狦и盢琘摸疭﹚块ㄧ计癳秈琘╰参狦┮眔块ㄧ计ご礛ㄣΤ块ㄧ计Α玥ㄧ计嘿╰参㏕Τㄧ计Eigen Functionセ竊盢弧计ㄧ计┒猧ㄧ计碞琌 LTI ╰参㏕Τㄧ计狦и块ㄧ计琌计ㄧ计
x[n]=epn ê或沮ぇ玡崩旧そΑ眔癸莱块琌传杠弧块ㄧ计 y[n] 单块ㄧ计盽计 H(ep)= Ske-pk h[k]琌ぃ繦丁τ跑てㄧ计и弧计ㄧ计琌 LTI ╰参㏕Τㄧ计
y[n] = x[n]*h[n] = Skx[n-k] h[k] = Skep(n-k) h[k] = Skepn-pk h[k] = epnSke-pk h[k] = epnH(ep) 眖硂柑崩約ヴ块ㄧ计璶镑ボΘ计ㄧ计絬┦舱碞ㄏノ舼瞶衡硂ㄇ计ㄧ计癸莱块秈︽絬┦舱碞眔块ㄧ计癸莱块ノ计厩Αボ
x[n] = aepn + beqn △ y[n] = aH(ep) + bH(eq) 癸┒猧ㄧ计иㄏノ Euler Identity ㄓ传Θ计ㄧ计
ejq = cos(q) + j sin(q) 传杠弧cos(q) = (ejq + e-jq)/2 = Re{ejq} 讽块琌
sin(q) = (ejq - e-jq)/(2j) = Im{ejq}x[n] = cos(wn) = Re{ejwn} 癸莱块玥琌传杠弧块ㄧ计临琌 cosぃ筁熬簿 q = $H(ejw)綺碩 |H(ejw)|碭闽迭弧
y[n] = Re{ejwnH(ejw)} = Re{ejwn |H(ejw)| ejq}, q = $H(ejw) = Re{|H(ejw)| ej(wn+q)} = |H(ejw)| cos(wn + q) 瞶讽块琌
- 狦иぃê或块计 |H(ejw)| ╰参癸ぃà繵瞯 w 癟腹耎┪溃罽疭┦и硄盽嘿 |H(ejw)| 臫繵瞯臫莱Magnitude Frequency Response
- $H(ejw) 玥嘿繵瞯臫莱Phase Frequency Responseτē耕ぶ砆ノφ癸稰谋ぃ庇綰
- H(ejw) 参嘿琌╰参繵瞯臫莱Frequency Response
x[n] = sin(wn) = Im{ejwn} 玥块琌и眔挡阶癸 LTI ╰参τē讽块ㄧ计琌虫┒猧ㄧ计块﹚琌繵瞯┒猧ㄧ计Τ綺碩㎝穦砆╰参┮э跑τэ跑よΑЧㄌ酚╰参繵瞯臫莱 H(ejw) τ﹚
y[n] = Im{ejwnH(ejw)} = Im{ejwn |H(ejw)| ejq}, q = $H(ejw) = Im{|H(ejw)| ej(wn+q)} = |H(ejw)| sin(wn + q) 瓃ㄢ贺┒猧块иэノ店计计ㄧ计ㄓ阀珹
x[n] = ejwn ê或癸莱块琌y[n] = ejwnH(ejw) ㄤい H(ejw) 嘿 h[n] 瞒床丁撑ミ腑锣传Discrete-time Fourier TransformボH(ejw) = Skh[k]e-jwk ㄆ龟瓃块㎝块瞷龟ぃ╰参块㎝块ぃ琌狡计琌硂ㄇ计厩笲衡瞶阶琌Θミиㄏノ硂ㄇΑㄓ琵и崩旧虏间ㄇ
Audio Signal Processing and Recognition (癟矪瞶籔侩醚)