1、-. z.- - - .可修編 .基于固定線的遠程控制與防盜報警器的設(shè)計與制作*方威*理工學(xué)院 物理與電信工程學(xué)院 通信工程專業(yè)，2009級1班，* * 723003指導(dǎo)教師：龍光利 摘 要為了利用現(xiàn)有的線路對家庭中設(shè)備和電器進展遠程控制，采用單片機和DTMF解碼芯片，設(shè)計并制作了一種基于固定線的遠程控制器?？刂破靼布蛙浖删植浚布娐酚蒑T8880電路、摘機掛機電路、響鈴檢測電路、紅外檢測電路、觸發(fā)開關(guān)電路、液晶顯示電路、I2C存儲電路、繼電器輸出控制電路、鍵盤控制電等電路組成；軟件由主程序、振鈴檢測計數(shù)程序、DTMF解碼處理程序、鍵盤掃描程序、語音控制程序、EEPROM讀寫程序、L

2、CD顯示等子程序組成。軟件用C語言編程，利用Keil軟件編譯，通過后將生成的HE*文件下載到單片機STC89C52上，Proteus硬件仿真通過后，用Altium Designer設(shè)計PCB板，手工制作PCB板，將單片機和其它相關(guān)元器件焊接在PCB板上，和固話連接，上電，當(dāng)家中發(fā)生警情時, 此時家中設(shè)定的無線模塊或者其他傳感器模塊會發(fā)出異常信號給單片機, 單片機承受到信號后立即發(fā)出現(xiàn)場聲光報警信號來威懾侵入者, 同時將單片機自動撥打預(yù)先存儲在存儲芯片中的給主人或者小區(qū)物業(yè)報警, 以便及時采取防盜措施防止財產(chǎn)損失。通過撥打連接的固定的，可控制家用電器開啟和關(guān)閉，液晶顯示有關(guān)，通過蜂鳴器報警。 關(guān)

3、鍵詞線；控制器；防盜報警；單片機；雙音多頻；紅外感應(yīng)Design and production of remote controller based on the fi*ed telephone lineLiu Fangwei(Grade09,Class1,Major of munication Engineering，School of Physics and telemunication Engineering , Shaan*i University of Technology, Hanzhong 723003, Shaan*i) Tutor: Long GuangliAbstract:

4、In order to control devices and appliances which based the line of fi*ed telephone,a remote controller based on the fi*ed telephone line was designed and production by using MCU and DTMF decoder.The implementation of the controller includes hardware design and software design,hardware was posed of M

5、CU minimum system,ringing circuit,simulation of off-hook and on-hook,drive circuit of appliances,decoder of DTMF, LCD,keyboard and EEPROM Cell;software was posed of main program,program which could count the number of ringing,DTMF decode program,keyboard-scan program,voice program,EEPROM reading and

6、 writing program,display program.The software was based on programmed with C language,using Keil C51 for developing program,piled HE* file and downloaded to the MCU AT89S52,circuit simulation by Proteus.The board of PCB was designed by the sofware which named Altium Designer and was welded manually

7、with other electronic ponents,which will be used.After connecting with the line of fi*ed telephone and power on,the home appliances is controlled to turn on or turn off,the password is showed on the LCD,the tip of voice is played when the telephone number was called.Key words:Telephone line;Controll

8、er;Appliances;MCU 目錄 TOC o 1-3 h z u HYPERLINK l _Toc327224749引言 圖 4.7所示圖 STYLEREF 1 s 4. SEQ 圖 * ARABIC s 1 7 Altium Designer設(shè)計的PCB圖2手工制作雙面PCB板用激光打印機，分別在熱轉(zhuǎn)印紙上面打印頂層和底層線路。熱轉(zhuǎn)印底層打印圖如圖圖 STYLEREF 1 s 4. SEQ 圖 * ARABIC s 1 8 所示。熱轉(zhuǎn)印頂層打印圖如圖 STYLEREF 1 s 4.9 所示。在打印頂層的時選擇鏡像選項。找出至少4個定位孔，并將它用針扎小孔，頂層和底層的定位孔要對應(yīng)起來

9、，都要扎小孔。將雙面覆銅板的氧化層打磨掉。漏出有光澤的銅皮。將任意一面熱轉(zhuǎn)印紙貼在銅皮上，并用高溫膠帶固定。然后在銅板上將定位孔打穿并將另一面也貼在覆銅板的另一面，通過定位孔對準(zhǔn)后，用高溫膠帶固定。將貼好熱轉(zhuǎn)印紙的覆銅板放在熱轉(zhuǎn)印機里面，朝一個方向滾動大約3次后取出，待覆銅板冷卻以后，將熱轉(zhuǎn)印紙撕掉，檢查有沒有斷線或者模糊的地方。假設(shè)有須打磨掉碳膜以后重新壓膜，假設(shè)無則可進展下一步操作。圖 STYLEREF 1 s 4.8 熱轉(zhuǎn)印底層打印圖將壓好膜的覆銅板放在腐蝕液中復(fù)制，腐蝕液一般有兩種，一種是三氯化鐵和熱水混合攪勻后可進展腐蝕，不過腐蝕速度過慢。另一種是用雙氧水+鹽酸+水的方式腐蝕，這種方

10、式腐蝕速度快，但在使用是要注意，因為雙氧水是強氧化劑，而鹽酸是強酸。假設(shè)不慎濺在皮膚上，需盡快用大量清水清洗。腐蝕完成以后，開場打孔。打孔的時候要注意不能把焊盤打掉了。最后用砂紙打磨干凈。焊接，先將過孔用廢棄元器件管腳兩邊焊通。然后在按從低到高的順序依次焊接元器件。圖 STYLEREF 1 s 4.9 熱轉(zhuǎn)印頂層打印圖4.3硬件制作調(diào)試4.3.1 元器件的檢測和焊接各個元器件是實現(xiàn)電路的主要部件，一旦出現(xiàn)質(zhì)量問題，或者已經(jīng)損壞但未發(fā)現(xiàn)的情況，將會使調(diào)試變得異常困難。小到電阻、電容，大到集成電路等等。在焊接前一定要仔細檢查所焊接元器件是否符合電路要求。焊接好的板子，在加電之前，首先要先測量其電源

11、接口兩端的電阻，如果電阻值過小則不能加電，檢查電路中是否有連焊或走線錯誤等問題。另外，在第一次上電時最好不要插任何芯片，防止線路錯誤燒壞芯片。第一次上電以后，測量每個芯片座各管腳的電壓是否正常。假設(shè)全部正常便可插上芯片上電，并進展測試，否則檢查板子是否有焊接等問題。在焊接元器件時，要遵循從低到高的原則，就是先焊比擬扁的、矮小的，再依次焊個頭比擬大的，焊接時間不能過長，最好不要超過3秒以免損壞元件。焊接完成以后反復(fù)檢查，看看有沒有連焊的或者虛焊的地方。焊接的硬件實物圖如圖 STYLEREF 1 s 4.10所示。圖 STYLEREF 1 s 4.10 硬件實物圖4.3.2 硬件調(diào)試當(dāng)系統(tǒng)的整體硬

12、件電路和軟件編寫完成以后，整體的系統(tǒng)調(diào)試就要開場了。系統(tǒng)能否正常工作，取決于各個電路能否正常運作、電路之間是否有影響、軟件設(shè)計是否合理、是否考慮到現(xiàn)實生活的實際情況。以下主要介紹調(diào)試中出現(xiàn)的一些問題：1模擬摘機和家電驅(qū)動電路的調(diào)試為測試模擬摘機電路，引出來一根地線，然后給控制器上電，這個時候可以不接線，上電以后將接地線與模擬摘機的控制I/O口連接，聽繼電器是否有吸合和釋放的聲音。并觀察指示繼電器狀態(tài)的LED是否發(fā)光。實際上在測試的時候，該局部電路是非常可靠的運行的。與仿真的現(xiàn)象一模一樣。最后為了確定模擬摘機工作正常，上線，測量模擬摘機繼電器在未吸合的狀態(tài)下，線兩邊的電壓為50V，然后將模擬摘機

13、的控制I/O口接地，聽到吸合聲，而且LED指示燈亮起的時候，再測量線兩端的電壓為7V左右，說明模擬摘機電路運行正常10。家電驅(qū)動電路和模擬摘機電路根本類似，測試方法也大體一樣，只是在最后需要用萬用表測量繼電器吸合和釋放兩種狀態(tài)下，開關(guān)輸出的地方是否導(dǎo)通和斷開。實驗結(jié)果與預(yù)期目的完全一樣。2LCD1602及雙音多頻檢測電路的調(diào)試開場調(diào)試液晶的時候都沒有顯示，以為是電路引腳接錯了，然后就開場檢查電路，結(jié)果發(fā)現(xiàn)電路沒有問題。另外在寫液晶驅(qū)動的時候，直接按照時序圖，寫了讀寫程序測試，但是發(fā)現(xiàn)液晶顯示還是不正常，本來寫的數(shù)據(jù)沒有寫入，在查了一些資料后才發(fā)現(xiàn)，液晶是慢顯器件，每次寫數(shù)據(jù)之前要查詢液晶是否處

14、于忙碌的狀態(tài)。如果忙，要繼續(xù)等待，直到液晶空閑為止才能對它讀寫，也就是判斷液晶是否處于busy狀態(tài)。其次是在液晶1602的第二行進展數(shù)據(jù)讀寫的時候，就是以上的問題都解決了，但是還是不能正常顯示，查了半天資料也沒有弄明白，后來才知道是由于液晶的亮度低，顯示的數(shù)據(jù)沒有看到，所以經(jīng)過把液晶的亮度調(diào)亮了就沒有問題了。對于DTMF解碼電路，在檢查其接線沒有問題的情況下，需要編寫測試程序來判斷DTMF解碼電路是否正常工作。為了確認DTMF解碼的正確性，將LCD1602跟DTMF一起測試。編寫好測試程序后，進展硬件測試。對于DTMF解碼電路的測試，因為該芯片技術(shù)很成熟，在模塊測試的時候沒有出現(xiàn)不解碼或者解碼

15、錯誤等問題。I2C存儲電路的調(diào)試不知道為什么，有時候在調(diào)試的時候存儲芯片就寫不進了，在調(diào)試存儲電路AT24C02的存儲電路浪費的時間最多。換的芯片很多，開場時不知道問題出在哪里。由于很多資料上都這樣寫，就一直按照資料上寫的去操作，所以出現(xiàn)錯誤的時候，一直沒有找到適宜的解決方法。經(jīng)過反復(fù)的查找資料和調(diào)試，發(fā)現(xiàn)了原來國產(chǎn)的芯片和進口的芯片相差也很大，在讀寫時間的間隔上，還有在存儲容量上都有較大的區(qū)別，除此之外還有耐壓值和溫度指標(biāo)等在一定程度上都不能模糊。另外在I2C電路中遇到的問題是，由于單片機采用11.0592Mhz的晶振，所以時序要求特別的準(zhǔn)確，在延遲函數(shù)上也都要進展調(diào)整，在模擬I2C總線對A

16、T24C02讀寫的時候由于延時不夠多，讀寫數(shù)據(jù)不能完成要求。后來把延遲加長了延時，一切都正常讀寫了。4整體聯(lián)調(diào)整體聯(lián)調(diào)根本流程為編寫/修改程序、下載程序、系統(tǒng)上電、打進展測試。在進展整體聯(lián)調(diào)時在雙音頻編解碼檢測電路中遇到的問題比擬復(fù)雜，也是最不好調(diào)試的，下面列舉一些問題。1輸入的雙音多頻信號持續(xù)時間足夠長時，接收器視為有效并實時地進展接收，否則不接收。在整個雙音頻信號持續(xù)時間，對于由于外部干擾等造成的瞬間連續(xù)，假設(shè)雙音頻總持續(xù)時間足夠長，接收器會排除這些干擾，仍視為有效接收。2當(dāng)時開場調(diào)試MT8880的時候，由于一些原因，在接收數(shù)據(jù)的時候會出現(xiàn)亂碼并且不對應(yīng)的現(xiàn)象，如按下1鍵可能顯示的是2鍵的

17、碼，經(jīng)過查找資料和論證分析，才發(fā)現(xiàn)接收到信號時必須濾波排除干擾。完畢語 本系統(tǒng)的可行之處是由于單片機功能強大，其能和各種電路連接起來。在此系統(tǒng)中單片機以它強大的功能引領(lǐng)各個模塊電路，組成一個價格低廉、功能強大、用途廣泛的智能控制系統(tǒng)。本系統(tǒng)通過測試，系統(tǒng)精度及其他指標(biāo)均到達了設(shè)計要求。相信在未來將得到廣泛的應(yīng)用。在實際的應(yīng)用中,本系統(tǒng)還有很大的拓展空間。通過此次畢業(yè)設(shè)計的研究過程，首先了解了進展一項科技設(shè)計時所必不可少的幾個過程。從課題的選取、到論文的完成，深深體會到完成一項技術(shù)研究的執(zhí)著。經(jīng)過這次系統(tǒng)的設(shè)計，熟悉了對一項課題進展研究、設(shè)計和實驗的詳細過程。這次設(shè)計不僅要設(shè)計系統(tǒng)的硬件電路，還

18、要進展軟件的編寫和優(yōu)化。這些在將來的工作和學(xué)習(xí)當(dāng)中會有很大的幫助。其次對硬件知識有了一個系統(tǒng)的全新的掌握與提高，同時也使我認識到軟件的編寫流程及優(yōu)化的重要性。這些極大提高了我自己的動手能力和實踐能力。 致謝 本論文是在我的教師龍光利指導(dǎo)下完成的。從課題的選取、開題報告的撰寫、文獻綜述的查閱、英文翻譯的開展直到論文的完成，每一個步驟都顯示出龍教師無微無至的關(guān)心，每一個細節(jié)都凝聚著龍教師的辛勞。他淵博的知識體系、豐厚的教學(xué)經(jīng)臉和和藹可親的細膩品質(zhì)時時鼓勵和感動著我；他嚴(yán)謹?shù)闹螌W(xué)態(tài)度和刻苦的科研精神令我敬仰并影響我一生的奮斗精神；他平易近人讓我懂得了為人師表的崇高；他正直坦率讓我懂得了如何面對生活。

19、 此外，王戰(zhàn)備教師也給了我?guī)椭?，在我調(diào)試遇到問題時，他給了我程控實驗的指導(dǎo)手冊，讓我順利地完成了硬件實物圖的調(diào)試，在此表示深深的謝意。同時也感謝一起做畢業(yè)設(shè)計的靳花同學(xué)對我的不斷鼓勵，與我共同研究、探討、學(xué)習(xí)，使我從中學(xué)到了很多東西。致謝人：2012年6月8日參考文獻1李朝青.單片機原理及接口技術(shù)簡明修訂版M.*：航空航天大學(xué),1998.50-55.2李朋飛,魯凱生,羅剛.基于網(wǎng)的嵌入式遠程控制器的設(shè)計微計算機信息論文J.知識詞典, 2006，5(6)：58-60.3嚴(yán)麗平, 袁可風(fēng).基于PSTN 的遠程控制器的研究J.華東交通大學(xué)學(xué)報，2005，7(22)：118-121.4王嵐，*謙，阮華

20、莉. 遙控智能遠程控制器的設(shè)計與實現(xiàn)M.*：中原工學(xué)院,2008.118-123.5*立臣.DTMF信號收、發(fā)芯片MT8888原理及應(yīng)用J.國外電子元器件，2001, 12(9)：30-31.6楊為理.現(xiàn)代通訊集成電路應(yīng)用技術(shù)手冊M.：電子工業(yè)，2002，25-28.7李佳旭，丁鵬飛.基于ISD1760的智能語音計費顯示系統(tǒng)設(shè)計J.電子元器件應(yīng)用，2010, 8(6):20-23.8譚成豪，許建明.試述51系列單片機矩陣鍵盤編程J.科技傳播,2011, 17(6)：30-34.9蔣偉，文昱.SPI總線及其在單片機系統(tǒng)中的應(yīng)用J.科技廣場,2008, 20(10)：89-90.10陳振源.機原理

21、與維修通信技術(shù)專業(yè)第2版M.：高等教育，2009，60-69.11C.K.Das,M.Sanaullah,H.M.G.Sarower.Development of a cell phone based remote control system an effective switching system for controlling home and office appliancesJ.International Journal of Electrical & puter Sciences,2008,4(10)：37-43.12 Justin Klumpp, Leo Wan.Home Se

22、curity System with Remote Home Automation ControlM.2006，1-8.13 Yavuz EROL1,Hasan H. BALIK2,Serkan INAL1.Safe and Secure PIC Based Remote Control Application for Intelligent HomeJ. International Journal of puter Science and Network Security, 2007, 18(5)：179-182.附錄A 英文文獻原文Development of a cell phone b

23、ased remote controlsystem: an effective switching system for controllinghome and office appliances.C. K. Das, M. Sanaullah, H. M. G. Sarower and M. M. HassanAbstract：This paper demonstrates a novel method which enableusers to control their home appliances and systems from remoteusing a cell phone-ba

24、sed interface. To access the control unit, theuser should send an authentication code (DTMF) along with therequired/desired function/action to his/her home control systemvia Global Sytem for Mobile munication(GSM). Upon beingproperly authenticated, the cell phone-based interface at home(control unit

25、) would relay the mands to a microcontrollerthat would perform the required function/action, and return afunction pletion code that would be sent to the source of theoriginal mand (users cell phone).Inde* Terms：Decoder, DTMF, GSM, HACS, MicrocontrollerI. INTRODUCTIONThe aim of the proposed system is

26、 to develop a cost effectivesolution that will provide controlling of home appliancesremotely and enable home security against intrusion in theabsence of homeowner. The system provides availability dueto development of a low cost system. The home appliancescontrol system with an affordable cost was

27、thought to be builtthat should be mobile providing remote access to theappliances and allowing home security. Though devicesconnected as home and office appliances consume electricalpower. These devices should be controlled as well as turn on/off if required. Most of the times it was done manually.

28、Nowit is a necessity to control devices more effectively andefficiently at any time from anywhere. In this system, we aregoing to develop a cellular phone based home/office appliancecontroller 6, 9. This system is designed for controllingarbitrary devices, it includes a cell phone (not included with

29、the system kit, end user has to connect his/her cell phone tothe system) which is connect to the system via head set. Toactive the cellular phone unit on the system a call is to bemade and as the call is answered, in response the user wouldenter a two/three digit password to access the system tocont

30、rol devices. As the caller press the specific password, itresults in turning ON or OFF specific device. The deviceswitching is achieved by Relays 10. Security preservedbecause these dedicated passwords owned and known byselected persons only. For instance, our system containsan alarm unit giving the

31、 user a remote on/off mechanism, which is capable of informing up to fivedifferent numbers over telephony network about thenature of the event 8.II. SYSTEM DEVELOPMENTIn this system we developed the overall method in two way.First one is that the targeted devices can be controlled bysending DTMF 2 (

32、dual tone multi frequency) sent by user.Another way is that targeted devices can be controlled byvoice messages.A. Block DiagramFigure1 Block diagram of the system using DTMFIn this system, there is a control unit/module. The control unitis able to connect to the cellular network automatically, tore

33、ceive DTMF 8 and will be able to decode for passwordidentification and instructions to be sent to themicrocontroller. The microcontroller 5 within the controlunit will issue the mand to the electrical appliancesthrough a simple control circuit.B. Circuit DiagramFigure2 Circuit diagram(1) for the sys

34、tem.Figure3 Circuit diagram (2) for the system.In the circuit diagram, the systems mechanism has described.Here, a cell phone is connected in the control unit via headset.When a call is made the cell phone in the control unit autoanswered. Then password is being pressed. These DTMFdecoded by a dedic

35、ated decoder MT-8870 (shown in Figure2:circuit diagram (1) for the system).Then decoded output sentto the microcontroller, which issues mand to controldevices connected to it(shown in Figure3: circuit diagram (2)for the system). Device switching is performed by relay.C. Voice Message CircuitThe circ

36、uit diagram for the voice message unit is shownin Fig4.When the microcontroller detects a triggeringsignal from the scanned units, the numbers recorded onthe SIM card of the mobile phone are called sequentiallyand the MC activates the voice message unit. The MCalso sends a deactivation signal when t

37、he recordedmessage is played back. This operation continues in thesame manner until the last call is performed. Thespeaker output of the ISD is connected to the cellularphone speaker so that the recorded message is directlyheard by the receiving end of the phone that has beencalled.Figure4 Circuit d

38、iagram for voice message.D. The DTMF Generation And DecodingDTMF is Short for Dual Tone Multi frequency and thesystem used by touch-tone telephones. DTMF assigns aspecific frequency (consisting of two separate tones) to eachkey so that it can easily be identified by a microprocessor.1209Hz1336Hz1477

39、Hz1633Hz697Hz123A770Hz456B852Hz789C941Hz*0#DFigure5 Typical DTMF keypadDTMF generation is a posite audio signals of two tonesbetween the frequency of 697Hz and 1633Hz 2, 3. TheDTMF keypad is arranged such that each row will have itsown unique tone frequency and also each column will haveits own uniq

40、ue tone. The figure-5 is a representation of thetypical DTMF keypad and the associated row/columnfrequencies. The tone frequencies were selected such thatharmonics and intermodulation products will not cause anunreliable signal. The DTMF spectrum is shown in figure-6.Figure6 Dual Tone Multi Frequenc

41、y(DTMF)spectrum.As the above frequency spectrum illustrates, each tone mustfall within the proper bandpass before a valid decoding willtake place. If one tone falls outside the bandpass spectrum, thedecoder will bee unreliable or not operate at all.The purpose of DTMF decoding is to detect sinusoida

42、l signalsin the presence of noise. In many cases, the DTMF decoder ICinterfaces with a microcontroller. Here it is logocal that themicrocontroller should not be used to decode the sinusoids.Because the typical microcontroller based decoder requires anA/D converter. In addition, the signal processing

43、 associatedwith the decoding is usually beyond the scope of themicrocontrollers capabilities. So the designer is forced to usethe dedicated IC or upgrade the microcontroller to perhaps amore costly digital signal processor.The theory is quite similar to the classical signal processingtechnique4. One

44、 brute force way to detect DTMF signals isto digitize the ining signal and pute 8 DFTs (discretefourier transforms) centered around the 8 DTMF positefrequencies. DFTs are preferred over FFTs because thefrequencies are not equally spaced (in fact, they arelogarithmically spaced). In its simplest form

45、, the DFT goessomething like so:NDFT(*) = *(k) W(k)(1)where *(k) are the time samples and W(k) is the infamouskernal function:W(k) = e(j2fk/N) = cos(2fk/N)+ jsin(2fk/N)(2)It means that multiplying the samples by sine waves andcosine waves and adding them together the W(k) can befound. This will yiel

46、d eight ple* numbers. Themagnitudes of these numbers give the information roughlythat how much energy is present for each frequency of theinput signal. In other words, we have puted the frequencyspectrum at the 8 DTMF posite frequencies. The reasonwhy this works so well is because of the orthogonali

47、ty ofthe sine waves. In other words, this happens if the DFT isperformed on two sine waves as shown in the followingequation:DFT = sin(f1t) sin(f2t) .(3)From equation (3), it is clear that we will get the result as alarge number if the two frequencies are the same and asmall number or zero if theyre

48、 different.DFT With Square waves4The orthogonality concept applies equally well to squarewaves too. In fact, its even easy to illustrate with ASCII art.Let us consider the two e*amples as given below:1)+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1=25Figure7: Waveform Of E*ample1.2)Figure8 Wavef

49、orm Of E*ample2.In the first e*ample(figure7), the two square waves have thesame frequency and phase. When the individual samples aremultiplied and summed together, we get a large number:25. In the second case(figure8), the square waves differ infrequency by a factor of two. Again as e*pected, when

50、wemultiply the individual samples and add them up we get asmall number: 2. If we look closely, well notice that themultiplication is really an e*clusive OR operation.DFT In Quadrature Form4In the DFT, both the sine and cosine waves are used. The twotypes of wave are obviously related by 90 degree ph

51、ase shift.An analogously shifted square wave is needed for the DTMFdecoding too. The reason is that its possible to end up with asmall sum-of-products even if the two waveforms have thesame frequency. This idea can be cleared with the e*ample offigure-9.Figure9 Quadrature Form of Wave.On the other h

52、and, the DFT operation is a dot productoperation also. We can imagine the signal and the kernals asvectors whose indices are the sample number. The vectorscould be very large, e.g. 4096 samples.Signal Strength Calculation of DFTIf the DFTs are puted with sine and cosines, then thesignal strength of

53、a particular frequency is easily ascertainedwith help of following equation:strength ( real(DFT)2 + imaginary(DFT)2) .(4)In other words, the result of a DFT is a ple* number whenthe ple* kernal is used. And the magnitude of a ple*number is the square root of the sum of the real part squaredplus the

54、imaginary part squared. This is a cumbersomeoperation that we would rather avoid. The square root of thesum of the squares normalization is called the square norm.It is a subset of the general class of normed linear spacescalled the p-norm. In our case, the linear space consists oftwo ponents: the r

55、eal and imaginary parts of the DFT. Thep-norm for our case isstrength P(abs(real(DFT)p + abs(imaginary(DFT)p) (5)And this is the same as the square norm when p is 2.Now if p is 1, we end up with an e*tremely simple formula,the 1-norm:strength abs(real(DFT) + abs(imaginary(DFT).(6)Digitization proces

56、s of +1 and -1 OR +1 and 0:So far weve been digitizing to +1 and -1. However, in a realprogram well probably want to digitize to +1 and 0 sincethese are the numbers which are most fortable formicrocontroller operation. The ne*t point is how does thisimpact the DFT calculations. Suppose we have two s

57、quarewaves that are digitized to +1 and - 1. What will happen totheir dot product if we digitize them to +1 and 0 instead. Letf1 and f2 be the two square waves as like below:f1 = -1 or +1 andf2 = -1 or +1For the conversion from +1 and 1 to 1s and 0s: q1=(f1+1)/2= f1=2q1 -1 .(7)=(f2+1)/2=q2 f2=2q2 -1

58、. (8)So, q1 and q2 represent the re-digitized f1 and f2 squarewaves. Now the dot product:DFT = f1.f2 (2q1 - 1) .(2q2 - 1)=(4q1q2 - 2q2 - 2q1 + 1) = 4 q1q2 - 2 q2 - 2 q1 + 1.(9)The last term evaluates N. In other words, 1+1+1+ . +1 = N.The middle two terms require a closer e*amination. Assumethat f1

59、and f2 contain no DC ponent:N f1 = 0(10)0Then the sum of q1 is: (f1 + 1)/2q1 =0 + N/2 = N/2(11)Similarly, the sum of q2 is N/2. bining these results it canbe shown that:f1.f2 = 4 q1.q2 - 2N/2 - 2N/2 + N= 4(q1.q2) - N.(12)Therefore, in conclusion, we can say that the digitization with0s and 1s is ess

60、entially the same as digitizing with +1s and -1s. But a new DC term of N has been introduced and thedot product has been scaled which are the only differences 4.Decoding ProcessIn DTMF there are 16 distinct tones. Each tone is the sum oftwo frequencies: one from a low and one from a highfrequency gr