Applications of digital signal processing - Continuous and Discrete Time Signals and Systems - page 789

Table 17.2. Comparison of JPEG compression performance for sanjukta gray image

Quality factor, Q Name of the compressed file Size of the file (kbytes) Compression ratio MSE

100 sanjukta - 100 41.7 3 0.05

50 sanjukta - 50 11.1 11 12.34

25 sanjukta - 25 4.8 26 18.98

10 2.9 43 36.69

sanjukta - 10

5 2.3 54 76.05

sanjukta - 5

that decreasing the quality factor increases the compression ratio at the cost of
the reconstruction quality, apparent from the increase in MSE.
To provide a subjective comparison, the reconstructed images are shown in
Fig. 17.24. We observe that the perceived quality of the reconstructed images
degrades with the decrease in the quality factor. In other words, there is a
trade-off between quality and size of the compressed file.

17.8 Summary

This chapter presented applications of digital signal processing in audio and
image processing. Digital signals, including audio, images, and video, are ran-
dom in nature. Section 17.2 presented an overview of spectral analysis methods
for random signals based on the short-time Fourier transform, spectrogram, and
periodogram. Section 17.3 covered fundamentals of audio signals, their storage
format, and spectral analysis of audio signals. Filtering of audio signals was
covered in Section 17.3, and principles of audio compression were presented
in Section 17.4.
Section 17.5 extended digital signal processing to 2D signals. In particular,
we introduced digital images, their storage format, and the spectral analysis
of image signals. Section 17.6 covers 2D filtering, including the application
of lowpass filters to eliminate high-frequency noise and highpass filters for
edge detection. In each case, we presented examples of image filtering through
M ATLAB . Section 17.7 introduced principles of image compression including
the 2D differential pulse-code modulation (DPCM) and the Joint Photographic
Expert Group (JPEG) standard. Using M ATLAB , we compared the perfor-
mance of JPEG at different compression ratios.

Problems

17.1 Consider the following deterministic signal:

x 1 [ k ] = 2 sin(0 . 2 π k ) + 3 cos(0 . 5 π k ) .

Using a DFT magnitude spectrum, estimate the spectral content of
x [ k ] for the following cases: (a) a 20-point DFT and a sample size