Lab #5.1 Pulse Amplitude Modulation/ BPSK EE 445S Real-Time Digital Signal Processing Lab Fall 2013 Lab #5.1 Pulse Amplitude Modulation/ BPSK 1

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 2

Symbol Rate: Rd/J bits/sec 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 2J Mapping 3 3

Expressions for Transmitter An Impulse Modulator is Output of Transmit Filter it Rectangular pulse shaped BPSK: 4 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 5

Expressions for Receiver Let us define g(t) as Output of receive filter is 6 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 7

Inter Symbol Interference (eye pattern) Superimpose every two symbols on each other for several times Binary PSK with ISI Binary PSK without ISI Courtesy: http://www.answers.com/topic/intersymbol-interference Courtesy: http://www.answers.com/topic/intersymbol-interference 8 8

Raised Cosine Filter Frequency Domain Time Domain 9 9 Courtesy: http://en.wikipedia.org/wiki/Raised-cosine_filter 9 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 10

Digital Interpolation Example 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 FIR filter performs interpolation Lowpass filter with stopband frequency stopband   / 4 For fsampling = 176.4 kHz, =  / 4 corresponds to 22.05 kHz Digital 4x Oversampling Filter 16 bits 44.1 kHz 28 bits 176.4 kHz 4 FIR Filter 16 bits 176.4 kHz 1 2 Input to Upsampler by 4 n n’ Output of Upsampler by 4 1 2 3 4 5 6 7 8 1 2 Output of FIR Filter 3 4 5 6 7 8 n’ 13 - 11

Pulse Shaping Filter Bank Example L = 4 samples per symbol Pulse shape g[m] lasts for 2 symbols (8 samples) bits …a2a1a0 …000a1000a0 encoding ↑4 g[m] x[m] s[m] s[m] = x[m] * g[m] s[0] = a0 g[0] s[1] = a0 g[1] s[2] = a0 g[2] s[3] = a0 g[3] s[4] = a0 g[4] + a1 g[0] s[5] = a0 g[5] + a1 g[1] s[6] = a0 g[6] + a1 g[2] s[7] = a0 g[7] + a1 g[3] No multiplication by zeros L polyphase filters {g[0],g[4]} {g[1],g[5]} {g[2],g[6]} {g[3],g[7]} s[m] …,s[4],s[0] …,s[5],s[1] …,s[6],s[2] …,s[7],s[3] …,a1,a0 m=0 Commutator (Periodic) Filter Bank 13 - 12