cs109 lecture 4: digital audiosnyder/cs109/lecture04.pdfcs109 lecture 4: digital audio ......

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Computer Science CS109 Lecture 4: Digital Audio Basics of sound waves Digital sound Digitizing sound: Sampling and quantizing Consequences of choice of sample rate and bit depth CD quality sound vs MP3 No class next Monday, no discussions, no HW next week.

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Computer Science

CS109 Lecture 4: Digital Audio

Basics of sound waves Digital sound Digitizing sound: Sampling and quantizing Consequences of choice of sample rate and bit depth CD quality sound vs MP3

No class next Monday, no discussions, no HW next week.

Computer Science

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Hearing

We “hear” sound when a series of air compressions vibrate a membrane in our ear. The inner ear sends signals to our brain. The rate of this vibration is measured in Hertz, and the human ear can hear sounds in the range of roughly 20Hz - 20KHz.

Computer Science

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Sound Wave Properties

Wavelength: distance between waves (affects pitch -- high or low sounds)

Amplitude: strength/height of waves (volume)

Frequency: the number of times a wave peak occurs in a second.

Wavelength = Speed of sound / wavelength E.g.: 340 meters per second .77 meters

= 440 Hz = note “A”

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Microphones and Speakers

Microphones convert acoustical energy (sound waves) into electrical energy (the audio signal).

Speakers do the same thing in reverse: convert electrical energy into acoustical energy.

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Audio Playback

A stereo sends an electrical signal to a speaker to produce sound.

The voltage in the signal varies in direct proportion to the sound wave: it is analog.

Digitizing a sound/electrical wave means converting it into a series of bits: Again, this involves sampling and quantizing.

11001010100101010101010

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Important Note about Electronic Signals

An analog signal continually fluctuates in voltage up and down.

A digital signal is a series of numbers, with discrete amplitudes.

0 120 58 328 ....

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Recall: Digitizing an Image

Sampling: Taking measurements (of color) at discrete locations within the image. Resolution: 16 samples per inch (in each direction)

Computer Science

Recall: Digitizing an Image

Quantizing: Measure the RGB color for each pixel, and record the 8+8+8 = 24 bit number for that sample. 224 = 16,777,216 possible colors per pixel (in TrueColor)

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Digitizing Audio

Sampling: Decide on a sample rate (how many times a second to measure the wave); Example: CD quality sound is measured 44,100 Hertz = 44.1 KHz.

Computer Science

Choosing a Sampling Rate

Consider this waveform. What sampling rate should we choose?

Computer Science

Choosing a Sampling Rate

How about this sampling rate? (6 samples)

Computer Science

Choosing a Sampling Rate

How about this sampling rate? (11 samples)

Computer Science

Choosing a Sampling Rate

How about this sampling rate? (21 samples)

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Choosing a Sampling Rate

Consider this waveform, and these two sampling strategies. What’s going on here? A. B.

Samples: 100 -100 100 .... 0 0 0 0

100 0 -100

Computer Science

Nyquist Sampling Theorem

The Nyquist Sampling Theorem states that the sampling rate must be greater than twice the value of the highest frequency component of the analog signal.

Since humans can hear to about 20 KHz, this means that you would have to sample at 40 KHz to capture “all” the sound humans perceive, hence, the 44.1 KHz sample rate for CD quality sound.

Computer Science Digitizing Audio

Sampling: Decide on a sample rate (how many times a second to measure the wave); Example: CD quality sound is measured 44,100 times a second (44.1 KiloHertz) Decide on a “bit depth” (how many bits for each measurement); Example: CD quality sound is 16 bits, giving 216 = 65,536 possible values.

Computer Science Digitizing Audio

Quantizing: Measure the signal at the sample rate, representing the analog sound level with a number (must round the analog value to an integer). Each of these decisions, as with images, affects how well the digital information approximates the “perfect” analog signal. Let’s try an example on the board......

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CD-Quality Audio Compact Disc audio is encoded by sampling:

§  44,100 samples per second §  16 bits per sample per channel (2 channels) §  thus: 44,100 * 16 * 2 = 1,411,200 bits per sec §  Or about 10,600,000 bytes per minute

CD Audio uses about 10 megabytes per minute of audio. At 700 MG, a CD thus holds about 70 minutes of music in uncompressed form. At this rate, you would get about 1600 minutes = 26.6 hours of audio on an 16 GB iPhone 6. But this is without applying various compression algorithms.

Computer Science Sampling, Bitrate, Quality

Let’s listen to some examples……

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Digital Audio Formats

Audio Formats §  CDA, WAV, AU, AIFF, VQF, and MP3

MP3 (MPEG-2, audio layer 3 file) is most popular §  Music signal is “simplified” using psychoacoustic

principles §  The sequence of bits is then compressed using

algorithms from psychoacoustics.

Computer Science Psychoacoustics

Computer Science

Auditory Masking

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MP3 Encoding Principles

§  Break file into small “frames” of a fraction of a second each;

§  Analyze each frame in terms of frequencies present;

§  Eliminate frequencies which would be masked anyway;

§  Recalculate the samples; and §  Record the new signal. §  Some times additional compression algorithms

are applied…. Encoding music files in MP3 is a “lossy” process; you lose some information---you could not recreate the original music file from the MP3 version!

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Representing Audio Information

§  MP3 compression rates are based on how much bandwidth the final file will use to play music in real time:

§  128kbps ~ 128,000 bits per second is “CD Quality” §  Or about 960,000 bytes per minute §  Much smaller rates can be used for voice, e.g., news

broadcasts, etc.

Compare to uncompressed CD audio – 10,600,000 bytes per minute! A CD holds about 700 MB (700,000,000 bytes)

§  About 70 minutes of CD audio format §  Or about 911 minutes of MP3 audio format at 128 kbps

Punchline: MP3 compression can keep the same quality still reduces the size by ~90%.

Computer Science

Next Time: Lossless Compression

Long sequences of bits, especially for media, have many features which allow them to be encoded in much less space, with no loss of information:

Compression Algorithm

Decompression Algorithm

0101001010100101010101010111010000101110111011010101010101010101010101010

101001010101010101110100001011101110

Original File Compressed File

The encoding is “lossless”; compressing and then decompressing gives same file!