Lecture 2–Signal Processing MP3 Player

Lecture 2–Signal Processing

ECE 197SA – Systems Appreciation

MP3 Player § Stores and plays back audio § Extremely widely used 350 million iPods sold through 2012 Over 280 million MP3 players sold annually Functionality integrated into many cell phones § How can it play music?

1 Audio as Physical Phenomenon § Vibrations of object generate sound § Sound propagates as pressure wave § Ear can sense pressure wave

§ How can we convert audio into electrical signal?

Audio as Analog Signal § Microphone translates waves into varying voltage § Speaker converts electrical signal into pressure wave

§ How can we record, store, and play back signal?

2 Audio Recording § Need ECE system to perform signal processing

ECE System: Audio recording, storage, playback

Analog Signal Recording § Mechanical signal representation

§ Magnetic signal representation

§ Analog recording introduces a lot of noise

3 Digital Signal Recording § Need process to represent analog signal in binary r e w o p

l a n g i s time 01000101110110…

§ How to do conversion?

Digital Signal Recording § Need process to represent analog signal in binary r e w o p

l a n g i s time 01000101110110…

§ Steps 1. Measure signal (“sampling”) 2. Translate into binary (“quantization”) 3. Store or transmit 4. [Reconstruct signal (“excite filter”)]

4 Sampling § Measuring signal at discrete times

§ Samples are representation of signal

Sampling Rate § Sampling rate determines quality of representation high sampling rate medium sampling rate low sampling rate

§ Low-rate sampling fails to capture high frequencies § Nyquist-Shannon sampling theorem “If a function f(t) contains no frequencies higher than W hertz, it is completely determined by giving its ordinates at a series of points spaced 1/2 W seconds apart.” Intuition: f(t) cannot change substantially in less than half cycle of highest frequency

5 Sampling Rate § Nyquist frequency is half the sampling frequency No aliasing if bandwidth of signal is below Nyquist frequency § What is a good sampling frequency for audio? r e w o p

l a n g i s

frequency

§ How to represent sampled values digitally?

Sampling Rate § Nyquist frequency is half the sampling frequency No aliasing if bandwidth of signal is below Nyquist frequency § What is a good sampling frequency for audio? r

e Nyquist sampling w

o frequency frequency p

l a n g i s

frequency

§ How to represent sampled values digitally?

6 Quantization § Samples have continuous value No way to represent digitally with arbitrary precision § “Quantization” assigns discrete value to each sample § Analog-to-digital (A/D) converter n-bit digital output As you know from ENGIN112: n bits have 2n possible values original sample quantized value

Quantization § Quantization is lossy Coarser quantization levels provide less accuracy original sample quantized value

7 Digital Representation § Digital representation Encode quantized values in binary Concatenate binary codes of samples Add meta-information (can be implied if standard is used) 011 011 011 010 010 010 010 001 001 001 001 000 000 000 000 000 encoded samples 101 101 101 101 101 110 110 110 110 110 111

sample stream 101 001 000 110 101 010 011 101 110 000 010 110 110 001 000 000 101 010 011 001

audio file

meta-information 101001000110101010011101110000010110110001000000101010011001 (sampling rate, coding, …)

Playback § Digital-to-analog (D/A) converter Generates voltage of sample value Voltage is held for duration of sample period § Low-pass filter to “smooth out” signal

§ Signal is amplified and sent to speaker

8 Aliasing § Difference between original and reconstructed signal

original reconstructed

Sampling and Quantization Tradeoffs § Sampling rate and quantization levels impact quality

low sampling rate, coarse quantization high sampling rate, coarse quantization

low sampling rate, fine quantization high sampling rate, fine quantization

9 Parameters § Configurations used in practice Telephony: pulse code modulation (PCM) » ITU-T standard G.711 » Sampling: 8000 samples per second » Quantization: 8-bit samples § Encoded from non-linear quantization of larger samples § µ-law in U.S. (14-bit samples) § A-law in Europe (13-bit samples) » Encoded signal: 64 kb/s (8kB/s) CD-quality audio: PCM » Sampling: 44,100 samples per second » Quantization: 16-bit samples » Encoded signal (stereo): 1.411 Mb/s (176.4kB/s) § How can we reduce bandwidth/storage?

Compression § Example for loss-less compression: Huffman coding Variable-length code Code length inversely related to symbol probability § Huffman coding for our example

101001000110101010011101110000010110110001000000101010011001

2-bit symbol frequency: 100% » 10 (37%), 01 (30%), 00 (23%), 11 (10%) 0 1

10 New encoding 63% 37%

» 10→0, 01→10, 11→110, 00→111 0 1

01 33% 00101111000001011010110111111101001101111011111111100010010 30%

0 1 Encoded sequence marginally better 11 00 » Only 1 bit (2%) shorter 10% 23% » Better on sequences with more redundancies

10 MP3 Compression § MPEG-1 Audio Layer 3 (MP3) § Lossy compression Uses perceptual coding » Reduces precision of audio components less audible to humans Sound is analyzed in a short windows » Analysis in time domain and frequency domain Coding exploits masking effects » Simultaneous masking: loud sound masks soft sound » Temporal masking: Loud sound masks following soft sound » Etc. § Reduces data rate considerably MP3 uses 128kb/s (16kB/s) for CD-quality audio Less than 1/10 of uncompressed CD § Typical 5-minute song: 4.8MB 16GB MP3 player: more than 3,000 songs

Courses in ECE Curriculum § ECE 313 – Signals and Systems § ECE 563 – Introduction to Communications and Signal Processing § ECE 565 – Digital Signal Processing § ECE 608 – Signal Theory

11 Upcoming… § Labs are available now See web site § Lecture 3 – Cell Phones Wireless communication Usual time, place § Moodle quiz