quadrature sampling

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Post on 22-Jan-2018




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  1. 1. Two Channel Analysis Tejus Adiga M tejus.adiga@pelmicrosystems.net 1
  2. 2. Transmultiplexers tejus.adiga@pelmicrosystems.net 2 TDM - FDM FDM - TDM
  3. 3. tejus.adiga@pelmicrosystems.net 3 Transmultiplexers (FDM to TDM) A/D Converter: Sampling rate: 96khz 12 channels of 4khz each. Frequency Translation: Band pass to Baseband all 12 channels. Decimator: Reduce redundancy in each channel due to 12x oversampling to 4k Commutate: Multiplex 12 channel samples of each 4k samples/sec to form 96k samples/sec TDM signal. Sub band Decomposition: N point DFT as Filter bank of N band pass filters; each DFT value representing approximate value of each sub band. Twidel Factor: = cos 2 + 2
  4. 4. tejus.adiga@pelmicrosystems.net 4 Transmultiplexers (TDM to FDM)
  5. 5. Problem with only re-scaling Downsampler Upsampler X[n] X[2n] x1[n] Downsampler Upsampler X[n] X[2n] x1[n] H() G() tejus.adiga@pelmicrosystems.net 5
  6. 6. The Lost Information (Recedue) X[2n] x1[n] Downsampler Upsampler X[n] H() G() - E[n] E[n] error is significant Losses occur in H(w) and G(w) as they are LPFs; High frequency components are lost. PERFECT RECONSTRUCTION: In parallel keep track of High pass Frequencies filtered by LPFs and add it to the up sampled output x1[n]. tejus.adiga@pelmicrosystems.net 6
  7. 7. Quadrature Mirror Filter (QMF) Xa0 X1[n] Downsampler Upsampler X[n] H1() G1() H2() G2()Downsampler Upsampler Xa1 tejus.adiga@pelmicrosystems.net 7
  8. 8. Removing Aliasing H0(z) = H(z) H1(z) = H(-z) G0(z) = H(z) G1(z) = -H(-z) H0(w) = H(w) H1(w) = H(w-) G0(w) = H(w) G1(w) = - H(w-) h0[n] = h[n] h1[n] = (-1)n h[n] g0[n] = h[n] g1[n] = (-1)n h[n] tejus.adiga@pelmicrosystems.net 8
  9. 9. tejus.adiga@pelmicrosystems.net 9