




版權(quán)說明:本文檔由用戶提供并上傳,收益歸屬內(nèi)容提供方,若內(nèi)容存在侵權(quán),請(qǐng)進(jìn)行舉報(bào)或認(rèn)領(lǐng)
文檔簡(jiǎn)介
1、fourier transform and applicationsby njegos nincic fourierovervieww transformsnmathematical introductionw fourier transformntime-space domain and frequency domainndiscret fourier transformlfast fourier transformnapplicationsw summaryw referencestransformsw transform:nin mathematics, a function that
2、results when a given function is multiplied by a so-called kernel function, and the product is integrated between suitable limits. (britannica)w can be thought of as a substitutiontransformsw example of a substitution:w original equation: x + 4x 8 = 0w familiar form: ax + bx + c = 0w let: y = xw sol
3、ve for yw x = y4transformsw transforms are used in mathematics to solve differential equations:noriginal equation: napply laplace transform: ntake inverse transform: y = l(y)y9y15e2ts2ly9ly15s2l y15s 2 s29fourier transformw property of transforms:nthey convert a function from one domain to another w
4、ith no loss of informationw fourier transform: converts a function from the time (or spatial) domain to the frequency domaintime domain and frequency domainw time domain:ntells us how properties (air pressure in a sound function, for example) change over time:lamplitude = 100lfrequency = number of c
5、ycles in one second = 200 hztime domain and frequency domainw frequency domain:ntells us how properties (amplitudes) change over frequencies:time domain and frequency domainw example:nhuman ears do not hear wave-like oscilations, but constant tonew often it is easier to work in the frequency domaint
6、ime domain and frequency domainw in 1807, jean baptiste joseph fourier showed that any periodic signal could be represented by a series of sinusoidal functions in picture: the composition of the first two functions gives the bottom onetime domain and frequency domainfourier transformw because of the
7、 property:w fourier transform takes us to the frequency domain:discrete fourier transformw in practice, we often deal with discrete functions (digital signals, for example)w discrete version of the fourier transform is much more useful in computer science:w o(n) time complexityfast fourier transform
8、w many techniques introduced that reduce computing time to o(n log n)w most popular one: radix-2 decimation-in-time (dit) fft cooley-tukey algorithm: (divide and conquer)applicationsw in image processing:ninstead of time domain: spatial domain (normal image space)nfrequency domain: space in which ea
9、ch image value at image position f represents the amount that the intensity values in image i vary over a specific distance related to f applications: frequency domain in imagesw if there is value 20 at the point that represents the frequency 0.1 (or 1 period every 10 pixels). this means that in the
10、 corresponding spatial domain image i the intensity values vary from dark to light and back to dark over a distance of 10 pixels, and that the contrast between the lightest and darkest is 40 gray levels applications: frequency domain in imagesw spatial frequency of an image refers to the rate at whi
11、ch the pixel intensities change w in picture on right:nhigh frequences:lnear centernlow frequences:lcornersapplications: image filteringw other applications of the dftw signal analysisw sound filteringw data compressionw partial differential equationsw multiplication of large integerssummaryw transf
12、orms:nuseful in mathematics (solving de)w fourier transform:nlets us easily switch between time-space domain and frequency domain so applicable in many other areasneasy to pick out frequenciesnmany applicationsreferenceswconcepts and the frequency domainnhttp:/www.spd.eee.strath.ac.uk/interact/fourier/concepts.htmlwthe frequency domain introductionnhttp:/nam.vn/unescocourse/computervision/91.htmwjpnm physics fourier transform nhttp:/
溫馨提示
- 1. 本站所有資源如無特殊說明,都需要本地電腦安裝OFFICE2007和PDF閱讀器。圖紙軟件為CAD,CAXA,PROE,UG,SolidWorks等.壓縮文件請(qǐng)下載最新的WinRAR軟件解壓。
- 2. 本站的文檔不包含任何第三方提供的附件圖紙等,如果需要附件,請(qǐng)聯(lián)系上傳者。文件的所有權(quán)益歸上傳用戶所有。
- 3. 本站RAR壓縮包中若帶圖紙,網(wǎng)頁內(nèi)容里面會(huì)有圖紙預(yù)覽,若沒有圖紙預(yù)覽就沒有圖紙。
- 4. 未經(jīng)權(quán)益所有人同意不得將文件中的內(nèi)容挪作商業(yè)或盈利用途。
- 5. 人人文庫網(wǎng)僅提供信息存儲(chǔ)空間,僅對(duì)用戶上傳內(nèi)容的表現(xiàn)方式做保護(hù)處理,對(duì)用戶上傳分享的文檔內(nèi)容本身不做任何修改或編輯,并不能對(duì)任何下載內(nèi)容負(fù)責(zé)。
- 6. 下載文件中如有侵權(quán)或不適當(dāng)內(nèi)容,請(qǐng)與我們聯(lián)系,我們立即糾正。
- 7. 本站不保證下載資源的準(zhǔn)確性、安全性和完整性, 同時(shí)也不承擔(dān)用戶因使用這些下載資源對(duì)自己和他人造成任何形式的傷害或損失。
最新文檔
- 大學(xué)化學(xué)考試化學(xué)態(tài)勢(shì)觀察試題及答案
- 電商社區(qū)營(yíng)銷的實(shí)踐探索試題及答案
- 如何科學(xué)備考建筑施工安全考試的試題及答案
- 公司借用協(xié)議合同范例
- 新材料化學(xué)的研究熱點(diǎn)試題及答案
- 人形機(jī)器人行業(yè)的未來與發(fā)展動(dòng)向分析
- 農(nóng)村生活污水治理項(xiàng)目可持續(xù)發(fā)展方案
- 可再生能源儲(chǔ)能項(xiàng)目可行性分析報(bào)告
- 北京個(gè)人借款合同標(biāo)準(zhǔn)文本
- 包工責(zé)任合同范例
- 聲波吹灰系統(tǒng)安裝、調(diào)試、操作說明書
- 鏡頭蓋注塑模具
- GA 1801.2-2022國(guó)家戰(zhàn)略儲(chǔ)備庫反恐怖防范要求第2部分:通用倉庫
- GB/T 4744-1997紡織織物抗?jié)B水性測(cè)定靜水壓試驗(yàn)
- 教師公開招聘考試結(jié)構(gòu)化面試試題
- 操作規(guī)程編制導(dǎo)則
- Dijkstra最短路徑算法的優(yōu)化和改進(jìn)
- 偵探推理題(含答案)
- 熱塑性聚酯彈性體(TPEE)
- 畢業(yè)論文機(jī)電一體化發(fā)展歷程及其面臨的形勢(shì)和任務(wù)
- 《中小學(xué)綜合實(shí)踐活動(dòng)課程指導(dǎo)綱要》教育部2022版
評(píng)論
0/150
提交評(píng)論