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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