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「ひよこは高く空を舞い」について

2007-03-22

[]無名関数 無名関数 - 雲雀は高く空を舞い を含むブックマーク はてなブックマーク - 無名関数 - 雲雀は高く空を舞い 無名関数 - 雲雀は高く空を舞い のブックマークコメント

使用方法

fhandle = @(arglist) expr

arglistは0個以上。

例題 (1)

A, Bはあらかじめ定義されているとして

sumAxBy = @(x, y) (A*x + B*y);
sumAxBy(5, 7)

例題 (2)

多出力

fh = @(x)[x, x^2, x^3]
fh(3)

ans =
     3     9    27

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トラックバック - http://chick.g.hatena.ne.jp/allegro/20070322

2007-03-15

[]コメントの書き方 コメントの書き方 - 雲雀は高く空を舞い を含むブックマーク はてなブックマーク - コメントの書き方 - 雲雀は高く空を舞い コメントの書き方 - 雲雀は高く空を舞い のブックマークコメント

1行コメント

行頭に%を使う。

% comment here

ブロックコメント

%{, %}で囲む。

%{
  comment here
%}

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画像処理 画像処理 - 雲雀は高く空を舞い を含むブックマーク はてなブックマーク - 画像処理 - 雲雀は高く空を舞い 画像処理 - 雲雀は高く空を舞い のブックマークコメント

近傍処理

多くの場合3x3のサイズからなるウィンドウを画像データの全域を操作して処理がなされる。つまり、ある画素に隣接する周りの8画素(8近傍画素)の値を用いて、中心の画素の値を順次決めていく処理。

[]スクリーンサイズの取得とFigure Sizeの指定 スクリーンサイズの取得とFigure Sizeの指定 - 雲雀は高く空を舞い を含むブックマーク はてなブックマーク - スクリーンサイズの取得とFigure Sizeの指定 - 雲雀は高く空を舞い スクリーンサイズの取得とFigure Sizeの指定 - 雲雀は高く空を舞い のブックマークコメント

スクリーンサイズの取得

[左縁の位置、下縁の位置、幅、高さ]=get(0, 'ScreenSize');

Figure Sizeの指定

figure('Position', [左縁の位置、下縁の位置、幅、高さ])

横長のFigure Windowの作成

S = get(0, 'ScreenSize');
figure('Position', [1 S(4)/3 3*S(3)/4 S(4)/3 ])

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1.3 音のエネルギー的取り扱い 1.3 音のエネルギー的取り扱い - 雲雀は高く空を舞い を含むブックマーク はてなブックマーク - 1.3 音のエネルギー的取り扱い - 雲雀は高く空を舞い 1.3 音のエネルギー的取り扱い - 雲雀は高く空を舞い のブックマークコメント

1.3.1 音響エネルギー密度

音場内のある点(x,y,z)にいおける音響エネルギー密度(acoustic energy deensity)の瞬時値E[J/m^3]は次式で表される。

E(t,x,y,z) = \frac{1}{2}[u^2(t,x,y,z)+\frac{1}{\rho^2c^2}p^2(t,x,y,z)\]

上式で、右辺第一項は運動エネルギー、第二項はポテンシャルエネルギーである。

上式の時間平均をとると

\bar{E(x,y,z)} = \frac{1}{T}\int^T_0E(t,x,y,z)dt = \frac{1}{2}\rho[u^2_e+\frac{p^2_e}{\rho^2c^2}

ここで pe:音圧の実効値[Pa], ue:粒子速度の実効値[m/s]

平面波の場合は比音響インピーダンスより

E(t,x)= \frac{p^2(t,x)}{\rho c^2}=\rho u^2(t,x)

\bar E = \frac{p^2_e}{\rho c^2}=\rho u^2_e

となる。

音のエネルギーの流れがすべての方向について一様であるような完全拡散音場についても次の関係が成り立つ。

\bar E = \frac{p^2_e}{\rho c^2}

球面波の場合には、次式のように表される。

\bar E = \frac{p^2_e(r)}{\rho c^2}(1+\frac{1}{2k^2r^2})

遠距離音場では右辺の第二項が無視でき、平面波の場合と等しくなる。

1.3.2 音響インテンシティ

音の伝播方向に対して垂直な単位面積を通して単位時間に通過する音のエネルギーを音響インテンシティ(sound intensty)あるいは音の強さと言う。

単位面積を持つ仮想断面を考え、その面に音圧p(t)が作用した結果、その面が速度(粒子速度)u(t)で運動したと考えれば、時間dtの間にp×1がなす仕事(エネルギー)は

dE=p(t)u(t)dt

であるので、その時間平均を取って音響インテンシティI とすると次式となる。

I=\frac{1}{T}\int_{0}^{T}p(t)u(t)dt=\bar {p(t)u(t)}

1.3.3 音響パワー

音源が単位時間に放射する音のエネルギーを音源の音響パワー(sound power)と言う

P = \int_xI_nds

In:音源を取り囲む閉曲面上における音響インテンシティの法線方向成分[W/m^2], S:閉曲面の全面積[m^2]

定常的な音源の場合には、上記の音響パワーで音源の強さを記述できるが、過渡的・衝撃的な音源の場合には、時間平均の概念は成り立たず、音源が発生する音響エネルギー[J]に着目しなければならない

1.4 デシベル表示  1.4 デシベル表示 - 雲雀は高く空を舞い を含むブックマーク はてなブックマーク -  1.4 デシベル表示 - 雲雀は高く空を舞い  1.4 デシベル表示 - 雲雀は高く空を舞い のブックマークコメント

音についてデシベル表示が用いられる理由としては、まず人間の聴覚が刺激の絶対値よりもむしろその対数に比例する傾向があること(Fechnerの法則)、すなわちデシベル値で表示したほうが大きさの感覚ともよく合うことがあげられる。

1.5 音の伝搬式 1.5 音の伝搬式 - 雲雀は高く空を舞い を含むブックマーク はてなブックマーク - 1.5 音の伝搬式 - 雲雀は高く空を舞い 1.5 音の伝搬式 - 雲雀は高く空を舞い のブックマークコメント

1.5.1 自由音場または半自由音場における音の伝搬

音源から放射された音波は広がって伝搬し、音源から遠ざかるにつれて減衰する。これを距離減衰と言う。そのて一度は音源の形状・寸法によって異なる。

音源の寸法が伝搬距離に比べて十分に小さい場合、音源は点とみなせる。このような点音源から距離rの点における音響インテンシティIあるいはエネルギー密度Eを考えると、半径rの球面全体を単位時間に通過する音響エネルギーは音源の放射パワーPに等しいことから次式が成り立つ。

I = \frac{P}{4\pi r^2}

E = \frac{I}{c} = \frac{P}{4\pi r^2c}

これらの式をデシベル表示すると次式。

L = L_W-10log_{10}r^2 -11

ただし、L:音響インテンシティレベル, LW:音源の音響パワーレベル

音源が反射性の地面や床などの上に接しているとき(半自由音場)には、上式は次式となる。

L=L_W-10log_{10}r^2 -8

これら2式より距離r1, r2の二つの点におけるレベルL1, L2の差は

L_1 - L_2=10log_{10}(\frac{r_2}{r_1}) ^2

となり、距離が2倍になるごとに6dBだけ減衰することがわかる。これを逆二乗則(inverse square law)による減衰と言う。

1.5.2 室内における音の伝搬

室内(表面積S, 平均吸音率\bar \alpha)に音響パワーがPの音源があるとき、それから距離rだけ離れた点の音響エネルギー密度Eは、音源からの直接恩によるエネルギーEdと周壁で一回以上反射された拡散音のエネルギーの和として表される。

略。


5. 音響伝搬特性の測定  5. 音響伝搬特性の測定 - 雲雀は高く空を舞い を含むブックマーク はてなブックマーク -  5. 音響伝搬特性の測定 - 雲雀は高く空を舞い  5. 音響伝搬特性の測定 - 雲雀は高く空を舞い のブックマークコメント

5.1 インパルス応答・周波数応答関数

対象とするシステムにインパルスを入力し、それに対する応答を調べる。

線形・時不変性が仮定できる物理システムに継続時間が無限に短いインパルス(数学的にはデルタ関数)を入力したときの出力をインパルス応答と言う。原理的には、インパルスはすべての周波数成分を含んでいるので、インパルス応答にはシステムのすべての時間的・周波数的情報が含まれている。

インパルス応答を周波数領域で表現したものを周波数応答。これを

H(f) = |H(f)|e^{j\Phi (f)}

の形で表した場合、|H(f)|は振幅、\Phi(f)は位相情報を表しており、前者をゲイン要素、後者を位相要素と呼ぶ。線形システムでは、入力信号に対して出力信号は振幅と位相が変化するが、周波数はまったく変化しない。スピーカや振動代に単一の制限は信号を入力したとき、その周波数以外の周波数の音や振動(非線形ひずみ)も同時に発生することがある。

トラックバック - http://chick.g.hatena.ne.jp/allegro/20070303

2007-03-02

[]「環境騒音・建築音響の測定」写経 (1) 「環境騒音・建築音響の測定」写経 (1) - 雲雀は高く空を舞い を含むブックマーク はてなブックマーク - 「環境騒音・建築音響の測定」写経 (1) - 雲雀は高く空を舞い 「環境騒音・建築音響の測定」写経 (1) - 雲雀は高く空を舞い のブックマークコメント

[]「環境騒音・建築音響の測定」写経 (2) 1.1音波 「環境騒音・建築音響の測定」写経 (2) 1.1音波 - 雲雀は高く空を舞い を含むブックマーク はてなブックマーク - 「環境騒音・建築音響の測定」写経 (2) 1.1音波 - 雲雀は高く空を舞い 「環境騒音・建築音響の測定」写経 (2) 1.1音波 - 雲雀は高く空を舞い のブックマークコメント

気体・液体・固体などの物質の一部に何らかの力が加わると、その内部に生じる弾性力と慣性力によって振動が生じ、物質内部を波動として伝わる。このような波動を広い意味で音波と言う。

空気(一般に気体・液体)中では体積変化に対してのみ弾性力が生じ、これによって音波が発生する。その場合、空気の粒子が波の伝播方向と同じ方向に往復振動するので、この種の波動を縦波(longitudinal wave)あるいは疎密波(dilatational wave)という。

このような振動によって生じる空気粒子の振動変位を粒子変位(particle displacement)[tex \xi ]、振動速度を粒子速度(particle velocity)[tex u (=d \xi /dt)]という。

また粒子の動きによって気圧の高い箇所と低い箇所が交互に出来るが、大気圧に対するこの気圧の変化文を音圧(sound pressure) [tex p]と呼ぶ。このような音波が存在する空間を音場(sound field)と言う。


[]「環境騒音・建築音響の測定」写経 (3) 1.2音の波動的取り扱い 「環境騒音・建築音響の測定」写経 (3) 1.2音の波動的取り扱い - 雲雀は高く空を舞い を含むブックマーク はてなブックマーク - 「環境騒音・建築音響の測定」写経 (3) 1.2音の波動的取り扱い - 雲雀は高く空を舞い 「環境騒音・建築音響の測定」写経 (3) 1.2音の波動的取り扱い - 雲雀は高く空を舞い のブックマークコメント

以下、平面波と球面波に関する波動方程式の解より。

1.2.1 平面波の伝播

音圧
p(t,x) = Ae^{j(\omega t - kx)}
粒子速度
u(t, x) = \frac{A}{\rho c} e^{j(\omega t - kx)}
比音響インピーダンス(固有音響インピーダンス/特性インピーダンス)
Z = \frac{p(t,x)}{u(t,x)} = \rho c

ただし、t:時間[s], x:位置[m], j:虚数単位, \omega:各周波数(=2\pif,f:周波数[Hz]), \rho:伝播物質密度[kg/m^3], k=\omega/c (波長定数)

1.2.2 球面波の伝播 (点音源からの音の放射)

音圧
p(t,x) = \frac{A}{\gamma }e^{j(\omega t - kx)}
粒子速度
u(t, x) = \frac{1}{\rho c}(1+\frac{1}{jkr})\frac{A}{\gamma} e^{j(\omega t - kx)}
比音響インピーダンス
Z(r) = \rho c \frac{k^2 \gamma ^2}{1+k^2 \gamma ^2} + j\rho c \frac{k \gamma}{1+k^2 \gamma ^2}

r:点音源からの距離[m]

トラックバック - http://chick.g.hatena.ne.jp/allegro/20070302
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