1 Manipulating Audio

2 Why Digital Audio  Analogue electronics are always prone to noise time amplitude

3 The Digital Domain  Based on numbers  Digital representation of analogue signal: time number

4 Digital Electronics  Less expensive to design  Less expensive to manufacture  Offer high noise immunity  Age immunity  Temperature immunity  Increased reliability

5 The Digital Domain s s Analogue signal 6, 7, 6, 5, 3, 2, 1, 2 Digital stream Digital waveform

6 Nyquist  The highest frequency which can be accurately represented is one- half of the sampling rate  CD: Sample Rate = 44,100 Hz  Nyquist Frequency = SR/2 = 22,050 Hz

7 Aliasing

8  Bach trumpet  SR= highest frequency in music is about 7000 Hz (no aliasing)  SR= (some aliasing; adds a little dullness and a metallic quality)  SR= (lots of aliasing; sounds like bad video game)

9 Low Pass Filtering  The original signal must be low-pass filtered to remove signals higher than 0.5 of the sampling rate  CD: SR = 44,100Hz thus original signal must not exceed 22,050Hz to be completely sampled  Low-pass filtering avoids frequency fold-over

10 Filters low-pass filterband-pass filterhigh-pass filter White noise (unfiltered) Filtered white noise (low pass, band pass, high pass)

11 Filters

12 Oversampling

13 Sampling reality  Critical sampling is not attempted  Lowpass filters can not attenuate the signal precisely at the Nyquist frequency  DVD audio – 96 KHz?  CD – 44.1KHz  Telephone – 8KHz

14 Quantization s s Analogue signal 6, 7, 6, 5, 3, 2, 1, 2 Digital stream Digital waveform

15 Quantization  The number of quantization levels (N) is dependant on binary word length  N = 2 n  n = number of bits 2 8 = = (CD) 2 24 = (DVD)  The more bits the better the approximation  Worst error is 0.5 LSB

16 Quantization Error  Difference between the actual analogue value and the selected quantization interval value

17 Dithering  A small amount of noise that is uncorrelated with the input signal is added

18 Dithering

19 Dithering

20 A to D Principal elements Multiplexer Processing (error correction) Dither generator Sample and Hold Anti- aliasing filter A to D Converter Sample and Hold Anti- aliasing filter A to D Converter Analogue input (L) Analogue input (R)

21 Summary  Sampling and Quantization are the two fundamental criteria for a digitisation system  Aliasing occurs when sampling theory is not observed  Sampling is lossless  Quantisation is lossy  Dither can substantially reduce quantization distortion

22 Fin