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(b) From the result of part a, Mdb 20 log jA j! j 20 log !RC 40 log j j!RC 1j % 20 log !RC 20 log !RC for !RC 1 for !RC ! 1

public class ArrayQueue<E> implements Queue<E> { private E[] elements; private int front; private int back; private static final int INITIAL_CAPACITY = 4; public ArrayQueue() { elements = (E[]) new Object[INITIAL_CAPACITY]; } public ArrayQueue(int capacity) { elements = (E[]) new Object[capacity]; } public void add(E element) { if (size() == elements.length - 1) { resize(); } elements[back] = element; if (back < elements.length - 1) { ++back; } else { back = 0; //wrap } } public E element() { if (size() == 0) { throw new java.util.NoSuchElementException(); } return elements[front]; } public boolean isEmpty() { return (size() == 0); } public E remove() { if (size() == 0) { throw new java.util.NoSuchElementException(); } E element = elements[front]; elements[front] = null; ++front; if (front == back) { // queue is empty front = back = 0; }

Figure 9-15(b) is a plot of this approximate (asymptotic) expression for Mdb . For a true di erentiator, we would have vo K dvS dt or Vo sKVS

48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73

It s easy to design and use your own interfaces, too However, in this brief chapter we will not be discussing that topic ERROR HANDLING Java uses Exceptions to represent error conditions Exception is actually a class in Java, and when a program creates an Exception, it creates a new object, which is an instance of the Exception class An Exception object can have information about what went wrong, usually including an error message, and a stack trace showing which method created the error Having created an Exception object when something goes wrong, the program throws the Exception using the key word throw The JVM will print an error message and stop execution when a program throws an Exception, unless the programmer has provided code to catch the exception and handle the error condition in the program.

which would lead to Mdb 20 log !K. Thus the practical circuit di erentiates only components of the signal whose frequency is less than the break frequency f1 1=2 RC Hz. Spectral components above the break frequency including (and especially) noise will be attenuated; the higher the frequency, the greater the attenuation.

if (front == elements.length) { front = 0; } return element; }

In analog signal processing, the need often arises to introduce a level clamp (linear ampli cation to a desired output level or value and then no further increase in output level as the input continues to increase). One level-clamp circuit, shown in Fig. 9-16(a), uses series Zener diodes in a negative feedback path. Assuming ideal Zeners and op amp, nd the relationship between vo and vS . Sketch the results on a transfer characteristic.

public int size() { if (front <= back) { return back - front; } else { return back - front + elements.length; } } private void resize() { int size = size(); int len = elements.length; assert size == len; Object[] a = new Object[2*len]; System.arraycopy(elements, front, a, 0, len - front); System.arraycopy(elements, 0, a, len - front, back); elements = (E[])a; front = 0; back = size; } }

_ _ R1 V R2 Z2 _V (a)

This approach to handling program errors is called exception handling for obvious reasons, and it s a relatively modern idea One advantage of handling errors this way is that code to handle error conditions will be segregated into code blocks separate from the main logic of the program This makes it much easier to follow the intent of the programmer, both in the main logic and in the error handling code Java provides many subclasses of Exception so that different problems result in different classes of Exception objects being thrown Some examples include FileNotFoundException, NullPointerException, and NumberFormatException Java recognizes two types of Exceptions, checked and unchecked The names come from what the Java compiler does with them The compiler checks for appropriate handling of checked Exceptions, but does not check for handling of unchecked Exceptions.

Fig. 9-16