Digital Signal Processing Reference
In-Depth Information
one byte for 256
2
pixels. This is only 36% of the original size. Note that we do
not consider the size of the original image's le, since it is stored as a GIF encoded
image. The RMSE for the compressed image is 1.6, with a PSNR of 44 dB. Visually,
the resulting image compares favorably to the original.
In this section, we have seen the fundamentals of compression, and how the
transform, quantization, and entropy encoding steps allow us to store data in an
approximate, but ecient, manner. See the nal project les \compress test.m" and
\uncompress test.m," available on the CD-ROM. The former program encompasses
what we have covered above, while the latter reverses the operations at each step.
Together, they show that the lossy compression algorithm that we explored here
does a good job of storing the image eciently. The reader is encouraged to try
these programs and alter the wavelet and factor parameters to see their eects on
the compression.
10.12
Summary
This chapter presents several diverse applications of digital signal processing and
MATLAB. We started with the basics of sound manipulation, including recording,
reading and writing to disk, and playing back. Next, we saw how images can be
created, saved, and loaded. After that, we took images as input to the DWT, and
displayed the results of this transform as an image. Continuing with the wavelet
transform, the plus/minus transform presents a new way of thinking about it. We
then looked at a couple of programs from the CD-ROM that perform the DWT, then
undo the transform but preserve each channels' contributions. These programs are
good for analysis, such as locating edges within an image. We also saw how the
wavelet transform can be performed with matrix operations. We demonstrated re-
cursive programming with the Su Doku puzzle, and found that a poorly constructed
puzzle could have multiple solutions. Precision and data storage are important as-
pects of digital signal processing, and we looked at conversion to and from the IEEE
754 oating-point standard. Next, we had a sound-sampling program that responds
with a frequency plot to any nearby sound. We looked into lter design, and showed
how we could specify the lter coecients ourselves. Finally, this chapter includes
a brief introduction to compression.
10.13
Review Questions
1. Suppose variable x contains sound information, stored as double values. What
eect does the command sound(x*.7) have? What eect does the command
