MULTIRATE SIGNAL PROCESSING C. Williams & W. Alexander North Carolina State University, Raleigh, NC (USA) ECE 513, Fall 2019 C. Williams & W. Alexander (NCSU) MULTIRATE SIGNAL PROCESSING ECE 513, Fall 2019 1 / 303
Sample Rate Conversion Many digital systems perform all of the required operations at a single sampling rate. However, there are many practical digital systems that require the sampling rate to be changed one or more times during normal operation. Examples include, telecommunication systems which transmit and receive different types of signals, facsimile (Fax), speech compression, and video compression C. Williams & W. Alexander (NCSU) MULTIRATE SIGNAL PROCESSING ECE 513, Fall 2019 2 / 303
Sample Rate Conversion These applications require the processing of the signal at different rates commensurate with the corresponding bandwidths of the signals [ ? ]. In general, manipulation of the sampling rate of a digital signal is accomplished by increasing or decreasing the sampling rate by some factor. This process is generally called sampling rate conversion . Systems that use digital signals at different sampling rates are called multirate digital signal processing systems . C. Williams & W. Alexander (NCSU) MULTIRATE SIGNAL PROCESSING ECE 513, Fall 2019 3 / 303
Sample Rate Conversion There are two general methods for performing sampling rate conversions [ ? ]. One method is to pass the digital signal through a D/A converter and then sample the reconstructed, continuous–time signal at the new sampling rate. This method often leads to signal distortion due to signal reconstruction and quantization effects in the D/A converter and/or in the A/D, converter. The second method involves performing the sampling rate conversion directly in the digital domain. This method can can often result in less than the previous method. distortion. C. Williams & W. Alexander (NCSU) MULTIRATE SIGNAL PROCESSING ECE 513, Fall 2019 4 / 303
Sample Rate Conversion We will explore methods to perform sampling rate conversion in the digital domain in this chapter. The sampling rate of a discrete–time sequence can be changed using up sampling or down sampling. We define up sampling as the process of increasing the sampling rate by a factor of M by inserting M - 1 zeros between the samples. We define down sampling by a factor of M by only keeping every M th sample and deleting the M - 1 samples between every M th sample. C. Williams & W. Alexander (NCSU) MULTIRATE SIGNAL PROCESSING ECE 513, Fall 2019 5 / 303
Up Sampling Figure 1 shows a block diagram of the up sampling process. M x(n) y(n) Figure: Block diagram of the up sampling process. C. Williams & W. Alexander (NCSU) MULTIRATE SIGNAL PROCESSING ECE 513, Fall 2019 6 / 303
Up Sampling If we have an arbitrary input x ( n ) with N samples, then the output y ( n ) is defined as y ( Mn ) = x ( n ) ∀ 0 ≤ n ≤ N - 1 (1) y ( n ) = 0 otherwise (2) where M is an integer.
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