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Data blocks are used to store the actual file data in the file system. Generally each inode contains 13 data block address slots. The first eight address slots point at the first eight file data blocks of the file. The ninth address points to an incore inode structure. The disk inode information is copied to this structure when the file is opened. The 10th through 13th addresses point to indirect data blocks that are used to address data blocks for large files. Each indirect block supports 1024 addresses. Newer UNIX file systems may incorporate additional structures to represent much larger files and file systems.

the z-transform pair ffnu(n)

(b) For this sequence we write x(n) = cos(nwo)u(n) = [eJnq+ e-jnq M n ) Therefore, the z-transform is

1. Combining the two terms together, we have X(z) = 1 - (cos wdz-' I - 2(cos wo)z-I z-2

The leakage-injection model of equilibrium output focuses on saving and gross imports as leakages from the circular ow and on investment and gross exports as spending injections. Leakages depress aggregate spending, while injections increase aggregate spending. For example, spending on domestic output declines when individuals buy more imported rather than domestically produced commodities. An equilibrium level of output exists in the leakage-injection model when the sum of leakages equals the sum of injections.

Find the z-transform of each of the following sequences. Whenever convenient, use the properties of the z-transform to make the solution easier. (a) x ( n ) = (+)"u(-n)

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The UNIX directory and file structure is organized such that it resembles an inverted tree, beginning with the root directory at the top and subdirectory branches proceeding down from the root. Each directory level in the tree may contain files or additional subdirectories. Directories also act as mount points for connecting additional file systems to the tree. The root-level directory, designated "/", acts as the base mount point for the full tree structure. A listing of mounted file systems, their mount points and attributes can be displayed using the df command (Example 2.6). When perusing the mount information on various systems you may recognize a set of common directory names. There is a somewhat standard set of directories used to house various types of files.

(b) x ( n ) = ( i ) " u ( n 2 )

+ + (3)"u(-n - 1 )

121 i

Alternatively, note that the time-reversed sequence y(n) = x(-n) = (;)-"u(n) has a z-transform given by

with a region of convergence given by Izl > 3. Therefore, using the time-reversal property, Y(z) = X(z-I), we obtain the same result. (b) Because x(n) is the sum of two sequences, we will find the z-transform of x(n) by finding the z-transforms of each of these sequences and adding them together. The z-transform of the first sequence may be found easily using the shift property. Specifically, note that because

- 25 -

+ 2) is 4.2'

which has a region of convergence lzl > The second term is a left-sided exponential and has a z-transform that we have seen before, that is,

The paradox of thrift demonstrates that increases or decreases in consumers desire to save, ceteris paribus, affect the economy s output level but not its saving level. Suppose that there are no exports or imports and that the government neither taxes nor spends. Individuals begin to save more of their income, which is a leakage. If investment does not increase, leakages will not equal injections. However, output will be decreased because individuals are not spending as much with more saving. Since output becomes income to individuals, income will decrease until saving equals investment again, i.e., leakages equal injections. If investment does not change, saving must end up at its initial value. Individuals may be saving a greater percentage of their income, but they have less income. So saving stays the same while output decreases. Saving has hurt the economy, thus the paradox.

cos(nwo)u(n) 6 Therefore, using the exponentiation property,

I - (cos w")z-I I -~(COS O&)z-' z-2 '

These are listed in Table 2.7. Example 2.6 Mounted Filesystem Attributes # df Filesystem /dev/hd4 /dev/hd2 /dev/hd9var /dev/hd3 /dev/lv01 /dev/lv02

S(n)

Without explicitly solving for X(z), find the region of convergence of the z-transform of each of the following sequences:

(a, x ( n ) =

1 (b) x(n) = 0

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