JP2004317911A - Device and method for sound field simulation, computer program, and program recording medium - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To reproduce a natural and smooth sound field signal while using impulse responses to discrete points of time when the transmission state of a sound from a sound source to an observation point changes with time. <P>SOLUTION: An impulse response storage part 14 stores impulse responses h<SB>i</SB>(t) at respective points of time from the sound source to a listening point, and a response calculation part 20 calculates a convolution signal y<SB>i</SB>(t) of a sound source signal u(t) that a signal acquisition part 12 acquires and an impulse response at each point of time. A correlation coefficient storage part 18 stores a correlation coefficient r<SB>i</SB>between transfer functions at two adjacent points of time. A cross-fading calculation part 22 determines window functions according to the correlation coefficient and multiplies response signals at the two points of time by those window functions respectively, and the respective results are summed up, and a sound field signal is calculated. <P>COPYRIGHT: (C)2005,JPO&NCIPI

Description

ただし、相関係数演算部１６および相関係数記憶部１８を音場シミュレーション装置１０に設けるのではなく、音場シミュレーション装置１０とは別個の演算装置により相関係数ｒ_ｉを計算して記憶しておき、その相関係数を音場シミュレーション装置１０が読み出す構成としてもよい。
【００２４】
応答演算部２０は、インパルス応答記憶部１４に記憶されたインパルス応答ｈ_ｉ（ｔ）と、音源信号取得部１２により取得された音源信号ｕ（ｔ）との畳み込み信号ｙ_ｉ（ｔ）を次式に従って計算する。
【数２】

【００２５】
クロスフェード演算部２２は、以下に詳細に述べるように、畳み込み信号ｙ_ｉ（ｔ）と、相関係数記憶部１８に記憶された相関係数ｒ_ｉとに基づいて、隣接する時点間の区間［Ｐ_ｉ，Ｐ_ｉ＋１］での音場信号ｘ_ｉ（ｔ）を計算する。そして、信号合成部２４は各音場信号ｘ_ｉ（ｔ）をつなぎ合わせて時点Ｐ_０〜Ｐ_Ｎに亘る最終的な音場信号ｘ（ｔ）を生成する。出力部２６は、生成された音場信号ｘ（ｔ）をアナログ信号に変換し、適宜増幅器を介して外部のスピーカー等の音響装置へ出力する。
【００２６】
以下、クロスフェード演算部２２による演算処理について詳細に説明する。
【００２７】
本実施形態では、図３および図４に示すように、区間［Ｐ_ｉ，Ｐ_ｉ＋１］において、時点Ｐ_ｉから時点Ｐ_ｉ＋１に向けて次第に小さくなる窓関数ｆ_１（ｔ）を時点Ｐｉでの畳み込み信号ｙ_ｉ（ｔ）に掛け、また、時点Ｐ_ｉから時点Ｐ_ｉ＋１に向けて次第に大きくなる窓関数ｆ_２（ｔ）を時点Ｐ_ｉ＋１での畳み込み関数ｙ_ｉ＋１（ｔ）に掛けて、両者を足し合わせる。すなわち、区間［Ｐ_ｉ，Ｐ_ｉ＋１］における音場信号ｘ_ｉ（ｔ）を
ｘ_ｉ（ｔ）＝ｆ_１（ｔ）・ｙ_ｉ（ｔ）＋ｆ_２（ｔ）・ｙ_ｉ＋１（ｔ）
として計算する。
【００２８】
これらの窓関数ｆ_１（ｔ）、ｆ_２（ｔ）は、以下のように、相関係数ｒ_ｊの値に基づいて決定される。
【００２９】
先ず、相関係数ｒ_ｊが「０」の場合は、図３に示すように、窓関数ｆ_１（ｔ），ｆ_２（ｔ）を区間［Ｐ_ｉ，Ｐ_ｉ＋１］で値が「０」と「１」との間を曲線状に変化する関数とする。具体的には、次式で表される基準窓関数ｆ_ａ１（ｔ），ｆ_ａ２（ｔ）を用いる。ただし、Ｔ_ｉは、区間［Ｐ_ｉ，Ｐ_ｉ＋１］の区間長、ｔは時点Ｐ_ｉを基準とした時間であり０≦ｔ≦Ｔ_ｉとする。
ｆ_１（ｔ）＝ｆ_ａ１（ｔ）＝ｃｏｓ（π・ｔ／（２・Ｔ_ｉ））
ｆ_２（ｔ）＝ｆ_ａ２（ｔ）＝ｓｉｎ（π・ｔ／（２・Ｔ_ｉ））
【００３０】
また、相関係数ｒ_ｊが「１」の場合には、図４に示すように、窓関数ｆ_１（ｔ），ｆ_２（ｔ）を区間［Ｐ_ｉ，Ｐ_ｉ＋１］で値が「０」と「１」との間を直線状に変化する関数とする。具体的には次式で表される基準窓関数ｆ_ｂ１（ｔ），ｆ_ｂ２（ｔ）を用いる。
ｆ_１（ｔ）＝ｆ_ｂ１（ｔ）＝１−ｔ／Ｔ_ｉ
ｆ_２（ｔ）＝ｆ_ｂ２（ｔ）＝ｔ／Ｔ_ｉ
【００３１】
これらの基準窓関数ｆ_ａ１（ｔ），ｆ_ａ２（ｔ）およびｆ_ｂ１（ｔ），ｆ_ｂ２（ｔ）は、区間［Ｐ_ｉ，Ｐ_ｉ＋１］において計算される音場信号ｘ_ｉ（ｔ）の二乗振幅の時間平均 （以下、二乗振幅平均という）が、時点Ｐ_ｉ，Ｐ_ｉ＋１での畳み込み信号ｙ_ｉ（ｔ），ｙ_ｉ＋１（ｔ）の二乗振幅平均に等しいという条件を満たすように求められたものである。以下、このことを検証する。なお、以下の各式においては、記載を簡潔にするため関数のパラメータを省略することがある。
【００３２】
先ず、相関係数ｒ_ｉが「０」の場合については、区間［Ｐ_ｉ，Ｐ_ｉ＋１］における音場信号
ｘ_ｉ（ｔ）＝ｃｏｓ（π・ｔ／（２・Ｔ））・ｙ_ｉ（ｔ）＋ｓｉｎ（π・ｔ／（２・Ｔ））・ｙ_ｉ＋１（ｔ）
の二乗振幅和は
【数３】

ｈ_ｉ（ｔ）とｈ_ｉ＋１（ｔ）の相関係数ｒ_ｉは「０」であるから、それらの畳み込みであるｙ_ｉ（ｔ），ｙ_ｉ＋１（ｔ）について、
【数４】

が成立する。
【００３３】
したがって、
【数５】

となる。
【００３４】
ここで、隣接する時点間で音場のパワー変化はほとんど無いと考えられることから、畳み込み信号ｙ_ｉ（ｔ），ｙ_ｉ＋１（ｔ）は次式を満足するものとする。
【数６】

したがって、
【数７】

となり、音場信号ｘ_ｉ（ｔ）の二乗振幅平均が畳み込み信号ｙ_ｉ（ｔ），ｙ_ｉ＋１（ｔ）の二乗振幅平均に一致することがわかる。
【００３５】
すなわち、上記（１）式を前提として、相関係数が「０」の場合の基準窓関数ｆ_ａ１（ｔ），ｆ_ａ２（ｔ）は、それらの２乗和｛ｆ_ａ１（ｔ）｝^２＋｛ｆ_ａ２（ｔ）｝^２の振幅の平均が「１」となるように設定される。
【００３６】
また、相関係数ｒ_ｊが「１」の場合について、区間［Ｐ_ｉ，Ｐ_ｉ＋１］における音場信号
ｘ_ｉ（ｔ）＝（１−ｔ／Ｔ_ｉ）・ｙ_ｉ（ｔ）＋（ｔ／Ｔ_ｉ）・ｙ_ｉ＋１（ｔ）
の二乗振幅平均は
【数８】

ここで、ｈ_ｉ（ｔ），ｈ_ｉ＋１（ｔ）の相関係数が１であるから、それらと音源信号ｕ（ｔ）との畳み込みであるｙ_１（ｔ），ｙ_２（ｔ）は互いに等しい。したがって、ｙ_１（ｔ）＝ｙ_２（ｔ）＝ｙ（ｔ）とおくと、
【数９】

となり、音場信号ｘ（ｔ）の二乗振幅平均が畳み込み信号ｙ_ｊ（ｔ），ｙ_ｊ＋１（ｔ）の二乗振幅平均に一致することがわかる。
【００３７】
すなわち、相関係数が「１」の場合、ｙ_１（ｔ）＝ｙ_２（ｔ）であることを前提として、基準窓関数ｆ_ｂ１（ｔ），ｆ_ｂ２（ｔ）は、それらの和ｆ_ｂ１（ｔ）＋ｆ_ｂ２（ｔ）の二乗振幅平均が「１」となるように設定される。
【００３８】
このように、区間［Ｐ_ｉ，Ｐ_ｉ＋１］において、音場信号ｘ_ｉ（ｔ）の二乗振幅平均が畳み込み信号ｙ_ｉ（ｔ），ｙ_ｉ＋１（ｔ）の二乗振幅平均に一致することにより、各区間［Ｐ_ｉ，Ｐ_ｉ＋１］でｙ_ｉ（ｔ）とｙ_ｉ＋１（ｔ）とをつなぎ合わせに伴って音場信号ｘ（ｔ）のレベルに不連続的な変化が生ずることがなくなり、自然な音場を生成することができるのである。
【００３９】
以上のことを実証するため、音源信号ｒ（ｔ）としてホワイトノイズを用い、相関の低い２つのインパルス応答ｈ_ｓ１（ｔ）、ｈ_ｓ２（ｔ）と、相関の高い２つのインパルス応答ｈ_ｔ１（ｔ）、ｈ_ｔ２（ｔ）について、各基準窓関数を用いて音場信号を計算した。なお、相関の低いインパルス応答ｈ_ｓ１（ｔ）、ｈ_ｓ２（ｔ）としては、ある建物内の環境が全く異なる２つの地点（実験室内とエントランスホール）での実測値を用いた。図５（ａ），（ｂ）にインパルス応答ｈ_ｓ１（ｔ）、ｈ_ｓ２（ｔ）の波形を示す。また、相関の高いインパルス応答ｈ_ｔ１（ｔ）、ｈ_ｔ２（ｔ）として、同じ室内の位置だけ異なる２つの地点での実測値を用いた。図６（ａ），（ｂ）にインパルス応答ｈ_ｔ１（ｔ）、ｈ_ｔ２（ｔ）の波形を示す。
【００４０】
先ず、相関の低いインパルス応答ｈ_ｓ１（ｔ）、ｈ_ｓ２（ｔ）についてホワイトノイズとの畳み込み信号を計算し、それらに夫々、曲線状の窓関数ｆ_ａ１（ｔ）＝ｃｏｓ（π・ｔ／（２・Ｔ）），ｆ_ａ２（ｔ）＝ｓｉｎ（π・ｔ／（２・Ｔ））を掛けて、両者を足し合わせたところ、図７に示す波形の信号が得られた。ただし、Ｔは適宜な定数とした。図７に示すように、得られた信号波形は振幅がほぼ一定に保たれており、インパルス応答がｈ_ｓ１（ｔ）からｈ_ｓ２（ｔ）へ変化する際に、音場信号が滑らかに推移していることがわかる。
【００４１】
一方、これらのインパルス応答ｈ_ｓ１（ｔ）、ｈ_ｓ２（ｔ）についてホワイトノイズとの畳み込み演算を行い、それらの演算結果に夫々直線状の窓関数ｆ_ｂ１（ｔ）＝１−ｔ／Ｔ，ｆ_ｂ２（ｔ）＝ｔ／Ｔをかけて、両者を足し合わせたところ、図８に示す波形の信号が得られた。同図に示すように、得られた信号波形にはレベルの低下（図中矢印Ｘで示す）が生じており、相関の低いインパルス応答ｈ_ｓ１（ｔ）、ｈ_ｓ２（ｔ）について直線状の窓関数ｆ_ｂ１，ｆ_ｂ２を用いると、インパルス応答がｈ_ｓ１（ｔ）からｈ_ｓ２（ｔ）へ変化する際に、音場信号は滑らかに推移しないことがわかる。
【００４２】
次に、相関の高いインパルス応答ｈ_ｔ１（ｔ）、ｈ_ｔ２（ｔ）についてホワイトノイズとの畳み込み信号を計算し、それらに夫々、直線状の窓関数ｆ_ｂ１（ｔ）＝１−ｔ／Ｔ，ｆ_ｂ２（ｔ）＝ｔ／Ｔを掛けて、両者を足し合わせたところ、図９に示す波形の信号が得られた。同図に示すように、得られた信号波形は振幅がほぼ一定に保たれており、インパルス応答がｈ_ｔ１（ｔ）からｈ_ｔ２（ｔ）へ変化する際に、音場信号が滑らかに推移していることがわかる。
【００４３】
一方、これらインパルス応答ｈ_ｔ１（ｔ）、ｈ_ｔ２（ｔ）についてホワイトノイズとの畳み込み信号を計算し、それらに夫々、曲線状の窓関数ｆ_ａ１（ｔ）＝ｃｏｓ（π・ｔ／（２・Ｔ）），ｆ_ａ２（ｔ）＝ｓｉｎ（π・ｔ／（２・Ｔ））をかけて、両者を足し合わせたところ、図１０に示す波形の信号が得られた。同図に示すように、得られた信号波形にはレベルの上昇 （図中矢印Ｙで示す）が生じており、相関の高いインパルス応答ｈ_ｔ１（ｔ）、ｈ_ｔ２（ｔ）について曲線状の窓関数ｆ_ａ１，ｆ_ａ２を用いると、インパルス応答がｈ_ｔ１（ｔ）からｈ_ｔ２（ｔ）へ変化する際に、音場信号は滑らかに推移しないことがわかる。
【００４４】
以上のように、インパルス応答の相関係数が低い場合には、曲線状の窓関数ｆ_ａ１（ｔ），ｆ_ａ２（ｔ）を用い、相関係数が高い場合には、直線状の窓関数ｆ_ｂ１（ｔ），ｆ_ｂ２（ｔ）を用いることで、インパルス応答ｈ_ｉ（ｔ）が変化する区間［Ｐ_ｉ，Ｐ_ｉ＋１］において滑らかで自然な音場信号を生成できることが実証された。
【００４５】
ただし、実際にはインパルス応答の相関係数は「０」と「１」の中間の値を取る。そこで、本実施形態では、曲線状の基準窓関数ｆ_ａ１（ｔ），ｆ_ａ２（ｔ）と直線状の基準窓関数ｆ_ｂ１（ｔ），ｆ_ｂ２（ｔ）とを相関係数ｒ_ｉの値に応じた重みで加え合わせたものを窓関数ｆ_１（ｔ），ｆ_２（ｔ）として用いることとしている。すなわち、重み係数をｋ_１、ｋ_２として、
ｆ_１（ｔ）＝ｋ_１・（１−ｔ／Ｔ_ｉ）＋ｋ_２・ｃｏｓ（π・ｔ／（２・Ｔ_ｉ）） ・・・（Ａ）
ｆ_２（ｔ）＝ｋ_１・ｔ／Ｔ_ｉ ＋ｋ_２・ｓｉｎ（π・ｔ／（２・Ｔ_ｉ）） ・・・（Ｂ）
なる窓関数を用い、ｋ_１，ｋ_２の値を相関係数に応じて設定する。ただし、ｋ_１＋ｋ_２＝１が満足されるものとする。
【００４６】
図１１は、相関係数から重み係数ｋ_１，ｋ_２を決定するためのグラフ（以下、重み決定グラフという）である。この重み決定グラフは、次のようにして実験的に求められたものである。すなわち、様々な相関係数を有するホワイトノイズの組を用意し、それらホワイトノイズの各組について、ｋ_１，ｋ_２の値を様々に変化させながら、上式（Ａ），（Ｂ）で定められる窓関数ｆ_１（ｔ）、ｆ_２（ｔ）を掛けて足し合わせた信号を計算し、その信号波形のレベル変動が最も少なくなるようなｋ_１，ｋ_２の値を求める。こうして求められたｋ_１，ｋ_２とホワイトノイズの相関係数との関係をプロットすることで、図１１に示す重み決定グラフが得られる。このような重み決定グラフを記憶しておき、このグラフを参照して相関係数ｒ_ｉから重み係数ｋ_１，ｋ_２を決定する。
【００４７】
図１２は、本実施形態の音場シミュレーション装置１０における処理手順を示すフローチャートである。本シミュレーションにあたっては、シミュレーションの対象となる状況について、時点Ｐ_ｉを設定し、各時点Ｐ_ｉでの音源から受聴位置までのインパルス応答ｈ_ｉ（ｔ）を求めて、インパルス応答記憶部１４に格納しておくものとする。
【００４８】
同図に示すように、先ず、信号取得部１２により音源信号ｕ（ｔ）が入力され、あるいは、予め記憶しておいた音源信号ｕ（ｔ）が読み出される（Ｓ１００）。また、相関係数計算部１６が、インパルス応答記憶部１４に記憶されたインパルス応答ｈ_ｉ（ｔ）に基づいて、隣接する時点間のインパルス応答の相関係数ｒ_ｉを計算し、相関係数記憶部１８に格納する（Ｓ１０２）。次に、応答演算部２０が、音源信号ｕ（ｔ）とインパルス応答ｈ_ｉ（ｔ）との畳み込み信号ｙ_ｉ（ｔ）を計算する（Ｓ１０４）。また、クロスフェード計算部２２が、各区間［Ｐ_ｉ，Ｐ_ｉ＋１］について、インパルス応答ｈ_ｉ（ｔ），ｈ_ｉ＋１（ｔ）の相関係数ｒ_ｉに基づき、上記図１１に示す重み決定グラフを参照して、重み係数ｋ_１，ｋ_２を決定する（Ｓ１０６）。そして、その重み係数ｋ_１，ｋ_２を用いて上記式（Ａ），（Ｂ）に従って窓関数ｆ_１（ｔ），ｆ_２（ｔ）を決定し、夫々を畳み込み信号ｙ_ｉ（ｔ），ｙ_ｉ＋１（ｔ）に乗じて足し合わせることにより、区間［Ｐ_ｉ，Ｐ_ｉ＋１］での音場信号ｘ_ｉ（ｔ）を計算する（Ｓ１０８）。信号合成部２４はこの信号ｘ_ｉ（ｔ）をｉ＝１〜Ｎについてつなげることにより、音場信号ｘ（ｔ）生成する（Ｓ１１０）。こうして生成された音場信号ｘ（ｔ）は出力部２６により外部へ出力される（Ｓ１１２）。
【００４９】
本実施形態の音場シミュレーション装置１０を用いて、図１に示す状況下での音場をシミュレーションし、実際に図１に示す受聴者Ｏの位置で集音した音と比べたところ、実際の音場とほぼ同じ音場を再生できることが確認できた。
【００５０】
以上説明したように、本実施形態の音場シミュレーション装置１０によれば、離散的な時点Ｐ_ｉ（ｔ）でのインパルス応答ｈ_ｉ（ｔ）を用いて得られる畳み込み信号ｙ_ｉ（ｔ）を、相関係数ｒ_ｉに応じた窓関数ｆ_１（ｔ），ｆ_２（ｔ）を用いて接続することで、インパルス応答ｈ_ｉ（ｔ）の変化に伴う不連続的なレベル変動のない滑らかで自然な音場信号を生成することができる。
【００５１】
ところで、以上の説明では、音源信号ｕ（ｔ）に基づいて音場信号ｘ（ｔ）を生成したうえで、その音場信号ｘ（ｔ）を出力するものとしたが、演算部１６，２０，２２等をＤＳＰで構成した場合のように、十分に早い演算速度が得られる場合は、リアルタイムで入力される音源信号ｕ（ｔ）に対して音場信号ｘ（ｔ）を生成しながらリアルタイムで出力することも可能である。
【００５２】
【発明の効果】
本発明によれば、音源から受聴位置までの音の伝達状況が時間と共に変化する場合に、離散的な時点でのインパルス応答を用いながら、自然かつ滑らかな音場信号を生成することができる。
【図面の簡単な説明】
【図１】音場のシミュレーション計算の対象となる状況の一例を示す図であり、受聴者が音源に向けて移動する場合を示す。
【図２】本発明の一実施形態である音場シミュレーション装置のブロック構成図である。
【図３】相関係数が「０」の場合の窓関数の波形を示す図である。
【図４】相関係数が「１」の場合の窓関数の波形を示す図である。
【図５】図５（ａ），（ｂ）は、検証実験で用いた相関の低いインパルス応答を示す図である。
【図６】図６（ａ），（ｂ）は、検証実験で用いた相関の高いインパルス応答を示す図である。
【図７】相関の低いインパルス応答についてのホワイトノイズとの畳み込み信号に、曲線状の窓関数を掛けて足し合わせた結果の波形を示す図である。
【図８】相関の低いインパルス応答についてのホワイトノイズとの畳み込み信号に、直線状の窓関数を掛けて足し合わせた結果の波形を示す図である。
【図９】相関の高いインパルス応答についてのホワイトノイズとの畳み込み信号に、直線状の窓関数を掛けて足し合わせた結果の波形を示す図である。
【図１０】相関の高いインパルス応答についてのホワイトノイズとの畳み込み信号に、曲線状の窓関数を掛けて足し合わせた結果の波形を示す図である。
【図１１】相関係数から重み係数を決定するためのグラフである。
【図１２】本実施形態の音場シミュレーション装置における処理手順を示すフローチャートである。
【符号の説明】
１０ 音場シミュレーション装置
１２ 信号取得部
１４ インパルス応答記憶部
１６ 相関係数計算部
１８ 相関係数記憶部
２０ 応答演算部
２２ クロスフェード演算部
２４ 信号合成部
２６ 出力部[0001]
TECHNICAL FIELD OF THE INVENTION
The present invention relates to an apparatus and a method for simulating a sound field, and is particularly suitable for simulating a sound field at a listening position when a transfer function of sound from a sound source to a listening position changes with time. Method and apparatus. The present invention also relates to a program for causing a computer to execute the method and a recording medium on which the program is recorded.
[0002]
[Prior art]
Conventionally, as described in Non-Patent Document 1, for example, a system that simulates a sound field equivalent to a sound field observed at an actual listening position using a sound transfer function is known. In this system, an impulse response from a sound source to a specific listening position is obtained, and convolution calculation of the impulse response and the sound source signal is performed to generate a sound field at the listening position.
[0003]
[Non-patent document 1]
Taisei Corporation Technical Research Institute, “Sound field simulator“ Listen ””,
Journal of the Acoustical Society of Japan, 1992, 48, 4, p. 266-267
[0004]
[Problems to be solved by the invention]
By the way, the transfer function of the sound from the sound source to the listening position may change with time, for example, when the listener moves or the sound source moves. In such a case, as a method of simulating the sound field at the listening position, an impulse response from the sound source at each point in time to the listening position is obtained in advance, and the impulse response is switched over time, and It is conceivable that a sound field is generated by convolution of the impulse response and the sound source signal in. However, if the convolution is calculated simply by switching the impulse response, the generated sound field changes discontinuously at the time of the switching and becomes unnatural.
[0005]
The present invention has been made in view of the above points, and when the transmission state of sound from a sound source to a listening position changes with time, natural and smooth sound is generated while using impulse responses at discrete points in time. It is intended to be able to generate a field signal.
[0006]
[Means for Solving the Problems]
In order to achieve the above object, the invention according to claim 1 provides a sound source for reproducing a sound field at the listening position when a transfer function of the sound from the sound source to the listening position changes with time. A field simulation device,
Acquiring means for acquiring a sound source signal u (t);
Discrete time points P_i(I = 1,..., N) the impulse response h of the sound from the sound source to the listening position_iStorage means for storing (t);
The sound source signal u (t) and the impulse responses h at the plurality of time points_i(T), a response signal y at the listening position to the sound source signal u (t) at each time point_iResponse operation means for calculating (t);
The response signal y at two adjacent time points_i(T), y_{i + 1}(T) respectively shows a first window function f gradually decreasing with time.₁(T) and a second window function f that gradually increases with time.₂(T) and add them together to obtain the sound field signal x between the two points in time._iAnd (C) a cross-fade calculating means for calculating (t).
[0007]
According to the present invention, the response signal y at two adjacent time points is calculated by the cross-fade calculating means._i(T), y_{i + 1}(T) respectively shows a first window function f gradually decreasing with time.₁(T) and a second window function f that gradually increases with time.₂(T) and add them together to obtain the sound field signal x between the two points in time._iSince (t) is calculated, the generated sound field signal x_i(T) is the response signal y_i(T) to y_{i + 1}The signal smoothly transitions to (t). Therefore, according to the present invention, when the state of sound transmission from a sound source to an observation point changes with time, a natural and smooth sound field signal is generated using the impulse response at each discrete point in time. Can be.
[0008]
According to a second aspect of the present invention, in the sound field simulation apparatus according to the first aspect, the cross-fade calculating means includes an impulse response h at two adjacent time points._i(T), h_{i + 1}Correlation coefficient r between (t)_iThe first and second window functions f based on₁(T), f₂It is characterized by including means for determining (t).
[0009]
Further, according to a third aspect of the present invention, in the sound field simulation apparatus according to the first or second aspect, the response calculating means includes the sound source signal u (t) and the impulse response h at each time point._i(T) and the response signal y_i(T) is calculated.
[0010]
According to a fourth aspect of the present invention, in the sound field simulation apparatus according to any one of the first to third aspects, the cross-fade calculating means includes a first window function f and a second window function f.₁(T), f₂For each of (t), the correlation coefficient r_iFirst reference window function f corresponding to the case where_a1(T), f_a2(T) and a second reference window function f corresponding to the case where the correlation coefficient is large._b1(T), f_b2(T) and a first reference window function f according to the correlation coefficient._a1(T), f_a2(T) and the second window function f_b1(T), f_b2(T) each weight k₁, K₂Are determined by adding the functions obtained by multiplying the weights to the first and second reference window functions, respectively, to obtain the first and second window functions f.₁(T), f₂(T) is determined.
[0011]
According to a fifth aspect of the present invention, in the sound field simulation apparatus of the fourth aspect, the first reference window function f_a1(T), f_a2(T) is the sum of squares {f} when the correlation coefficient is 0._a1(T)｝²+ ｛F_a2(T)｝²Are set so that the time average of the amplitude of
The second reference window function f_b1(T), f_b2(T) is the sum f of the correlation coefficients when the correlation coefficient is 1._b1(T) + f_b2It is characterized in that the time average of the square amplitude of (t) is set to 1.
[0012]
According to a sixth aspect of the present invention, in the sound field simulation apparatus according to the fifth aspect, the first reference window function f_a1(T), f_a2(T) and the second reference window function f_b1(T), f_b2(T) is characterized by being represented by the following equation. Here, T is the interval between the two adjacent points.
f_a1(T) = cos (π · t / (2 · T))
f_a2(T) = sin (π · t / (2 · T))
f_b1(T) = 1−t / T
f_b2(T) = t / T
[0013]
The invention described in claim 7 is a sound field simulation method for reproducing a sound field at the listening position when a transfer function of sound from a sound source to a listening position changes with time. ,
Obtaining a sound source signal u (t);
The acquired sound source signal u (t) and an impulse response h of a sound from the sound source to the listening position at a plurality of discrete points in time._i(T), a response signal y at the listening position to the sound source signal u (t) at each time point_iCalculating (t);
The response signal y at two adjacent time points_i(T), y_{i + 1}(T) respectively shows a first window function f gradually decreasing with time.₁(T) and a second window function f that gradually increases with time.₂(T) and add them together to obtain the sound field signal x between the two points in time._iCalculating (t).
[0014]
The invention according to claim 8 relates to a program for causing a computer to execute the method according to claim 7, and the invention described in claim 9 relates to a recording medium on which the program is recorded. It is related.
[0015]
BEST MODE FOR CARRYING OUT THE INVENTION
Hereinafter, a sound field simulation apparatus according to an embodiment of the present invention will be described. The sound field simulation apparatus of the present embodiment is such that, when the listener moves, or the sound source moves, the transfer function of the sound from the sound source to the listening position changes with time. A simulation of a sound field reflecting a temporal change is performed.
[0016]
For example, as shown in FIG. 1, it is assumed that a listener O enters a room R by opening a door D from outside and approaches the sound source S with respect to a sound source S fixed in a certain room R. In such a situation, the position of the listener O changes over time, and the transfer function of the sound from the sound source S to the listening position changes as the door D is opened and closed. In the present embodiment, some discrete time points P_iA transfer function from the fixed sound source S to the position of the listener O at (i = 1 to N) is obtained by an experiment or calculation, and the transfer function is switched over time to change the transfer function at the listening position. Simulate the sound field.
[0017]
To explain with reference to the example of FIG.₀~ P_NThe impulse response h as a transfer function from the sound source S to the position of the listener O in the state (N = 12 in FIG. 1) (the position of the listener O and the open / closed state of the door D) in the state (N = 12)_i(T) (i = 0 to N) is obtained in advance. And each time point P_iImpulse response h_iThe sound field at the position of the listener O is calculated by convolving (t) with the signal of the sound source S (hereinafter referred to as a sound source signal) u (t). Although the listener O moves in FIG. 1, the same applies to the case where the sound source S moves.
[0018]
By the way, each time point P_iTo accurately calculate the sound field at the point P_iIt is desirable to take However, as described above, it is necessary to perform a convolution operation to calculate the sound field at the listening position, and this operation requires a considerable amount of calculation. Therefore, the time point P_iIf the interval is too small, the amount of calculation becomes enormous, which is not realistic. Therefore, in a period in which the change of the transfer function is considered to be gradual (for example, a period in which the listener O is walking indoors or outdoors), the time point P_iIs set to a relatively large interval, and during a period in which the change of the transfer function is considered to be abrupt (for example, a period when the door D is opened and closed), the time P_iTo take.
[0019]
As described above, the discrete time point P_iThe impulse response h_i(T) is each time point P_iWill change discontinuously. Therefore, the impulse response h_iIf the result of the convolution operation of (t) and the sound source signal u (t) is directly used as the sound field signal at the listening position, the sound field generated_iIn this case, it becomes unnatural that changes discontinuously. On the other hand, the sound field simulation device of the present embodiment_iResponse h at_iA characteristic feature is that a natural sound field can be generated by smoothly connecting the convolution signals obtained from (t). Hereinafter, the configuration and operation of the sound field simulation device of the present embodiment will be described in detail.
[0020]
FIG. 2 is a block diagram of the sound field simulation apparatus 10 of the present embodiment. As shown in FIG. 1, the sound field simulation apparatus 10 includes a signal acquisition unit 12, an impulse response storage unit 14, a correlation coefficient operation unit 16, a correlation coefficient storage unit 18, a response operation unit 20, a cross-fade operation unit 22, A signal combining unit 24, an output unit 26, and the like are provided. Note that the sound field simulation device 10 is configured by, for example, a computer system, and each of the arithmetic units 16, 20, and 22 and the signal synthesizing unit 24 are realized when a computer executes a predetermined arithmetic program. However, some or all of the operation units 16, 20, and 22 having a large processing load may be configured by a hardware operation circuit such as a DSP (Digital Signal Processor).
[0021]
The signal acquisition unit 12 is configured by, for example, an A / D converter, and converts an analog sound source signal input from the outside into a digital signal. Alternatively, the sound source signal may be digitized in advance and stored in the storage device, and the signal acquisition unit 12 may read out the stored sound source signal.
[0022]
Each time point P is stored in the impulse response storage unit 14._iResponse h at_i(T) is stored. The user obtains an impulse response in advance by an experiment, a simulation calculation, or the like, and stores the impulse response in the impulse response storage unit 14.
[0023]
The correlation coefficient calculator 16 calculates the impulse response h stored in the impulse response storage 14._iBased on (t), the impulse response h at the adjacent time_i(T), h_{i + 1}Correlation coefficient r between (t)_iIs calculated according to the following equation, and stored in the correlation coefficient storage unit 18.
(Equation 1)

However, the correlation coefficient calculation unit 16 and the correlation coefficient storage unit 18 are not provided in the sound field simulation device 10, but the correlation coefficient r is calculated by a calculation device separate from the sound field simulation device 10._iMay be calculated and stored, and the correlation coefficient read out by the sound field simulation apparatus 10.
[0024]
The response calculation unit 20 calculates the impulse response h stored in the impulse response storage unit 14._i(T) and the convolution signal y of the sound source signal u (t) acquired by the sound source signal acquisition unit 12_i(T) is calculated according to the following equation.
(Equation 2)

[0025]
The cross-fade operation unit 22 converts the convolution signal y as described in detail below._i(T) and the correlation coefficient r stored in the correlation coefficient storage unit 18_iAnd the interval [P_i, P_{i + 1}Sound field signal x at_iCalculate (t). Then, the signal synthesizing section 24 outputs each sound field signal x_i(T) is connected and the time point P₀~ P_NTo generate a final sound field signal x (t). The output unit 26 converts the generated sound field signal x (t) into an analog signal, and outputs the analog signal to an external audio device such as a speaker via an amplifier.
[0026]
Hereinafter, the calculation process by the crossfade calculation unit 22 will be described in detail.
[0027]
In the present embodiment, as shown in FIG. 3 and FIG._i, P_{i + 1}At time P_iFrom time point P_{i + 1}Window function f gradually decreases toward₁(T) is the convolution signal y at time Pi_i(T) and the time point P_iFrom time point P_{i + 1}Window function f gradually increasing toward₂(T) at time P_{i + 1}Convolution function y_{i + 1}(T) and add both. That is, the section [P_i, P_{i + 1}] The sound field signal x_i(T)
x_i(T) = f₁(T) · y_i(T) + f₂(T) · y_{i + 1}(T)
Is calculated as
[0028]
These window functions f₁(T), f₂(T) is the correlation coefficient r as follows:_jIs determined based on the value of.
[0029]
First, the correlation coefficient r_jIs "0", as shown in FIG.₁(T), f₂(T) in the section [P_i, P_{i + 1}] Is a function whose value changes between “0” and “1” in a curved manner. Specifically, a reference window function f expressed by the following equation_a1(T), f_a2(T) is used. Where T_iIs the interval [P_i, P_{i + 1}], And t is the time point P_i0 ≦ t ≦ T_iAnd
f₁(T) = f_a1(T) = cos (π · t / (2 · T_i))
f₂(T) = f_a2(T) = sin (π · t / (2 · T_i))
[0030]
Also, the correlation coefficient r_jIs "1", as shown in FIG.₁(T), f₂(T) in the section [P_i, P_{i + 1}] Is a function whose value changes linearly between “0” and “1”. Specifically, a reference window function f represented by the following equation_b1(T), f_b2(T) is used.
f₁(T) = f_b1(T) = 1−t / T_i
f₂(T) = f_b2(T) = t / T_i
[0031]
These reference window functions f_a1(T), f_a2(T) and f_b1(T), f_b2(T) corresponds to the section [P_i, P_{i + 1}], The sound field signal x calculated in_iThe time average of the square amplitude of (t) (hereinafter referred to as the square amplitude average)_i, P_{i + 1}Convolution signal y at_i(T), y_{i + 1}It is obtained so as to satisfy the condition that it is equal to the square amplitude average of (t). Hereinafter, this will be verified. In the following equations, function parameters may be omitted for simplicity.
[0032]
First, the correlation coefficient r_iIs “0”, the interval [P_i, P_{i + 1}Sound field signal at
x_i(T) = cos (π · t / (2 · T)) · y_i(T) + sin (π · t / (2 · T)) · y_{i + 1}(T)
Is the sum of the squared amplitudes of
(Equation 3)

h_i(T) and h_{i + 1}(T) correlation coefficient r_iIs "0", so their convolution, y_i(T), y_{i + 1}About (t),
(Equation 4)

Holds.
[0033]
Therefore,
(Equation 5)

Becomes
[0034]
Here, since it is considered that there is almost no change in the power of the sound field between adjacent time points, the convolution signal y_i(T), y_{i + 1}(T) shall satisfy the following equation.
(Equation 6)

Therefore,
(Equation 7)

And the sound field signal x_iThe mean square amplitude of (t) is the convolution signal y_i(T), y_{i + 1}It can be seen that it is equal to the square amplitude average of (t).
[0035]
That is, based on the above equation (1), the reference window function f when the correlation coefficient is “0”_a1(T), f_a2(T) is their sum of squares ｛f_a1(T)｝²+ ｛F_a2(T)｝²Are set so that the average of the amplitudes of “1” is “1”.
[0036]
Also, the correlation coefficient r_jIs [1], the interval [P_i, P_{i + 1}Sound field signal at
x_i(T) = (1-t / T_i) ・ Y_i(T) + (t / T_i) ・ Y_{i + 1}(T)
The mean squared amplitude of
(Equation 8)

Where h_i(T), h_{i + 1}Since the correlation coefficient of (t) is 1, y, which is a convolution of them with the sound source signal u (t),₁(T), y₂(T) is equal to each other. Therefore, y₁(T) = y₂If (t) = y (t),
(Equation 9)

And the mean square amplitude of the sound field signal x (t) is the convolution signal y_j(T), y_{j + 1}It can be seen that it is equal to the square amplitude average of (t).
[0037]
That is, when the correlation coefficient is “1”, y₁(T) = y₂(T), the reference window function f_b1(T), f_b2(T) is their sum f_b1(T) + f_b2The mean square amplitude of (t) is set to be “1”.
[0038]
Thus, the interval [P_i, P_{i + 1}], The sound field signal x_iThe mean square amplitude of (t) is the convolution signal y_i(T), y_{i + 1}(T), each interval [P_i, P_{i + 1}] And y_i(T) and y_{i + 1}(T) does not cause a discontinuous change in the level of the sound field signal x (t), and a natural sound field can be generated.
[0039]
To prove the above, two impulse responses h with low correlation are used using white noise as the sound source signal r (t)._s1(T), h_s2(T) and two highly correlated impulse responses h_t1(T), h_t2For (t), a sound field signal was calculated using each reference window function. Note that the impulse response h having a low correlation_s1(T), h_s2As (t), measured values at two points in a certain building where the environment is completely different (laboratory and entrance hall) were used. FIGS. 5A and 5B show the impulse response h._s1(T), h_s2The waveform of (t) is shown. In addition, a highly correlated impulse response h_t1(T), h_t2As (t), measured values at two points that differ only in the same room position were used. FIGS. 6A and 6B show the impulse response h._t1(T), h_t2The waveform of (t) is shown.
[0040]
First, the impulse response h with low correlation_s1(T), h_s2Compute the convolution signal with white noise for (t) and add them respectively to the curved window function f_a1(T) = cos (π · t / (2 · T)), f_a2When (t) = sin (π · t / (2 · T)) was multiplied and both were added, a signal having a waveform shown in FIG. 7 was obtained. Here, T is an appropriate constant. As shown in FIG. 7, the amplitude of the obtained signal waveform is kept almost constant, and the impulse response is h._s1(T) to h_s2It can be seen that when changing to (t), the sound field signal changes smoothly.
[0041]
On the other hand, these impulse responses h_s1(T), h_s2(T) is subjected to a convolution operation with white noise, and a linear window function f_b1(T) = 1−t / T, f_b2When (t) = t / T was applied and both were added, a signal having a waveform shown in FIG. 8 was obtained. As shown in the figure, the level of the obtained signal waveform is reduced (indicated by an arrow X in the figure), and the impulse response h having a low correlation_s1(T), h_s2A linear window function f for (t)_b1, F_b2, The impulse response is h_s1(T) to h_s2It can be seen that the sound field signal does not change smoothly when changing to (t).
[0042]
Next, a highly correlated impulse response h_t1(T), h_t2Compute the convolution signal with white noise for (t) and add them respectively to the linear window function f_b1(T) = 1−t / T, f_b2When (t) = t / T was multiplied and both were added, a signal having a waveform shown in FIG. 9 was obtained. As shown in the figure, the amplitude of the obtained signal waveform is kept almost constant, and the impulse response is h._t1(T) to h_t2It can be seen that when changing to (t), the sound field signal changes smoothly.
[0043]
On the other hand, these impulse responses h_t1(T), h_t2Compute the convolution signal with white noise for (t) and add them respectively to the curved window function f_a1(T) = cos (π · t / (2 · T)), f_a2(T) = sin (π · t / (2 · T)), and when they were added together, a signal having the waveform shown in FIG. 10 was obtained. As shown in the figure, the level of the obtained signal waveform is increased (indicated by the arrow Y in the figure), and the impulse response h having a high correlation is shown._t1(T), h_t2Curve window function f for (t)_a1, F_a2, The impulse response is h_t1(T) to h_t2It can be seen that the sound field signal does not change smoothly when changing to (t).
[0044]
As described above, when the correlation coefficient of the impulse response is low, the curved window function f_a1(T), f_a2If (t) is used and the correlation coefficient is high, a linear window function f_b1(T), f_b2By using (t), the impulse response h_iThe interval [P] where (t) changes [P_i, P_{i + 1}], It was demonstrated that a smooth and natural sound field signal can be generated.
[0045]
However, in practice, the correlation coefficient of the impulse response takes an intermediate value between “0” and “1”. Therefore, in the present embodiment, a curved reference window function f_a1(T), f_a2(T) and linear reference window function f_b1(T), f_b2(T) and the correlation coefficient r_iOf the window function f₁(T), f₂(T). That is, the weight coefficient is k₁, K₂As
f₁(T) = k₁・ (1-t / T_i) + K₂・ Cos (π · t / (2 · T_i)) ・ ・ ・ (A)
f₂(T) = k₁・ T / T_i      + K₂· Sin (π · t / (2 · T_i)) ・ ・ ・ (B)
Using a window function₁, K₂Is set according to the correlation coefficient. Where k₁+ K₂= 1 is satisfied.
[0046]
FIG. 11 shows that the weighting coefficient k₁, K₂(Hereinafter, referred to as a weight determination graph). This weight determination graph is obtained experimentally as follows. That is, a set of white noises having various correlation coefficients is prepared, and for each set of the white noises, k₁, K₂The window function f determined by the above equations (A) and (B) while changing the value of₁(T), f₂(T) is multiplied to calculate a sum signal, and k is such that the level fluctuation of the signal waveform is minimized.₁, K₂Find the value of. K obtained in this way₁, K₂By plotting the relationship between the correlation coefficient and the white noise correlation coefficient, a weight determination graph shown in FIG. 11 is obtained. Such a weight determination graph is stored, and by referring to this graph, the correlation coefficient r_iFrom the weighting factor k₁, K₂To determine.
[0047]
FIG. 12 is a flowchart illustrating a processing procedure in the sound field simulation device 10 of the present embodiment. In this simulation, the situation to be simulated_iIs set at each time point P_iResponse h from sound source to listening position at_i(T) is obtained and stored in the impulse response storage unit 14.
[0048]
As shown in the figure, first, the sound source signal u (t) is input by the signal acquisition unit 12, or the sound source signal u (t) stored in advance is read out (S100). Further, the correlation coefficient calculator 16 calculates the impulse response h stored in the impulse response storage 14._iBased on (t), the correlation coefficient r of the impulse response between adjacent time points_iIs calculated and stored in the correlation coefficient storage unit 18 (S102). Next, the response calculator 20 calculates the sound source signal u (t) and the impulse response h_iConvolution signal y with (t)_i(T) is calculated (S104). Further, the crossfade calculation unit 22 calculates each section [P_i, P_{i + 1}], The impulse response h_i(T), h_{i + 1}(T) correlation coefficient r_iAnd the weight coefficient k with reference to the weight determination graph shown in FIG.₁, K₂Is determined (S106). And the weight coefficient k₁, K₂And the window function f according to the above equations (A) and (B).₁(T), f₂(T) is determined and each is convolved signal y_i(T), y_{i + 1}(T) and adding them together, the section [P_i, P_{i + 1}Sound field signal x at_i(T) is calculated (S108). The signal synthesizing unit 24 calculates the signal x_iBy connecting (t) for i = 1 to N, a sound field signal x (t) is generated (S110). The sound field signal x (t) thus generated is output to the outside by the output unit 26 (S112).
[0049]
Using the sound field simulation apparatus 10 of the present embodiment, the sound field under the situation shown in FIG. 1 was simulated and compared with the sound actually collected at the position of the listener O shown in FIG. It was confirmed that the same sound field as the sound field could be reproduced.
[0050]
As described above, according to the sound field simulation apparatus 10 of the present embodiment, the discrete time points P_iImpulse response h at (t)_iConvolution signal y obtained using (t)_i(T) is calculated by the correlation coefficient r_iWindow function f according to₁(T), f₂By connecting using (t), the impulse response h_iIt is possible to generate a smooth and natural sound field signal without a discontinuous level change accompanying the change in (t).
[0051]
In the above description, the sound field signal x (t) is generated based on the sound source signal u (t), and then the sound field signal x (t) is output. , 22 and the like are constituted by a DSP, when a sufficiently high calculation speed can be obtained, the sound field signal x (t) is generated while generating the sound field signal x (t) for the sound source signal u (t) input in real time. It is also possible to output with.
[0052]
【The invention's effect】
ADVANTAGE OF THE INVENTION According to this invention, when the transmission state of the sound from a sound source to a listening position changes with time, a natural and smooth sound field signal can be generated using the impulse response at discrete time points.
[Brief description of the drawings]
FIG. 1 is a diagram illustrating an example of a situation to be subjected to a sound field simulation calculation, showing a case where a listener moves toward a sound source.
FIG. 2 is a block diagram of a sound field simulation apparatus according to an embodiment of the present invention.
FIG. 3 is a diagram showing a waveform of a window function when a correlation coefficient is “0”.
FIG. 4 is a diagram showing a waveform of a window function when a correlation coefficient is “1”.
FIGS. 5A and 5B are diagrams showing impulse responses with low correlation used in a verification experiment. FIGS.
FIGS. 6A and 6B are diagrams showing highly correlated impulse responses used in a verification experiment. FIGS.
FIG. 7 is a diagram showing a waveform obtained as a result of multiplying a convolution signal with white noise for a low-correlation impulse response by a curved window function and adding the convolution signal.
FIG. 8 is a diagram showing a waveform obtained as a result of multiplying a convolution signal with white noise for a low-correlation impulse response by a linear window function and adding the convolution signal.
FIG. 9 is a diagram illustrating a waveform obtained by multiplying a convolution signal with white noise for a highly correlated impulse response by a linear window function and adding the result;
FIG. 10 is a diagram showing a waveform obtained as a result of multiplying a convolution signal with white noise for a highly correlated impulse response by a curved window function and adding the convolution signal.
FIG. 11 is a graph for determining a weight coefficient from a correlation coefficient.
FIG. 12 is a flowchart illustrating a processing procedure in the sound field simulation device of the present embodiment.
[Explanation of symbols]
10 Sound field simulation device
12 Signal acquisition unit
14 Impulse response storage
16 Correlation coefficient calculator
18 Correlation coefficient storage unit
20 Response calculation unit
22 Crossfade operation unit
24 signal synthesis unit
26 Output unit

Claims (9)

A sound field simulation device for reproducing a sound field at the listening position when a transfer function of sound from a sound source to a listening position changes with time,
Acquiring means for acquiring a sound source signal u (t);
Storage means for storing impulse responses h _i (t) of sounds from the sound source to the listening position at a plurality of discrete time points P _i (i = 1,..., N);
Based on the impulse response h _{i (t)} in the plurality of time points and said sound source signal u (t), calculates the response signal y _{i (t)} at the listening position relative to the sound source signal u (t) at each time point Response calculation means for performing
The response signals y _i (t) and y _{i + 1} (t) at two adjacent time points respectively include a first window function f ₁ (t) that gradually decreases over time, and a gradually increasing function over time. And a cross-fade calculating means for calculating a sound field signal x _i (t) between the two points in time by multiplying by a _second window function f ₂ (t). Equipment to do. The cross-fade calculating means calculates the first and second window functions f ₁ (t based on a correlation coefficient r _i between the impulse responses h _i (t) and h _{i + 1} (t) at two adjacent times. _2. The sound field simulation apparatus according to claim 1, further comprising means for determining f ₂ (t). The response calculating means, according to claim 1 or 2, wherein the calculating the response signal y _{i (t)} by convolution of the said sound source signals u (t) and the impulse response h _{i (t)} for each time point Sound field simulation device. The cross-fade calculation means, said first and second window function f _{1 (t),} for each of f 2 _(t), a first reference window function f corresponding to the case where the correlation coefficient r _i is smaller _a1 (t), f _a2 (t) and second reference window functions f _b1 (t), f _b2 (t) corresponding to the case where the correlation coefficient is large, and stores the correlation coefficient. , The weights k ₁ and k ₂ of the first reference window functions f _a1 (t) and f _a2 (t) and the second window functions f _b1 (t) and f _b2 (t) are determined. Determining the first and second window functions f ₁ (t) and f ₂ (t) by adding functions obtained by multiplying the weights by the first and second reference window functions, respectively. The sound field simulation device according to any one of claims 1 to 3. When the correlation coefficient is 0, the first reference window functions f _a1 (t) and f _a2 (t) are sums of their squares {f _a1 (t)} ² + _{Δf a2} (t)時間 The time average of the amplitude of ² is set to be 1,
When the correlation coefficient is 1, the second reference window functions f _b1 (t) and f _b2 (t) are the time average of the square amplitude of the sum f _b1 (t) + f _b2 (t). 5. The sound field simulation apparatus according to claim 4, wherein is set to 1. The first reference window function f _a1 (t), f _a2 (t) and the second reference window function f _b1 (t), f _b2 (t) are represented by the following equations. Item 6. The sound field simulation device according to item 5. Here, T is the interval between the two adjacent points.
f _a1 (t) = cos (π · t / (2 · T))
f _a2 (t) = sin (π · t / (2 · T))
f _b1 (t) = 1−t / T
f _b2 (t) = t / T A sound field simulation method for reproducing a sound field at the listening position when a transfer function of sound from the sound source to the listening position changes with time,
Obtaining a sound source signal u (t);
Wherein the acquired sound source signal u (t), on the basis of the sound source in a plurality of discrete time points to the impulse response h _i sound to the listening position _(t), the sound source signal u at each time point (t) Calculating a response signal y _i (t) at the listening position for
The response signals y _i (t) and y _{i + 1} (t) at two adjacent time points respectively include a first window function f ₁ (t) that gradually decreases over time, and a gradually increasing function over time. Multiplying by a _second window function f ₂ (t) and adding them together to calculate the sound field signal x _i (t) between the two points in time. A program for causing a computer to execute the method according to claim 7. A recording medium on which the program according to claim 8 is recorded.

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