Analog to Digital Conversion in Signal Processing
Dive into the concept of analog to digital conversion in signal processing, covering topics such as PCM, Nyquist law, quantization, companding, digital encoding, and data rates. Learn how analog signals are converted to digital pulses and the techniques involved in signal reconstruction. Explore the impact of noise corruption and the importance of sampling frequency in signal processing.
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Presentation Transcript
Audio/video signals are analog Analog signals can take infinite Hence more difficult to detect at receiver after noise corruption analog in nature infinite number of values PCM converts analog signals to digital pulses 3-step process: sampling Extensions of PCM include DPCM and ADPCM sampling, quantization quantization, encoding encoding Pulses can take only finite For example, binary pulses can be either 0 or 1 Easier to detect at receiver (50% chance!) finite number of values
Nyquist law Nyquist law specifies sampling conditions Sampling interval T,sec /(2xsignal bandwidth,Hz) Sampling frequency fs, Hz 2xsignal bandwidth,Hz Signal can be reconstructed from samples (at or higher than Nyquist frequency)
Design step size n x x ) ( step size , for signal dynamic range : xM 2 = x M M L Construct quantizer input-output diagram with number of levels L = 2p Determine quantizer output ( n x )
Rounding off error Rounding off signal amplitude creates Quantizer SNR varies with signal x(n) and error e(n) x2 = Average signal power (W) e2 = Average noise power (quantizer error) ~ 2/12
Speech is compressed (before quantizing) and expanded (after quantizing) compander compander Companding improves quantizer SNR
Digital encoding converts L quantizer levels to binary format (p bits) Normal Binary Code (NBC) goes from 000.. to 111 2 s complement code can be obtained by complementing left-most bit in NBC 2 s complement can include levels Reconstruction of levels from binary level .......... ...... a a a a a 0 1 2 B B Decimal value =
Data rate Data rate or bit rate (bps) Rb= Sampling Rate (fs) x Bits/symbol (p) Channel Capacity C Channel Capacity C or maximum bit rate C = B log2(1 + SNR) This is Shannon s theorem Shannon s theorem
Rectangular pulses are not practical due to sharp edges => leads to Inter Symbol Interference (ISI) Inter Symbol Interference (ISI) Pulse is shaped using Nyquist criterion for zero ISI Raised Cosine filter Raised Cosine filter
Digital modulation combines sinusoid carrier (analog) and information (digital) Digital AM Examples: BPSK, QPSK, OPSK Differential AM Example DPSK Digital FM Examples: FSK, GMSK
PSK generates levels by shifting carrier phase carrier phase A cos(wct + k), k = 2 k/N Binary PSK (BPSK): N=2 Quadrature PSK (QPSK): N=4 Octal PSK (OPSK): N=8
FSK generates levels by shifting carrier frequency carrier frequency A cos[( c )t + ) c + ( ) and c ( )
PSK technique with data transition (0-1 or 1-0) causing carrier phase shift DPSK improves noise performance compared to PSK and FSK
Bandwidth B BPSK = Rb BFSK = Rb BDPSK = Rb /2 Rb = Data rate of system (bps) DPSK can have twice the data rate of BPSK or FSK, for the same available bandwidth
Definition of Q function Approximation of Q function (z > 3.0)
Error detecting codes (EDCs) Cyclic Redundancy Checks Checksums Cryptographic Hash Functions Error correcting codes (ECCs) Convolutional Codes Block Codes Turbo codes Low Density Parity Check codes
Equalization is an adaptive to minimize channel interference adaptive filtering process Two-step process Training-Fixed sequence pulse is sent from T-R to estimate frequency response of channel Tracking Receiver filter adapts frequency response to compensate channel response Equalization data sequence Training pulse - Data - Training pulse - Data-..
