By Woon Siong Gan

''Acoustical Imaging begins with an creation to the fundamental theories and ideas of acoustics and acoustical imaging, then progresses to debate its various functions: nondestructive trying out, scientific imaging, underwater imaging and SONAR and geophysical exploration. the writer attracts jointly the various applied sciences, highlighting the similarities among subject parts and their universal underlying concept. Some

''Introduces the fundamental theories and rules of acoustics and acoustical imaging''--Provided by means of publisher. Read more...

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**Extra info for Acoustical imaging : techniques and applications for engineers**

**Example text**

N − 1} is conjugate symmetric about N/2. 16) n=0 and v N − k = v∗ 2 N +k , 2 k = 0, . . 18) By considering the periodic extension of v(k), we have V(–k) = v(N – k). The DFT or unitary DFT of an N × 1 real sequence has N degrees of freedom and requires the same storage capacity as the sequence itself. 21) where in which DFT{x(n)}N denotes the DFT of the sequence x(n) of size N. 21) and then taking its inverse DFT. 19). 5 Extension from One-Dimensional Signal Processing to Two-Dimensional Image Processing Just as a one-dimensional signal can be represented by an orthogonal set of basis functions, an image can also be expanded in terms of a discrete set of basic arrays called basis images.

2 Magniﬁcation and Interpolation (Zooming) It is often necessary to zoom into a certain region of an image when one needs to view that region in more detail. 3 Replication Replication is a zero-order hold where each pixel along a scan line is repeated once and each scan line is then repeated. 43) This gives v(m,n) = u(k, l),k = Int n m , l = Int , m,n = 0, 1, 2 . . 2 shows some examples of interpolation by replication. 4 Linear Interpolation Linear interpolation is a ﬁrst-order hold where a straight line is ﬁrst ﬁtted between pixels along a row.

The digitization process for images can be understood by modelling the images as bandlimited signals. Although real-world images are rarely band-limited, they can be approximated by band-limited functions. 45) Here, ξx0 and ξy0 are known as the x and y bandwidths of the image. 4. 1 Sampling versus Replication The sampling theory can be easily understood by remembering that the Fourier transform of an arbitrarily sampled function is a scaled, periodic replication of the Fourier transform of the original function.