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Signals can be, and are, studied in both the time domain and the frequency domain. In the time domain we principally study the manner in which the amplitude and time delay of a signal change with time. In the frequency domain we study the amplitudes and phase shifts of the di erent sinusoidal frequency components present in a signal (the fundamental and harmonics, as outlined in note 18 in the Appendix). The result of such a study is summarized in terms of the frequency response characteristic of a system. An electric FILTER is a network designed to have a SPECIFIC FORM of frequency response characteristic. Thus we have low-pass lters, high-pass lters, and so on. You ll recall that it s convenient to display such results graphically, in the form of frequency response curves. By frequency it s always understood that we mean the frequencies of the sinusoidal component waves of a signal. As always, frequency in radians per second is denoted by omega, !, while frequency in cycles per second (hertz) is denoted by f , in which, as you know, ! 2 f . In practical work it s convenient to express results in terms of FREQUENCY of SINUSOIDAL waves of voltage and current. Thus in the time domain we work with the basic equations v sin !t and v cos !t. We have found, however, that the ALGEBRAIC work can be greatly simpli ed if we are not restricted to the use of real numbers only but are allowed to work in the total complex plane of all numbers. This is because the algebraic operations of multiplication, division, roots, and powers are easier to express and carry out in the complex plane than in

the ordinary x; y plane of real number pairs. (This is fundamentally true because complex numbers can be expressed in EXPONENTIAL FORM to which the laws of exponents can be applied to simplify the foregoing mentioned algebraic operations.) But now let us get on with the subject of digital lters. In the study of such lters much use is made of the unit circle in the complex plane. Let us therefore begin by returning brie y to Figs. 352 and 353 and eq. (598) in section 13.7. In that discussion we show that the EQUATION of the unit circle IN THE COMPLEX PLANE is given by z j cos j sin which we can also regard as being the basic EQUATION of a SINUSOIDAL WAVE of peak value 1 when expressed in complex numbers. Note that the real and imaginary parts of the equation each separately represent sinusoidal waves if sketched on the ordinary x; y plane of real numbers. Now let us note that the meaning of frequency response, as applied to digital networks, is basically the same as that de ned for analog networks,* except that in the digital case the input test signal will be a SAMPLED sinusoidal wave instead of a continuoustime sinusoidal wave as in the analog case. In this regard consider Fig. 357, which shows, in block diagram form, the test setup required to experimentally determine the frequency response of a digital lter (abbreviated DF). Note that the setup uses both analog-to-digital (A/D) an digital-to-analog (D/A) circuits.

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Downloading Web pages from the Internet in Java is quite simple, as evidenced by this method. First, a BufferedReader object is created for reading the contents of the page at the given URL. The BufferedReader s constructor is passed an instance of InputStreamReader, whose constructor is passed the InputStream object returned from calling pageUrl.openStream( ). Next, a while loop is used to read the contents of the page, line by line, until the reader.readLine( ) method returns null, signaling that all lines have been read. Each line that is read with the while loop is added to the pageBuffer StringBuffer instance. After the page has been downloaded, its contents are returned as a String by calling pageBuffer.toString( ). If an error occurs when opening the input stream to the page URL or while reading the contents of the Web page, an exception will be thrown. This exception will be caught by the empty catch block. The catch block has purposefully been left blank so that execution will continue to the remaining return null line. A return value of null from this method indicates to callers that an error occurred.

Vitamin C is a very potent antioxidant. It prevents nitrosamine formation in the stomach; prevents the activation of PAHs to cancer-causing agents; and decreases radiation-induced toxicity, mutations, and cancer. Vitamin C works synergistically with several other vitamins and minerals as well as other antioxidants to lower cancer and cardiovascular disorder rates and to increase the protective effect of the immune system. It is critical for producing and maintaining collagen, healing wounds, aiding tooth and bone formation, and producing hormones that regulate basal metabolic rate and body temperature. Vitamin C also aids in the metabolism of amino acids and calcium. It promotes stamina and contributes to the reduction of infection, colds, fatigue, stress, and allergies. Dr. Linus Pauling, a two-time Nobel Laureate, spent years studying vitamin C s beneficial effects. Vitamin C s effectiveness is enhanced when combined with certain other nutrients. In citrus fruits, vitamin C is kept in a reduced (antioxidant) state by various flavonoids. Without them, vitamin C would be unable to do its job of neutralizing free radicals. Once vitamin C finds its way to our cells, ascorbic acid reductase helps to keep it in a reduced state. Lipoic acid and dihydrolipoate help vitamin C (and vitamin E) to destroy many different types of free radicals. Vitamin C helps to keep vitamin E in a reduced and active (antioxidant) state so it can destroy free radicals in cellular membranes as well.

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