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Audio Coding

Audio Coding. Ketan Mayer-Patel. Overview of Today. PCM Linear m -LaW DPCM ADPCM MPEG-1 Vocoding. Sampling Techniques. Generic Coding Techniques. Psychoacoutic Coding. Speech Specific Techniques. Audio Signals. Analog audio is basically voltage as a continuous function of time.

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Audio Coding

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  1. Audio Coding Ketan Mayer-Patel CS 294-9 :: Fall 2003

  2. Overview of Today • PCM • Linear • m-LaW • DPCM • ADPCM • MPEG-1 • Vocoding Sampling Techniques Generic Coding Techniques Psychoacoutic Coding Speech Specific Techniques CS 294-9 :: Fall 2003

  3. Audio Signals • Analog audio is basically voltage as a continuous function of time. • Unlike video which is 3D, audio is a 1D signal. • Can capture without having to discretize the higher dimensions. • Audio sampling basically boils down to quantizing signal level to a set of values. • Digital audio parameters: • bits per sample • sampling rate • number of channels. CS 294-9 :: Fall 2003

  4. Sampling • Pulse Amplitude Modulation (PAM) • Each sample’s amplitude is represented by 1 analog value • Sampling theory (Nyquist) • If input signal has maximum frequency (bandwidth) f, sampling frequency must be at least 2f • With a low-pass filter to interpolate between samples, the input signal can be fully reconstructed CS 294-9 :: Fall 2003

  5. Quantization error (“noise”) 0100 0011 0010 0001 0000 1001 1010 1011 1100 SNR – 4.77 n = 6.02 PCM • Pulse Code Modulation (PCM) • Each sample’s amplitude represented by an integer code-word • Each bit of resolution adds 6 dB of dynamic range • Number of bits required depends on the amount of noise that is tolerated CS 294-9 :: Fall 2003

  6. Linear PCM • Uses evenly spaced quantization levels. • Typically 16-bits per sample. • Provides a large dynamic range. • Difficult for humans to perceive quantization noise. • Compact Disks • 16-bit linear sampling • 44.1 KHz sampling rate • 2 channels CS 294-9 :: Fall 2003

  7. Non-linear Sampling • If we try to use 8 bits per sample, dynamic range is reduced significantly and quantization noise can be heard. • In particular, we end up with not enough levels for the lower amplitudes. • Solution is to sample more densely in the lower amplitudes and less densely for the higher amplitudes. • Sort of like a log scale. CS 294-9 :: Fall 2003

  8. Non-linear Sampling Illustrated Output Input CS 294-9 :: Fall 2003

  9. m-law and A-law • Non-linear sampling called “companding” • 8-bits companded provides dynamic range equivalent to 12-bits. • U-law and A-law are companding standards defined in G.711 • Difference is in exact shape of piece-wise linear companding function. CS 294-9 :: Fall 2003

  10. ln(1 + |x|) f(x) = 127 x sign(x) x ln(1 + ) m -Law companding • Provides 14-bit quality (dynamic range) with an 8-bit encoding • Used in North American & Japanese ISDN voice service • Simple to compute encoding (x normalized to [-1, 1]) CS 294-9 :: Fall 2003

  11. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... m -Law Encoding High-resolution PCM encoding (12, 14, 16 bits) 8-bit -Law encoding Table Lookup Inverse Table Lookup 14-bit decoding Sender Receiver Input Amplitude 0-1 1-3 29-31 31-35 91-95 95-103 215-223 223-239 463-479 Step Size 1 2 4 8 16 Segment 000 001 010 011 Quanti- zation 0000 0001 1111 0000 1111 0000 1111 0000 1111 Code Value 0 1 15 16 31 32 47 48 63 CS 294-9 :: Fall 2003

  12. ... ... ... ... ... ... ... ... m -Law Decoding High-resolution PCM encoding (12, 14, 16 bits) 8-bit -Law encoding Table Lookup Inverse Table Lookup 14-bit decoding Sender Receiver m-Law Endoding 0000000 0000001 0001111 0010000 0011111 0100000 0101111 0110000 0111111 Multiplier 1 2 4 8 16 Decode Amplitude 0 2 30 33 93 99 219 231 471 CS 294-9 :: Fall 2003

  13. Difference Encoding • Differential-PCM (DPCM) • Exploit temporal redundancy in samples • Difference between 2 x-bit samples can be represented with significantly fewer than x-bits • Transmit the difference (rather than the sample) 0100 0011 0010 0001 0000 1001 1010 1011 1100 CS 294-9 :: Fall 2003

  14. “Slope Overload” Slope Overload Problem • Differences in high frequency signals near the Nyquist frequency cannot be represented with a smaller number of bits! • Error introduced leads to severe distortion in the higher frequencies 0100 0011 0010 0001 0000 1001 1010 1011 1100 CS 294-9 :: Fall 2003

  15. Adaptive DPCM (ADPCM) • Use a larger step-size to encode differences between high-frequency samples & a smaller step-size for differences between low-frequency samples • Use previous sample values to estimate changes in the signal in the near future CS 294-9 :: Fall 2003

  16. ADPCM • To ensure differences are always small... • Adaptively change the step-size (quanta) • (Adaptively) attempt to predict next sample value y-bit PCM sample x-bit ADPCM “difference” + Difference Quantizer + – Step-Size Adjuster Predicted PCM Sample n+1 + Predictor Dequantizer + + CS 294-9 :: Fall 2003

  17. IMA’s proposed ADPCM • Predictor is not adaptive and simply uses the last sample value • Quantization step-size increases logarithmically with signal frequency 16-bit PCM sample 4-bit ADPCM difference + Difference Quantizer + – Step-Size Adjuster PCM Sample n–1 + Register Dequantizer + + CS 294-9 :: Fall 2003

  18. IMA Difference Quantization + 16-bit PCM sample 4-bit ADPCM difference (in step-size units) Difference Quantizer + – PCM sample n–1 Step-Size Adjuster + Register Dequantizer + + Quantizer Output Step-Size Multiples Quantization difference < step_size 000 0.0 step_size < difference < step_size 001 0.25 step_size < difference < step_size 010 0.50 step_size < difference < step_size 011 0.75 step_size < difference < step_size 100 1.0 step_size < difference < step_size 101 1.25 step_size < difference < step_size 110 1.5 step_size < difference 111 1.75 1 4 1 4 1 2 1 2 3 4 3 4 5 4 5 4 3 2 3 2 7 4 CS 294-9 :: Fall 2003 7 4

  19. IMA Step-size Table Step Size Step Size Step Size Step Size Step Size Index Index Index Index Index 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 7 8 9 10 11 12 13 14 16 17 19 21 23 25 28 31 34 37 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 41 45 50 55 60 66 73 80 88 97 107 118 130 143 157 173 190 209 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 230 253 279 307 337 371 408 449 494 544 598 658 724 796 876 963 1060 1166 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 1282 1411 1552 1707 1878 2066 2272 2499 2749 3024 3327 3660 4026 4428 4871 5358 5894 6484 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 7132 7845 8630 9493 10442 11487 12635 13899 15289 16818 18500 20350 22358 24623 27086 29794 32767 CS 294-9 :: Fall 2003

  20. Adaptive Step-size Selection + 16-bit PCM Sample 4-bit ADPCM difference (in step-size units) Difference Quantizer + – PCM Sample n–1 Step-Size Adjuster + Register Dequantizer + + Index Adjustment Quantizer Output Step-Size Table Lookup Range Limit (0 to 88) Step-Size Table Index Adjustment Lookup + Previous Index Register CS 294-9 :: Fall 2003 New Step-Size

  21. Quantizer Output Step-Size Table Index Adjustment Step-Size Adjustment 000 001 010 011 100 101 110 111 X 0.91 X 0.91 X 0.91 X 0.91 X 1.21 X 1.46 X 1.77 X 2.14 Adaptive Step-size Selection Step-Size Table Lookup Range Limit (0 to 88) Step-Size Table Index Adjustment Lookup Difference Quantizer + Index Adjustment Previous Index Register New Step-Size Quantization difference < step_size step_size < difference < step_size step_size < difference < step_size step_size < difference < step_size step_size < difference < step_size step_size < difference < step_size step_size < difference < step_size step_size < difference -1 -1 -1 -1 1 4 1 4 1 2 1 2 3 4 3 4 2 4 6 8 5 4 5 4 3 2 3 2 7 4 CS 294-9 :: Fall 2003 7 4

  22. IMA ADPCM Example Reconstituted difference Step-Size table index Step-size multiplier Index Adjustment Quantizer output Predicted value Difference Step Size Input X Step Q Adj I M  Decode 150 7 0 150 155 5 7 010 -1 0 0.5 3.5 154 167 13 7 111 8 8 1.75 12 166 170 4 16 001 -1 7 0.25 4 170 250 80 14 111 8 15 1.75 24.5 195 250 55 31 111 8 23 1.75 54 249 250 1 66 000 -1 22 0.0 0 249 250 1 60 000 -1 21 0.0 0 249 200 -49 55 011 -1 20 0.75 -41 208 200 200 200 200 200 200 + Difference Quantizer + Xn – Step-Size Adjuster Xn–1 + Register Dequantizer + + CS 294-9 :: Fall 2003

  23. 1 4 1 2 1 4 1 2 3 4 3 4 5 4 5 4 3 2 3 2 7 4 7 4 Networking Considerations The IMA codec is reasonably robust to errors An interval with a low-level signal will correct any step-size error + Dequantizer + PCM sample n–1 + Step-Size Adjuster Register Quantizer Output Step-Size Table Index Adjustment Quantization difference < step_size step_size < difference < step_size step_size < difference < step_size step_size < difference < step_size step_size < difference < step_size step_size < difference < step_size step_size < difference < step_size step_size < difference 000 -1 001 -1 010 -1 011 -1 100 2 101 4 110 6 111 8 CS 294-9 :: Fall 2003

  24. Psychoacoustic Properties • Human perception of sound is a function of frequency and signal strength • (MPEG exploits this relationship.) 100 80 60 40 20 0 Audible Sound Level (dB) Inaudible Frequency (kHz) 0.02 0.05 0.1 0.2 0.5 1 2 5 10 20 CS 294-9 :: Fall 2003

  25. Auditory Masking • The presence of tones at certain frequencies makes us unable to perceive tones at other “nearby” frequencies • Humans cannot distinguish between tones within 100 Hz at low frequencies and 4 kHz at high frequencies 100 80 60 40 20 0 Audible Sound Level (dB) Masking tone Masked tone Inaudible Frequency (kHz) 0.02 0.05 0.1 0.2 0.5 1 2 5 10 20 CS 294-9 :: Fall 2003

  26. MPEG Encoder Block Diagram PCM Audio Samples (32, 44.1, 48 kHz) Mapping Quantizer Coding Psycho- acoutstic Model Frame Packing Encoded Bitstream Ancillary Data CS 294-9 :: Fall 2003

  27. Subband Filter • Transforms signal from time domain to frequency domain. • 32 PCM samples yields 32 subband samples. • Each subband corresponds to a freq. band evenly spaced from 0 to Nyquist freq. • Filter actually works on a window of 512 samples that is shifted over 32 samples at a time. • Subband coefficients are analyzed with psychoacoustic model, quantized, and coded. CS 294-9 :: Fall 2003

  28. Layer 1 • 384 samples per frame. • Iterative bit allocation process: • For each subband, determine MNR. • Increase number of quantization bits for subband with smallest MNR. • Iterate until all bits used. • Fixed allocation of bits among subbands for a particular frame. • Up to 448 kb/s CS 294-9 :: Fall 2003

  29. Layer 2 • 1152 samples per frame. • Iterative bit allocation. • Subband allocation is dynamic. • Up to 384 kb/s CS 294-9 :: Fall 2003

  30. Layer 3 • 1152 samples • Up to 320 kb/s • Each subband further analyzed using MDCT to create 576 frequency lines. • 4 different windowing schemes depending on whether samples contain “attack” of new frequencies. • Lots of bit allocation options for quantizing frequency coefficients. • Quantized coefficients Huffman coded. CS 294-9 :: Fall 2003

  31. Vo-coding • Concept: Develop a mathematical model of the vocal cords & throat • Derive/compute model parameters for a short interval and transmit to the decoder • Use the parameters to synthesize speech at the decoder • So what is a good model? • A “buzzer” in a “tube”! • The buzzer is characterized by its intensity & pitch • The tube is characterized by its formants CS 294-9 :: Fall 2003

  32. Vocoding - Basic Concepts • Formant — frequency maxima & minima in the spectrum of the speech signal • Vocoders group and code portions of the signal by amplitude 75 60 45 30 15 0 Amplitude Frequency (kHz) CS 294-9 :: Fall 2003

  33. p  k=1 “Buzzer” and “Tube” Model • Vocoding principles: • voice = formants + buzz pitch & intensity • voice – estimated formants = “residue” “yadda yadda yadda” • Linear Predictive Coding (LPC) • A sample is represented as a linear combination of p previous samples y(n) =aky(n – k) +Gxx(n) CS 294-9 :: Fall 2003

  34. LPC • Decoder artificially generates speech via formant synthesis • A mathematical simulation of the vocal tract as a series of bandpass filters • Encoder codes & transmit filter coefficients, pitch period, gain factor, & nature of excitation • Standards: • Regular Pulse Excited Linear Predictive Coder (RPE-LPC) • Digital cellular standard GSM 6.1 (13 kbps) • Code Excited Linear Predictive Coder (CELP) • US Federal Standard 1016 (4.8 kbps) • Linear Predictive Coder (LPC) • US Federal Standard 1015 (2.4 kbps) CS 294-9 :: Fall 2003

  35. Networking Concerns • Audio bandwidth is actually quite small. • But human sensitivity to loss and noise is quite high. • Netwoking concerns: • Loss concealment • Jitter control • Especially for telephony applications. CS 294-9 :: Fall 2003

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