal. Measured in Hertz (Hz), or cycles per second Measurement of how rapidly the audio signal cycles Musical Pitch – rate at which a sound wave repeats itself Slower frequency = “lower” tone A “lower” tone travels as quickly as a “higher” tone but causes air to vibrate at a slower rate Period (T), measured in seconds, is the time required to complete one cycle of the wave. Frequency (f) and period (T) are inversely proportional. T = 1/f and f = 1/T Important Concepts: Frequency, Period, and Amplitude

9 Characteristics of Signals Amplitude is the magnitude of the signal at any given point. Amplitude relates to volume Louder sounds have greater vertical displacement of sound wave

10 Characteristics of Signals Period: T=10 ms t (ms) 0 V 1 V 2 V 3 V -1 V -2 V -3 V -4 V 4 V Amplitude: A=4 V One cycle of the wave Frequency : f=1/(10x10 -3 )=100 Hz

11 Signal with Twice the Frequency Period: T=5 ms t (ms) Frequency : f=1/(5x10 -3 )=200 Hz 0 V 1 V 2 V 3 V -1 V -2 V -3 V -4 V 4 V Notice the period is half the value as before Notice the frequency is twice the value as before

12 In-Class Question The “A” note above “C” on a piano has a frequency of 440 Hz. How much time is required to complete a single cycle? Give answer in seconds and in milliseconds (ms).

13 Math Review - Waveform Functions Sinusoids are mathematical functions that describe oscillating waveforms produced by many physical systems. As just discussed, sinusoids have a frequency ( f ), which indicates how fast the sinusoid oscillates, and amplitude (A), which measures the size of the oscillation. Sinusoid functions are written as follows: Asin(2  f t) and Acos(2  ft)  = approximately

14 In-Class Example Consider the sinusoidal waveform: 30 sin (1000  t) V What is the amplitude of the signal? What is the period? What is the frequency?

15 Multipliers Giga (G) ,000,000,000. Mega (M)10 6 1,000,000. Kilo (k) ,000. milli (m) micro (  ) nano (n) The following are the common multipliers used for audio characteristics such as period (T) and frequency (f): For example, KHz = KiloHertz = 1000 Hz ms = millisecond = 1/1000 =.001 seconds

16 Audio Signal Components Concert “A” on a vibraphone Every sound wave is the sum of simple pure tones.

17 Frequency Composition (Spectrum) of a Signal The different frequency components which are added together to produce a complex waveform are called the frequency spectrum of that waveform.

18 Sound Wave Vs. Frequency Spectrum Note there is not much frequency content above 1 KHz Fortunately, we do not need to know the specific frequency content of a signal to digitize it. We only need to know the highest frequency signal in a sample. Why?

19 Digitizing Audio Signals In the previous lecture, we learned how continuous images are digitized first by dividing the image into a certain number of pixels, then determining the brightness level of each pixel and finally assigning a code of certain length to each pixel. A similar procedure is used to digitize audio signals. The first step is called “sampling” where the waveform is sampled at certain intervals. The second step, called “quantization,” involves rounding off the continuous values of the audio samples so they can be represented by a finite number of bits.

20 Two Step Process to Digitizing Audio Continuous function of time Infinite amount of information Must choose particular instants of time Continuous Audio Signal Made Discrete In Time Quantized into a Series of Binary Digits STEP 1STEP 2

21 Sampling Rate Sampling Interval (T) Amount of time separating the samples Also called sampling period Sampling Rate (f) Number of samples per second Also called sampling frequency T = 1/f orf = 1/T Sampling Interval Sampling Rate 1 milliseconds1 kHz = 1000 samples/sec 4 milliseconds250 Hz = 250 samples/sec The sampling rate determines how many values of the signal we choose to retain.

22 In-Class Problem If you are sampling a signal at intervals of 16 milliseconds, what is the sampling frequency?

23 In-Class Digital Telephone Problem In a digital telephone system, the speech signal is sampled 8,000 Hz. What is the sampling period? Give answer in  s.

24 Determining the Sampling Rate Harry Nyquist, working at Bell Labs developed what has become known as the Nyquist Sampling Theorem: In order to be ‘perfectly’ represented by its samples, a signal must be sampled at a sampling rate (also called sampling frequency) equal to at least twice its highest frequency component Or: f s = 2f Note that f s here is frequency of sampling, not the frequency of the sample How often do you sample? The sampling rate depends on the signal’s highest frequency.

25 In-Class Sampling Rate Examples Take Concert A: 440 Hz What would be the minimum sampling rate needed to accurately capture this signal? Take your telephone  used for voice, mostly Highest voice component is: 3000 Hz Minimum Sampling Rate?

26 Undersampling and Oversampling Undersampling Sampling at an inadequate frequency rate Aliased into new form - Aliasing Loses information in the original signal Oversampling Sampling at a rate higher than minimum rate More values to digitize and process Increases the amount of storage and transmission COST $$

27 Reconstructing Audio from Samples After receiving the signal, it is necessary to reconstruct it in order to hear it. The signal is reconstructed from its samples. Exact reconstruction is possible if the sampling rate is sufficiently high enough.

28 Reconstructing Audio Signal A short section of a speech waveform (highest frequency component is 3KHz) Reconstructed speech waveform with 1 KHz sampling rate (note the resulting waveform does not resemble original waveform)

29 Reconstructing Audio Signal Reconstructed speech waveform with 5 KHz sampling rate (the resulting waveform starts resembling the original waveform) Reconstructed speech waveform with 10 KHz sampling rate (the resulting waveform highly resembles the original waveform)

30 Effects of Undersampling Original waveform Reconstructed waveform

31 Digitization of Audio Signals Audio signals are continuous in time and amplitude Audio signal must be digitized in both time and amplitude to be represented in binary form. Discrete in time by sampling – Nyquist Discrete in amplitude by quantization Once samples have been captured, they must be made discrete in amplitude. The two step digitization process Step 1: SamplingStep 2: Quantization

32 The Process of Quantization Quantization Converts actual sample values (usually voltage measurements) into an integer approximation Process of rounding off a continuous value so that it can be represented by a fixed number of binary digits Tradeoff between number of bits required and error Human perception limitations affect allowable error Specific application affects allowable error Two approaches to quantization Rounding the sample to the closest integer. (e.g. round 3.14 to 3) Create a Quantizer table that generates a staircase pattern of values based on a step size.

33 Quantization Process Consider an audio signal with a voltage range between -10 and +10 Assume the audio waveform has already been time sampled, as shown How can the amplitude also be converted into discrete values?

34 In-Class Quantization Example For this example, let’s choose to represent each sample by 4 bits. There are an infinite number of voltages between -10 and 10. We will have to assign a range of voltages to each 4-bit codeword. How many steps will there be and why? How large will each step be?

35 Reconstruction Analog-to-Digital Converter (ADC) provides the sampled and quantized binary code. Digital-to-Analog Converter (DAC) converts the quantized binary code back into an approximation of the analog signal by clocking the code to the same sample rate as the ADC conversion. Quantization and Reconstruction example on next two slides:

36 Quantizing

37 Reconstructing

38 Quantization Error After quantization, some information is lost Errors (e.g. noise) introduced The difference between the original sample value and the rounded value is called the quantization error. A signal to noise ratio (SNR) is the ratio of the relative sizes of the signal values and the errors. The higher the SNR, the smaller the average error is with respect to the signal value, and the better the fidelity. Quantization is only an approximation.