EE123 Digital Signal Processing. Lecture 10 Practical ADC/DAC

Transcription

1 EE123 Digital Signal Processing Lecture 10 Practical ADC/DAC

2 Announcements Labs: audio problems on your PI, run alsamixer c 0 use M to toggle mute, up/down arrows to adjust volume Lab 3 part I due today, part II released today, due next Friday Last time: Multi-rate FilterBanks Today: Practical ADC/DAC

3 Ideal Anti-Aliasing ADC A/D Analog Anti-Aliasing Filter HLP(jΩ) sampler Quantizer and and

4 Non Ideal Anti-Aliasing interference noise Problem: Hard to implement sharp analog filter Tradeoff: Crop part of the signal Suffer from noise and interference (See lab II!)

5 Oversampled ADC ADC A/D Sharp Analog Anti-Aliasing Filter HLP(jΩ) C/D Quantizer Oversampled ADC A/D Simple Analog Anti-Aliasing Filter C/D Sharp Digital Anti-aliasing filter M Quantizer

6 Oversampled ADC

7 Oversampled ADC after oversampling x2 aliased noise

8 Oversampled ADC after oversampling x2 aliased noise after digital LP and decimation

9 Sampling and Quantization ADC A/D C/D Quantizer

10 Sampling and Quantization for 2 s complement with B+1 bits

11 Quantization Error Quantizer Model quantization error as noise + In that case:

12 Noise Model for Quantization Error Assumptions: Model e[n] as a sample sequence of a stationary random process e[n] is not correlated with x[n], e.g., E[e[n] x[n]] = 0 e[n] not correlated with e[m], e.g., E[e[n] e[m]] = 0 m n (white noise) e[n] ~ U " #, " # Result: Variance is:, or since Assumptions work well for signals that change rapidly, are not clipped and for small Δ

13 Quantization Noise Figure 4.57 (continued) (b) Quantized samples of the cosine waveform in part (a) with a 3-bit quantizer. (c) Quantization error sequence for 3-bit quantization of the signal in (a). (d) Quantization error sequence for 8-bit quantization of the signal in (a).

14 SNR of Quantization Noise For uniform B+1 bits quantizer: Quantizer range rms of amp

15 SNR of Quantization Noise Improvement of 6dB with every bit Quantizer range rms of amp The range of the quantization must be adapted to the rms amplitude of the signal Tradeoff between clipping and noise! Often use pre-amp Sometimes use analog auto gain controller (AGC) If σx = Xm/4 then SNRQ 6B dB so SNR of db requires 16-bits (audio)

16 Quantization noise in Oversampled ADC C/D + LPF ωc=π/m M ΩNM/π 1 σe 2 π/m ΩN/π σe 2 /M

17 Quantization noise in Oversampled ADC Energy of xd[n] equals energy of x[n] No filtering of signal! Noise var is reduced by factor of M For doubling of M we get 3dB improvement, which is the same as 1/2 a bit of accuracy With oversampling of 16 with 8bit ADC we get the same quantization noise as 10bit ADC!

18 Practical DAC (Ch ) D.T sinc pulse generator C.T Scaled train of sinc pulses Difficult to generate sinc Too long!

19 Practical DAC D.T Interp. Filter h0(t) H0(jΩ) C.T analog processing Recon. Filter hr(t) Hr(jΩ) h0(t) is finite length pulse easy to implement For example: zero-order hold 1 T

20 Practical DAC Zero-Order-Hold interpolation 0 T 2T 3T 4T 5T Taking a FT:

21 Practical DAC Output of the reconstruction filter: recon filter from zero-order hold Shifted copies from sampling

22 Practical DAC Ideally:

23 Practical DAC Practically:

24 Practical DAC Practically: = *

25 Practical DAC Practically:

26 Easier Implementation with Digital upsampling L LPF gain=l Practically:

27 Easier Implementation with Digital upsampling easier implementing with analog components Need analog components made of low-loss unobtainium transistors