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Sampling Rate Conversion
Overview
In discrete
‐
time signal processing, it is often necessary to convert a signal from one sampling rate to
another. A common example is the conversion from the sampling rate of a compact disk (CD); signal
(44.1 KHz) to that of a Digital Audio Tape (DAT) signal (48 KHz). Another example is the aud io standard
in High
‐
Definition Television (HDTV) transmission, where at least three sampling rates are supported
(32, 44.1, and 48 KHz). Although in principle we may convert the signal back to analog form and
resample at the desired rate, it is usually preferable to perform t he entire conversion digitally. This is
clue to many considerations including the fact that conversion to analog form often introduces noise in
the signal, and that digital signal processing can be much more cost
‐
effective and flexible.
This MATLAB project asks you to perform a sampling rate conversion on segments of audio signals. The
input audio signals are quantized to 8 bits and sampled with a sampling frequency of 11,025 Hz. You are
required to convert the signal to a sampling rate of 24,000 Hz in a computationally efficient manner.
Although one conceptual way of realizing this sampling rate conversion process is to upsample the
signal, lowpass filter, and downsample it, a more clever implementation can lead to an implementation
that is many times more efficient. To do this, you can exploit various aspects of class to optimize the
system, such as multistage filter implementation, filter design, and polyphase implementation. By the
end of the project, you hopefully will have a much better understanding of both the theoretical aspect
of the system as well as various issues in implementing a practical DSP system at a software level.
Project Goal
A sampling rate converter which produces an output signal with a sampling rate which is
M
L
times the
original sampling rate can be specified as shown in Figure 1.
Figure 1: Sampling rate conversion system.
For an ideal sampling rate converter, the lowpass filter in Figure 1 is an ideal lowpass filter with cutoff
frequency
⎟
⎠
⎞
⎜
⎝
⎛
=
L
M
c
π
ω
,
min
The goal of this project is to design an efficient DSP algorithm that
implements the system in Figure 1 subject to the following constraints:
•
The system performs the correct sampling rate conversion from 11,025 Hz to 24,000 Hz. In
particular, do not assume that 11,025 Hz
≈
11,000 Hz.