Multirate Signal Processing

Multirate Signal Processing : The implementation of a digital signal processing application using variable sampling rates

Can Improve the flexibility of a software radio Reduces the need for expensive anti-aliasing analog filters Enables processing of different types of signals with different sampling

rates Allows partitioning of the high-speed processing into parallel multiple

lower speed processing tasks reduced costs Can lead to a significant saving in computational power Wideband receivers take advantage of multirate signal processing for

efficient channelization Offers flexibility for symbol synchronization and downconversion of

software radios

Multirate Signal Processing

Sample Rate Conversion Principles

(Integer Rate Conversion)

- Decimation

- Interpolation: zero-insertion, zero-order-hold (ZOH), zero-insertion, raised-cosine filtering, fast Fourier transform (FFT) expansion

Multi-Stage Sampling rate conversion

- offer less computation and more flexibility in filter design

Cascaded Integrator Comb Filter (CIC)

Implement an interpolation or decimation filter CIC Decimation Filter

CIC Interpolation Filter

Polyphase Filter

A way to reduce computational cost for a multirate system, by replacing high-speed elements with low-speed processing elements

Polyphase Decimation

Polyphase Interpolation

Digital Filter Banks

Applications: -To break a wideband signal into multiple bands-Allowing lower-speed computational techniques-Converting a signal from frequency division multiplexing (FDM) to time division multiplexing (TDM) or vice versa.

Implementation

Two Basic Architectures:1. Filter Bank Analyzer: decomposes the input signal into several channels2. Filter Bank Synthesizer: reconstructs the input by combining the channel signals

Time Recovery in Digital Receivers Using Multirate Digital Filters

Reduces complexity compared to conventional timing recovery techniques

Timing recovery in a First Generation Digital Receiver

Timing recovery in an Analog Receiver

A Multirate Filtering Approach to Synchronization

Direct Digital Synthesis

Direct Digital Synthesis (DDS) offers a number of advantages to signal generation in software Radio. Its digital nature in particular makes it very attractive.

Precision - Possible to set frequency accurately, with high resolution. Flexibility - Easy to change output parameters. Switching Frequency - High switching speeds possible, Output is

smooth and transient free during frequency change. Possible to have continuous phase during frequency switching.

Equipment size - DDS can be implemented at a fraction of the size of analogue synthesizers.

Spectral purity – If accumulator size is an integral multiple of the step size, the will be no phase truncation, and signal quality will be very high.

Approaches to DDS

Pulse Output DDS• Simplest of all DDS models• Consists of N-Bit Adder and register to produce saw tooth waveform.• Fout = Δr*Fclk/2N

• Limited use due to high spur and jitter levels.

ROM Look Up Table Sampled Values of periodic wave stored in ROM Wave period defined by Δr. Subject to phase truncation

Performance Of DDS

Spectral Purity and Sideband noise are major drawbacks of DDS.

DDS performance closely related to DAC performance

In practice, Clock frequency impacts performance of DDS.

If output frequency is chosen to be an exact fraction of clock frequency, spurious outputs are reduced.