Multirate Signal Processing

1. 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

2. 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

3. Cascaded Integrator Comb Filter (CIC) • Implement an interpolation or decimation filter • CIC Decimation Filter • CIC Interpolation Filter

4. 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

5. 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 channels 2. Filter Bank Synthesizer: reconstructs the input by combining the channel signals

6. Time Recovery in Digital Receivers Using Multirate Digital Filters • Reduces complexity compared to conventional timing recovery techniques Timing recovery in an Analog Receiver Timing recovery in a First Generation Digital Receiver A Multirate Filtering Approach to Synchronization

7. 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.

8. 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

9. 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.