Saturday, 25 August 2007

Plato's View that Philosophers Should Rule

The famous philosopher Plato holds that the world should be ruled by true philosophers. This idea involves a great deal of wisdom and have been studied by many philosophers. It will be discussed in this essay.

Plato not only has the opinion that philosophers should rule, but also has developed a whole theory to support this. According to Plato's masterpiece the Republic, there are three distinctions between philosophers and non-philosophers and these are important factors which to some extent, determine philosophers' absolute ruler position. Firstly, unlike most lovers of beautiful things, philosophers in addition love beauty itself, which is the Form introduced by Plato. Secondly, philosophers live in the real world, non-philosophers in their dream world. Lastly, philosophers are people who have true knowledge,, but counterfeit philosophers only have beliefs or opinions. Plato further conceives a model containing images of the Sun, the Line and the Cave to strengthen his theory. To elaborate, this model mainly illustrates the relation and difference between knowledge and ignorance, dream and reality.

As for Plato's viewpoint of distinctions between philosophers and non-philosophers, I argue that this is enough to note that philosophers should rule and they can run the world in the most balanced state. This is not purely because philosophers have knowledge, which others don't, but also because there are no better alternatives for them. Cross (1964) says that the difference between true philosophers and their rivals is that true philosophers know reality of which many counterfeit philosophers' 'reality' is appearance. This means true philosophers grasp the eternal and internal knowledge of things and this knowledge acts in real world as theorems and axioms do in mathematics. They are the rules that determine how everything in the world works. So a philosopher's mind is like an abstraction of non-philosopher's thoughts. But this kind of abstraction or high level of understanding is somewhat away from practice. They can't adjust their knowledge with times, so there exists a distance between their knowledge and the real world (Pappas, 1995). However, as is known to all, what play the fundamental role in the world are the natures of things and only philosophers can reach them. So despite their limitation of practical knowledge, philosophers are still more qualified to rule than any other people because they are fundamentally correct.

Plato's model of the Sun, the Line and the Cave also indicates that philosophers have the utmost intelligence and should rule the world. Because it basically shows different levels of the world – the visible and the intelligible. Cross (1964) perceives the model that those who stand at the top know the Form of the Good – the Sun, knowledge – the top of the Line, and truth – one who receives education and has broken out of the Cave. This model also to some degree, proves the point that philosophers being the rulers mainly because there are no better alternatives for them – they are on the top, despite the fact that this point of view might be slightly different from Plato's original meaning of philosophers being the rules.

All in all, although there might arise many explanations, there's an agreement that philosophers have the highest level of knowledge and should rule the world in order to achieve the most balanced state of the world.


References

Bobonich . C, “Why Should Philosophers Rule? Plato's Republic and Aristotle's Protrepticus”, Philosophy, Stanford University, Available at:
http://journals.cambridge.org/action/displayAbstract;jsessionid=11DEBBE7A2E0E52611522068E4C2DA0E.tomcat1?fromPage=online&aid=1031904

Cross. R. C, Plato's Republic – A Philosophical commentary, London, New York St Martin's Press, 1964.

Pappas Nickolas, Plato and the Republic, from the Republic of Plato translated by Allan Bloom, 1995.

Plato, The republic, edited by G.R.F. Ferrari ; translated by Tom Griffith, Published by New York. Cambridge University Press, 2000.

Tuesday, 26 June 2007

last sem's essay

Didn't do it very well, but yeh, at last I handed in a full draft. If you wanna reference, PLEASE CITE THE SOURCE.

Chinese Post World War II Immmigration



INTRODUCTION

After World War II, the reconstruction effort and low birthrate in Australia called for more immigrants. Although encouraging immigration under the White Australian Policy resulted in dramatic increase of overseas-born population according to a report from DIMIA (2003), during which Chinese people were looked down, it was not satisfactory enough. In this phase the need for a more diverse population was increasing. It was not until 1973 that the White Australian Policy was abolished (DIMIA, 2003) and it was not long before the policy of multiculturalism was introduced in 1978, after which Chinese migration started to fluctuate and made contributions to the society. This paper will discuss issues in the period before the policy of multiculturalism was introduced as well as the period after that. Firstly, it will focus on society's attitudes towards Chinese immigrants in terms of their social cultural and economic impact on the country. Secondly, governments' policies towards immigrants will be talked about.



AUSTRALIANS' ATTITUDES TOWARDS CHINESE

Chinese immigrants as well as other non-white immigrants were looked down and were not encouraged to come to Australia in the period immediately after World War II. This was because of the Immigration Restriction Act, which was introduced in 1901 and mainly aimed against Chinese (Chan, 2000). This kind of viewpoint didn't fade away even after World War II. Although Chinese were not treated as bad as they were in the gold rush period, they were still viewed as an inferior group. London (1970) argues that Chinese were perceived as a threat to Australia's cultural heritage and development because of their generally lower standard of living as a threat to labour employer relations. Goot (1978) also points out that the antipathy to Chinese migrants was generated by some considerations, like concerns about the costs of immigration and the competition for jobs. This kind of attitude could be perceived from Queensland Parliament's revoke of a legislation under which any house where Asian women lived could be viewed as a house of prostitution in 1966 (London, 1970). This was really a down point after World War II. However, some positive attitudes existed despite the fact that the overall attitude was negative. London (1970) has the opinion that Chinese later were gradually accepted by the cities’ resident in Melbourne and Sydney and Australians’ sympathetic support of China accelerated the assimilation process. This was the trend of the shift of Australians’ attitudes towards Chinese in that time period as well as the Integration period.

According to a review report from DIMIA (2003) – Report of the Review of Settlement Services for Migrants and Humanitarian Engrant, the situation didn’t change much until the introduction of multiculturalism by Galbally report in 1978. The result of assimilation and integration was not satisfactory in spite of the fact that Australia had paid a considerable amount of effort to policy making to encourage immigration in order to increase the country’s population. The multiculturalism policy gave rise to a large-scale Chinese migration. As a result, Australia had a very high Chinese migration intake over the past two decades. Those Chinese immigrants not only made a culturally and linguistically diverse population together with other groups of immigrants (DIMIA, 2003), but also contributed to Australian society, which changed Australians' attitudes towards Chinese people dramatically. Their contributions mainly fell into three categories – social, cultural and economic aspects.

From a social perspective, Chinese immigration during this time period really gave Australia a new look. In the first place, the large number of arrivals changed the make-up of the population dramatically. The number of Chinese immigrants was over 92,000, ranking second among all the Asian counties in 1995 (Millbank, 2001). Millbank (2001) also states that in this time period – 1995 to 1996, recent surge from mainland China and Hong Kong resulted in the fact that Northeast Asian settlers outnumbered Southeast Asian settlers, which reflected the current trend of Chinese migration into Australia. This was important because immigrants' average ages were below the Australian average, which could to some extent solve the aging problem of Australian population. In the second place, the large-scale immigration also resulted in more investment that government put on education, and made the quality of education higher, especially for language training. Immigrants came from different counties, so English was a second language for most of them. Hence paying attention to language training was essential and beneficial because this cleared the main obstacles and hurdles for immigrants to contribute to the society. Last but not least, according to APMRN (2004), the large-scale Chinese migration as well as immigration of other groups made the government have laws against racial discrimination and incitement and have special agencies to enforce them. This is, to some extent, an advance of the discrimination of racism.

China is famous for its mysterious 5000-year history and the culture developed during the long time period, so under the light of the multiculturalism policy Chinese people brought their culture to Australia, which had great effects on the society. Firstly, Chinese migrants brought various Chinese food and products into Australia, which gave Australians more choices on food and a chance to experience this special culture around the world. There were Chinatowns in major cities in Australia, hence many Australians who were keen on Chinese food or history could go to Chinatown for lunch or dinner with their families, which would be very fantastic. Secondly, some Chinese festivals and customs were taken into practice in many places in Australia. For instance, many Australians ate dumplings on New Year's Day in Australia. In addition, plenty of Australians had the preference for Chinese tea culture; they drank tea and talked about tea with friends in leisure time and enjoyed it pretty much. Thirdly, Chinese culture contributed to the ever-increasingly cultural diversity greatly because of the large intake of Chinese immigrants during this period..

Chinese immigration over the past twenty years benefited Australia’s economy a great deal. It mainly affected Australia’s economy in two ways, the demand side and the supply side (DIEA Fact Sheet30, 1995). DIEA fact sheet 30 (1995) also states that in terms of the demand side, the first factor is migrants own demands. Their needs for food, housing and leisure activities stimulated factories and companies to invest more money and to produce more products, the economy benefited from this to some extent. More arrivals meant that more heath, education and welfare services were needed, hence these aspects advanced due to the immigration. With regard to the supply side, the most direct benefit Chinese immigrants brought to Australia was workforce, skills and money. Workforce shortage could, to some extent, be solved through immigration of younger people. Skeldon (2004) points out that the majority of Chinese migrants today are highly educated or have specialized skills selected through a special “points” system, so immigrants with high business skills also contributed much to the economy. In addition, new business can be introduced into Australia. Chinese immigrants contributed a great deal in this aspect because China was quite different from western countries in terms of dressing, eating habits and so on. So some Chinese food such as noodles and tea, and Chinese featured clothes were introduced into Australia and the demands for these kinds of products definitely helped the development of the economy. From another perspective, this also added productive diversity through knowledge of international business markets. (DIEA Fact Sheet 30, 1995).



GOVERNMENT'S POLICIES FOR CHINESE AND OTHER IMMIGRANTS

Australian government made a series of policies on migration throughout the post World War II period according to the times. It fell into two phases. The first phase was the period before multiculturalism, the second - the period after that. As mentioned at the beginning of this paper, immigration immediately after the war followed the Immigration Restriction Act introduced in 1901, which was widely known as White Australian Policy. The government then realized that only European immigrants were not enough - Australia still in a desperate need for a large population. Also a review report from DIMIA (2003) says that the Commonwealth Government established DIMIA in order to assist migration into Australia due to the concerns regarding Australia’s low birthrate and strong need for industrial labour. Hence the government put forward the assimilation policy, after which many non-British migrants came to Australia. The scale of Chinese migration in this period wasn't large because Australians still perferred Europeans instead of Asians. Although Australia witnessed a higher intake of migrants, the assimilation policy was limited. So the government shifted from the policy of assimilation to a policy of integration. And during this period, due to the removal of discrimination from within the immigration program, the White Australian Policy was abolished in 1973 and equal treatment for immigrants from different origin became an official standard (DIMIA, 2003). As a result of the process of this removal of discrimination, the shift towards multiculturalism on a policy level was finally seen in 1978, which according to Elliot (1984) was also because of an economic factor. Elliot points out that Australia had to develop and maintain trading relations with some neighbour countries. If Australia’s immigration policy was discriminatory against migrants from those countries, it would definitely not only have a negative effect on Australian economy, but also would have some more serious problems.

After the introduction of multiculturalism – the start of the second phase, the country went through a dramatic change, and the government paid a great deal of effort to policy making to benefit from and also to support these changes. Firstly, the definition of multiculturalism was being completed and changed according to the contemporary situation. Three principles were adopted 1989 – cultural identity, social justice and economic efficiency (DIMA, 1999). Secondly, DIMA (1999) also says that in 1986, Jupp argued that successful settlement by non-English speaking migrants needed not only the effort of the migrants, but also the services provided by the host society. The government thus had access and equity policy to help immigrants to adjust to the diverse society more easily and more quickly. This policy, according to Jupp's report in 1986, included two main aspects. The first one was to equip overseas-born families and idividuals the basic resources to enable them to function effectively on an equitable level in Australian society. The second was on an institutional level – let institutions which made decisions about making services and providing them implement them on an equitable basis. This kind of policy have been playing an important role in Chinese immigration, or we wouldn't see so many things reflecting Chinese culture around us here in Australia. Thirdly, the Australian government noticed that it should enourage more skilled and educated people to come to Australia to contribute to the society. So the Australian government put forward a series of laws to help highly skilled individuals and successful businessmen to have permanent residence in Australia. According to the fact sheet Assisting Skilled and Business people (DIC), applicants are classified into several categories, skilled independent, state/territory nominated independent, skilled – Australian sponsored, etc. Obviously, the Australian Government paid a considerable amount of attention to absorbing high-tech people to boost Australian economy. Last but never least, the Australian government also set up a policy a to meet the Chinese increasing interest in visiting Australia. Fact Sheet 58 (DIMIA) states that as Australia was the first western country approved by Chinese government a destination for tourists, Australia has paid some effort to make it easier. Although this is not about migration, some tourists could be would-be immigrants because of the beauty and power of Australia. So this could encourage Chinese people to migrate to Australa to some extent.



CONCLUSION

Whilst Chinese immigrants didn't have a good reputation at the beginning of the second World War, they have been doing their best to get adjusted to the society and their contributions to the society in many aspects really made a difference. It's very pleased to see that Chinese people were gradually accepted by the Australian society and the Australian government has been trying to incease the diversity and scale of the population – going on with the multicultural policy.

Having considered the fact that Australia is still short of industrial labour and workforce, it's believed that government will have more policies on immigration to support highly skilled and educated people to come to Australia, and more corresponding policies that can solve problems caused by the immigration. And it's also believed that Chinese people will play a more important role in Australia and make as many contributions as they can to the society to meet the government's original intention.



REFERENCES

DIEA, Fact Sheet 30, 1995.

Asia Pacific Migration Research Network (APMRN), Migration Issues in the Asia Pacific, ISSUES PAPER FROM AUSTRALIA, [online] Available:
http://www.unesco.org/most/apmrnwp5.htm

Assisting Skilled and Business People, (Fact Sheet) Department of Immigration and Citizenship, Australian Government, [online] Available:
http://www.immi.gov.au/media/fact-sheets/48assisting.htm

China - Approved Destination Status, (Fact Sheet) Department of Immigration and Citizenship, Australian Government, [online] Available:
http://www.immi.gov.au/media/fact-sheets/58china.htm

Chan, H. (2000) From Quong Tarts to Victor Changes: Being Chinese In Australia in the Twentieth Century. CSCSD Public Seminar at the Australian National University. 24 May 2000.

DIMA, New Agenda for Multicultural Australia,
DIMA, Canberra, 1999, p. 8.

DIMIA, Report of the Review of Settlement Services for Migrants and Humanitarian Entrants, May 2003.

Elliot, J. D. (1984). Immigration: The economic benefits. In F. Milne & P. Shergold (Eds.), The great immigration debate. Sydney: Federation of Ethnic Communities in Australia.

Goot. M, Immigrations and Immigration: Evidence and Argument From the Public, 1943 – 1987, Macquarie University.

London. H. I., 1970, Non-White Immigration and the “White Australian” Policy.

Millbank, A, Asian Immigration, Current Issues Brief 16 1996-97, Social Policy Group, [online] Available:
http://www.aph.gov.au/library/pubs/cib/1996-97/97cib16.htm

Skeldon, R, 2004 China: From Exceptional Place to Global Participant. [online], Available:
http://www.migrationinformation.org/Feature/display.cfm?D=9 – 41k

Monday, 28 May 2007

reminder

Always remember the expression in terms of exponentials and the identity equations when dealing with trigonometric and hyperbolic functions!

The hyperbolic identity equation:
Coshx squre minus sinhx squre equals 1.

Coshx = 1/2 times the sum of e to the x and e to the negative x.
Sinhx = 1/2 times the result of e to the x minus e to the negative x.

The trigonometric identity equation:
Cosx squre plus sinx squre is equal to 1.

Sinx = 1/2 times the result of e to the power of ix take away e to the power of -ix.
Cosx = minus i/2 times the sum of e to the ix and e to the -ix.

I won't forget them hopefully.

Thursday, 24 May 2007

look-ahead carry

When we use parallel adders to do addition operations, the main problem would be that the propagation delay could become quite long when the number of bits is increasing. This is mainly because the result in the current position depends on the carry which has been calculated in the previous position. Although modern super deluxe CPUs seem really powerful when doing a simple addition, we gotta keep in mind that small delays would reault in astronomically big delays when doing complex calculations especially in electronics and computer science.

Fortunately engineers came up with the idea of look-ahead carry, which uses a certain combinational circuit to calculate all the carries within a constant time and then does the addition for each bit synchronously. Each carry could be represented in terms of the inputs of the least significant bit, so each carry could have a similar expression and these expresstions only need a two-level AND-OR gates to be implemented. Hence the time to be consumed to calculate all the carries will become the time which does the two-level basic AND-OR operations instead of taking a multiple full adder calculation time. As a result, the total time consumed has been reduced from a linearly increasing number to a constant number, which has increased the calculation speed dramatically.

This is what I learned from the subject digital systems, especially after I've done question 1 in assignment 8. The reason why I wanted to spend 15 minutes on writing this is that I have gained some wisdom from the idea of look-ahead carry. We know that the carry is calculated by the full adder for each bit, but the time to be used for a whole addition operation depends on the number of bits to be handled. If engineers had spent plenty of time only on how to modify the full adder to reduce the whole propagation deley, they wouldn't have got look-ahead carry. So we should try not to stick to the object which we are supposed to put emphasis on when tackling a certain problem. I reckon this is also the essence of brainstorming to some extent.

Friday, 27 April 2007

The project thing

This post is mainly for the project discussion. Welcome to put forward your opnions and questions here, buddies! Maybe someone passes by can help you hit the jackpot!

Ken, I reckon we'd better take a closer look at task one to three and try to get the preliminary stuff done by ourselves. Personally, I don't think this project is suitable for group work. However, we don't need to do that much if we split tasks properly.

As for further task allocation (I'm not refering to the ones in the assignment requirement sheet but the actual coding work), you can post it here or send me an email.

Best luck to us all with the stupid project.

Tuesday, 27 March 2007

[quote] Larger 5 & 6-variable Karnaugh maps

Larger Karnaugh maps reduce larger logic designs. How large is large enough? That depends on the number of inputs, fan-ins, to the logic circuit under consideration. One of the large programmable logic companies has an answer.
Altera's own data, extracted from its library of customer designs, supports the value of heterogeneity. By examining logic cones, mapping them onto LUT-based nodes and sorting them by the number of inputs that would be best at each node, Altera found that the distribution of fan-ins was nearly flat between two and six inputs, with a nice peak at five.

The answer is no more than six inputs for most all designs, and five inputs for the average logic design. The five variable Karnaugh map follows.



The older version of the five variable K-map, a Gray Code map or reflection map, is shown above. The top (and side for a 6-variable map) of the map is numbered in full Gray code. The Gray code reflects about the middle of the code. This style map is found in older texts. The newer preferred style is below.



The overlay version of the Karnaugh map, shown above, is simply two (four for a 6-variable map) identical maps except for the most significant bit of the 3-bit address across the top. If we look at the top of the map, we will see that the numbering is different from the previous Gray code map. If we ignore the most significant digit of the 3-digit numbers, the sequence 00, 01, 11, 10 is at the heading of both sub maps of the overlay map. The sequence of eight 3-digit numbers is not Gray code. Though the sequence of four of the least significant two bits is.


Let's put our 5-variable Karnaugh Map to use. Design a circuit which has a 5-bit binary input (A, B, C, D, E), with A being the MSB (Most Significant Bit). It must produce an output logic High for any prime number detected in the input data.



We show the solution above on the older Gray code (reflection) map for reference. The prime numbers are (1,2,3,5,7,11,13,17,19,23,29,31). Plot a 1 in each corresponding cell. Then, proceed with grouping of the cells. Finish by writing the simplified result. Note that 4-cell group A'B'E consists of two pairs of cell on both sides of the mirror line. The same is true of the 2-cell group AB'DE. It is a group of 2-cells by being reflected about the mirror line. When using this version of the K-map look for mirror images in the other half of the map.


Out = A'B'E + B'C'E + A'C'DE + A'CD'E + ABCE + AB'DE + A'B'C'D


Below we show the more common version of the 5-variable map, the overlay map.



If we compare the patterns in the two maps, some of the cells in the right half of the map are moved around since the addressing across the top of the map is different. We also need to take a different approach at spotting commonality between the two halves of the map. Overlay one half of the map atop the other half. Any overlap from the top map to the lower map is a potential group. The figure below shows that group AB'DE is composed of two stacked cells. Group A'B'E consists of two stacked pairs of cells.

For the A'B'E group of 4-cells ABCDE = 00xx1 for the group. That is A,B,E are the same 001 respectively for the group. And, CD=xx that is it varies, no commonality in CD=xx for the group of 4-cells. Since ABCDE = 00xx1, the group of 4-cells is covered by A'B'XXE = A'B'E.



The above 5-variable overlay map is shown stacked.


An example of a six variable Karnaugh map follows. We have mentally stacked the four sub maps to see the group of 4-cells corresponding to Out = C'F'


A magnitude comparator (used to illustrate a 6-variable K-map) compares two binary numbers, indicating if they are equal, greater than, or less than each other on three respective outputs. A three bit magnitude comparator has two inputs A2A1A0 and B2B1B0 An integrated circuit magnitude comparator (7485) would actually have four inputs, But, the Karnaugh map below needs to be kept to a reasonable size. We will only solve for the A>B output.

Below, a 6-variable Karnaugh map aids simplification of the logic for a 3-bit magnitude comparator. This is an overlay type of map. The binary address code across the top and down the left side of the map is not a full 3-bit Gray code. Though the 2-bit address codes of the four sub maps is Gray code. Find redundant expressions by stacking the four sub maps atop one another (shown above). There could be cells common to all four maps, though not in the example below. It does have cells common to pairs of sub maps.



The A>B output above is ABC>XYZ on the map below.


Where ever ABC is greater than XYZ, a 1 is plotted. In the first line ABC=000 cannot be greater than any of the values of XYZ. No 1s in this line. In the second line, ABC=001, only the first cell ABCXYZ= 001000 is ABC greater than XYZ. A single 1 is entered in the first cell of the second line. The fourth line, ABC=010, has a pair of 1s. The third line, ABC=011 has three 1s. Thus, the map is filled with 1s in any cells where ABC is greater than XXZ.

In grouping cells, form groups with adjacent sub maps if possible. All but one group of 16-cells involves cells from pairs of the sub maps. Look for the following groups:

  • 1 group of 16-cells
  • 2 groups of 8-cells
  • 4 groups of 4-cells
The group of 16-cells, AX' occupies all of the lower right sub map; though, we don't circle it on the figure above.

One group of 8-cells is composed of a group of 4-cells in the upper sub map overlaying a similar group in the lower left map. The second group of 8-cells is composed of a similar group of 4-cells in the right sub map overlaying the same group of 4-cells in the lower left map.

The four groups of 4-cells are shown on the Karnaugh map above with the associated product terms. Along with the product terms for the two groups of 8-cells and the group of 16-cells, the final Sum-Of-Products reduction is shown, all seven terms. Counting the 1s in the map, there is a total of 16+6+6=28 ones. Before the K-map logic reduction there would have been 28 product terms in our SOP output, each with 6-inputs. The Karnaugh map yielded seven product terms of four or less inputs. This is really what Karnaugh maps are all about!

The wiring diagram is not shown. However, here is the parts list for the 3-bit magnitude comparator for ABC>XYZ using 4 TTL logic family parts:

  • 1 ea 7410 triple 3-input NAND gate AX', ABY', BX'Y'
  • 2 ea 7420 dual 4-input NAND gate ABCZ', ACY'Z', BCX'Z', CX'Y'Z'
  • 1 ea 7430 8-input NAND gate for output of 7-P-terms

  • REVIEW:
  • Boolean algebra, Karnaugh maps, and CAD (Computer Aided Design) are methods of logic simplification. The goal of logic simplification is a minimal cost solution.
  • A minimal cost solution is a valid logic reduction with the minimum number of gates with the minimum number of inputs.
  • Venn diagrams allow us to visualize Boolean expressions, easing the transition to Karnaugh maps.
  • Karnaugh map cells are organized in Gray code order so that we may visualize redundancy in Boolean expressions which results in simplification.
  • The more common Sum-Of-Products (Sum of Minters) expressions are implemented as AND gates (products) feeding a single OR gate (sum).
  • Sum-Of-Products expressions (AND-OR logic) are equivalent to a NAND-NAND implementation. All AND gates and OR gates are replaced by NAND gates.
  • Less often used, Product-Of-Sums expressions are implemented as OR gates (sums) feeding into a single AND gate (product). Product-Of-Sums expressions are based on the 0s, maxterms, in a Karnaugh map.

Wednesday, 14 March 2007

[quote] Vinyl records versus CDs and DVDs

The answer lies in the difference between analog and digital recordings. A vinyl record is an analog recording, and CDs and DVDs are digital recordings. Take a look at the graph below. Original sound is analog by definition. A digital recording takes snapshots of the analog signal at a certain rate (for CDs it is 44,100 times per second) and measures each snapshot with a certain accuracy (for CDs it is 16-bit, which means the value must be one of 65,536 possible values).


Comparison of a raw analog audio signal to the CD audio and DVD audio output

This means that, by definition, a digital recording is not capturing the complete sound wave. It is approximating it with a series of steps. Some sounds that have very quick transitions, such as a drum beat or a trumpet's tone, will be distorted because they change too quickly for the sample rate.

In your home stereo the CD or DVD player takes this digital recording and converts it to an analog signal, which is fed to your amplifier. The amplifier then raises the voltage of the signal to a level powerful enough to drive your speaker.

A vinyl record has a groove carved into it that mirrors the original sound's waveform. This means that no information is lost. The output of a record player is analog. It can be fed directly to your amplifier with no conversion.

This means that the waveforms from a vinyl recording can be much more accurate, and that can be heard in the richness of the sound. But there is a downside, any specks of dust or damage to the disc can be heard as noise or static. During quiet spots in songs this noise may be heard over the music. Digital recordings don't degrade over time, and if the digital recording contains silence, then there will be no noise.

From the graph above you can see that CD quality audio does not do a very good job of replicating the original signal. The main ways to improve the quality of a digital recording are to increase the sampling rate and to increase the accuracy of the sampling.

The recording industry has a new standard for DVD audio discs that will greatly improve the sound quality. The table below lists the sampling rate and the accuracy for CD recordings, and the maximum sampling rate and accuracy for DVD recordings. DVDs can hold 74 minutes of music at their highest quality level. CDs can also hold 74 minutes of music. By lowering either the sampling rate or the accuracy, DVDs can hold more music. For instance a DVD can hold almost 7 hours of CD quality audio.


CD Audio DVD Audio
Sampling Rate 44.1 kHz 192 kHz
Samples per second 44,100 192,000
Sampling Accuracy 16-bit 24-bit
Number of Possible Output Levels 65,536 16,777,216

DVD audio discs and players are rare right now, but they will become more common, and the difference in sound quality should be noticeable. To take advantage of higher quality DVD audio discs, however, you will need a DVD player with a 192kHz/24-bit digital to analog converter. Most DVD players only have a 96kHz/24-bit digital to analog converter. So if you are planning to take full advantage of DVD audio be sure to look for a 192kHz/24-bit DAC.


Quoted from Howstuffworks