EE 445 S RealTime Digital Signal Processing Lab
EE 445 S Real-Time Digital Signal Processing Lab Fall 2013 Lab #5. 1 Pulse Amplitude Modulation/ BPSK
Outline Block Diagram & Expressions of Transmitter Block Diagram & Expressions of Receiver Inter Symbol Interference & its Nyquist Criteria Raised Cosine Filter Digital Interpolation & Pulse Shaping Filter Banks Examples 2
Block Diagram of M-PAM Transmitter Bit Rate: Rd bits/sec Symbol Rate: Rd/J bits/sec Courtesy: Steven Tretters Chapter 11 Recitation Slides Example of 2 J Mapping 3
Expressions for Transmitter • An Impulse Modulator is • Output of Transmit Filter it • Rectangular pulse shaped BPSK: 4
Block Diagram of Receiver • Eliminate small deviations • Removes out of band noise • Forms perfect pulse shape with Tx Courtesy: Steven Tretters Chapter 11 Recitation Slides 5
Expressions for Receiver • Let us define g(t) as • Output of receive filter is 6
Inter Symbol Interference The received filter output: (Assuming no additive white Gaussian noise) We can rewrite this as: The condition on g(t) that needs to be satisfied for no ISI is: 7
Inter Symbol Interference (eye pattern) Superimpose every two symbols on each other for several times Binary PSK with ISI Courtesy: http: //www. answers. com/topic/intersymbolinterference Binary PSK without ISI Courtesy: http: //www. answers. com/topic/intersymbolinterference 8
Raised Cosine Filter Frequency Domain Time Domain Courtesy: http: //en. wikipedia. org/wiki/Raised-cosine_filter 9
Square Root Raised Cosine Filter The system should be designed in such a manner that the combined effect of Tx filter and Rx filter should be a Raised Cosine filter. 10
Digital Interpolation Example 16 bits 44. 1 k. Hz 4 16 bits 176. 4 k. Hz FIR Filter Digital 4 x Oversampling Filter Input to Upsampler by 4 28 bits 176. 4 k. Hz Upsampling by 4 (denoted by 4) Output input sample followed by 3 zeros Four times the samples on output as input Increases sampling rate by factor of 4 n 0 1 2 Output of Upsampler by 4 n’ 0 1 2 3 4 5 6 7 8 Output of FIR Filter FIR filter performs interpolation 0 1 2 3 4 5 Lowpass filter with stopband frequency stopband / 4 For fsampling = 176. 4 k. Hz, = / 4 corresponds to 22. 05 k. Hz n’ 6 7 8 13 - 11
Pulse Shaping Filter Bank Example L = 4 samples per symbol Pulse shape g[m] lasts for 2 symbols (8 samples) bits encoding s[m] = x[m] * g[m] No multiplication by zeros L polyphase filters {g[0], g[4]} …, a 1, a 0 {g[1], g[5]} {g[2], g[6]} {g[3], g[7]} …a 2 a 1 a 0 ↑ 4 s[0] = a 0 g[0] s[1] = a 0 g[1] s[2] = a 0 g[2] s[3] = a 0 g[3] …, s[4], s[0] …, s[5], s[1] … 000 a 1000 a 0 x[m] g[m] s[4] = a 0 g[4] + a 1 g[0] s[5] = a 0 g[5] + a 1 g[1] s[6] = a 0 g[6] + a 1 g[2] s[7] = a 0 g[7] + a 1 g[3] m=0 s[m] …, s[6], s[2] …, s[7], s[3] s[m] Commutator (Periodic) Filter Bank 13 - 12
- Slides: 12