Multirate Digital Signal Processing Fundamentals 1 Introduction Singlerate

Multirate Digital Signal Processing Fundamentals 1

Introduction • Single-rate systems: Sampling rates at the input and at the output and all internal nodes are the same • Multirate systems: DSP systems with unequal sampling rates at various parts of the system 2

Applications There are many applications where the signal of at a given sampling rate needs to be converted into another signal with a different sampling rate. • Sampling rates in some applications: v Digital audio applications • 32 k. Hz in broadcasting, • 44, 1 k. Hz in digital CD, • 48 k. Hz in digital audio tape (DAT) v Composite video signals • NTSC: 14, 3181818 MHz • PAL: 17, 734475 MHz v Digital component video • Luminance 13, 5 MHz • Color difference 6, 75 MHz 3

Multirate DSP Systems Basic Sampling Rate Alteration Devices • Up-sampler Used to increase the sampling rate by an integer factor • Down-sampler Used to decrease the sampling rate by an integer factor 4

Up-Sampling in Time-Domain 5

Up-Sampling in Time-Domain 6

Up-Sampling in Time-Domain 7

Down-Sampling in Time-Domain 8

Down-Sampling in Time-Domain 9

Down-Sampling in Time-Domain 10

Building Blocks of Multirate Systems • Down-sampler 11

Building Blocks of Multirate Systems 12

Frequency-Domain Characterization of Up-Sampling 13

Frequency-Domain Characterization of Up-Sampling 14

Frequency-Domain Characterization 15

Frequency-Domain Characterization of Down Sampling 16

Frequency-Domain Characterization of Down Sampling 17

Frequency-Domain Characterization of Down Sampling 18

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Cascade Equivalences Ø Complex multirate systems consist of the basic sampling rate alteration devices and LTI digital filters Ø In many applications, these devices appear in cascade connection Ø Computationally efficient structures are often obtained by interchanging the order of cascaded blocks Ø Specific cascade connections and their equivalences are investigated Ø Basic sampling rate alteration devices can be used for integer factors only 24

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Up sampler and Down- Sampler Cascade 26

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Filters in Multirate Systems Ø The sampling rate of a critically sampled discretetime system cannot be reduced without aliasing Ø Before down-sampling the bandwidth of critically sampled signal must be reduced by lowpass filtering Ø Similarly, the zero-valued samples introduced by an up-sampler must be interpolated to more appropriate values for an effective sampling rate increase Ø Interpolation can be achieved by lowpass filtering 30

Filters in Multirate Systems 31