Lecture 3 Review of Signals and Systems: Part 2. EE4900/EE6720 Digital Communications

Transcription

1 EE4900/EE6720: Digital Communications 1 Lecture 3 Review of Signals and Systems: Part 2

2 Block Diagrams of Communication System Digital Communication System 2 Informatio n (sound, video, text, data, ) Transducer & A/D Converter Source Encoder Channel Encoder Modulator Tx RF System Channel Output Signal D/A Converter and/or output transducer Source Decoder Channel Decoder Demodulator Rx RF System = Discrete-Time = Continuous-Time

3 Re-sampling What is Re-sampling? Change of the sampling rate and number of samples Decrease the number of samples by factor of N 3 Increase the number of samples by factor of N

4 Down-sampling Down-sampling factor N=2 4 Original Sequence of Samples Down-sampled Signal

5 Up-sampling Up-sampling factor N=2 5 Original Sequence of Samples Up-sampling= zero-stuffing Up-sampling followed by Low Pass Filtering: Interpolation

6 Re-sampling Why Re-sample? To match the sampling rates (shown by red arrows) between A/D, Microprocessor, and/or D/A 6 Low Pass Filter ADC Digital Signal Processing DAC Low Pass Filter Anti-aliasing Filter Reconstruction Filter

7 Sampling Process Recall that DTFT of the discrete-time signal is periodic: this is due to sampling process of A/D conversion 7 A/D Conversion

8 Down-sampling A/D Conversion is followed by down-sampling to limit the number of samples Down-sampling by N spreads the spectrum by factor of N 8 Down-sampling by N Spectrum spreads by N

9 Effect of Down-sampling Down-sampling by N spreads the spectrum by factor of N This can create overlapping frequency components 9 Aliasing can corrupt or change signal (in time-domain)

10 Down-sampling and Anti-alias Filtering: Decimation Anti-aliasing filter (low pass filter) is used eliminate the overlapping frequency components Low Pass Filter with cut-off frequency=π/n before Downsampling by N 10 Original DTFT Spectrum is now limited by LPF Satisfies Nyquist Sampling Rate

11 Up-sampling D/A Conversion is preceded by up-sampling to increase the number of samples Up-sampling by N narrows the spectrum by factor of N Up-sampling by N 11 Spectrum shrinks by N

12 Up-sampling and Filtering: Interpolation Up-sampling stuffs zeros in between two samples Filtering can interpolate the samples and remove the zeros 12 Interpolated Samples Spectral copies are spaced apart

13 Re-sampling and Filtering Why use Filtering? To prevent aliasing (A/D side) and to smoothen the signal (D/A side) Limits the frequency response 13 Interpolates (inserts averaged ) samples

14 Filtering Low Pass Filter Types Four major types: Butterworth, Chebyshev, Elliptic, Bessel Filter phase response is important. Why? 14 Amplitude Response Phase Response Check in Matlab later (type fdatool )

15 Linear Constant-coefficient Difference Equation Input and output relationship of discrete-time system: Eq Suppose that 1) Input signal samples are denoted by x(n) and output by y(n) 1) The filter coefficients are denoted by numerator b 0,, b M and denominator a 0,, a M with filter order=m Eq. 3.18: Infinite Impulse Response (IIR) Filter Eq. 3.29: Finite Impulse Response (FIR) Filter

16 IIR Filter Infinite Impulse Response (IIR) Filter 1) Feedback, recursive: current output depends on previous outputs 2) Implemented by using a series of delays, multipliers, and adders 16 M-1 delays Delay Delay Delay x n b M... b 2 b 1 b 0 Numerator Coefficients Tap y n Filter Order= M... -a 2 -a M -a 1 -a 0 Denominator Coefficients Delay Delay Delay a 0 yn a1 yn 1 am y0 b0 xn b1 xn b x M 0 Eq. 3.18

17 FIR Filter Finite Impulse Response (FIR) Filter 1) No feedback 2) Implemented by using a series of delays, multipliers, and adders 17 Filter Order= M M-1 delays Delay Delay Delay x n b M... b 2 b 1 b 0 Numerator Coefficients b M x 0 b 2 x n-2 Tap b 1 x n-1 b 0 x n Note: 1) Delay =1 clock delay in DSP FPGA/Microprocessor 2) Tap is implemented by Multiply-accumulator (MAC) unit in DSP Microprocessor y n y n b 0 xn b1 xn 1... bm x0 Eq (replace h with b)

18 Assignment 1 Design FIR Filter using FDATOOL Simulate Up-sampling and Down-sampling in Simulink 18 Submit the following: 1) Filter Magnitude and Phase Response Plots 2) Simulink model(s) 3) Time-domain plots 4) Frequency domain plots