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Once we grasp the principle of DP, we can modify DTW for our needs. In this section, we shall introduce another version of DTW with the following characteristics:
Query input: This is a frame-based pitch vector. (For our previous task on pitch labeling, the corresponding time unit for each pitch point is 256/8000 = 1/31.25 = 0.032 s = 32 ms.)
Reference song: This is a note-based pitch vector in which the note duration is discarded for simplicity.
只要我們掌握了 DP 的遞迴原則，就可以根據需要，對 DTW 進行各種變形。在本節中，我們介紹另一種 DTW，其輸入格式具有下列特性：
使用者輸入：以音框為基礎的音高向量，不進行音符切割。（通常這類資料稱為 mid 格式。以我們進行的人工標示音高而言，每一點的時間長度是 256/8000 = 1/31.25 = 0.032 s = 32 ms。）
資料庫格式：以音符為比對單位，但只考慮音高。（通常這類資料稱為 note 格式，以向量 [音高, 音長, 音高, 音長...] 來表示。以我們哼唱選歌的資料而言，音長的單位都是 1/64 秒。）
Let t be the input query vector and r be the reference vector. The optimum-value function D(i, j), defined as the minimum distance between t (1:i) and r (1:j), can be expressed in the following recursion:
假設使用者輸入的音高向量是 t 而標準答案的音符向量是 r，並假設 D(i, j) 是 t(1:i) 和 r(1:j) 之間的最短距離，則我們有下列遞迴式：
D(i, j) = min(D(i-1,j), D(i-1, j-1))+|t (i)-r (j)|
Please refer to the following figure:
請見下列示意圖：
For simplicity, we shall refer to DTW of this type as type-3 DTW, with the following characteristics:
Type-3 DTW computes the distance between a frame-based pitch vector and a note-based pitch vector. Therefore the computational complexity is lower than those of type-1 and type-2 DTW>
The note duration is not used in the note-based pitch vector for comparison. Hence the recognition rate should not be as good as type-1 and type-2 DTW.
There is no method for one-shot key transposition for type-3 DTW. So we have to rely on trial-and-error method for key transposition.
為便於說明，我們簡稱這一類方法為 type-3 DTW。此方法有下列特性：
由於資料庫格式是以音符為單位，所以計算量小於 type-1 及 type-2 DTW。
資料庫格式並沒有用到音符的音長資訊，所以理論上來說，辨識率應該低於 type-1 及 type-2 DTW。
無法進行一次到位的音高平移，這點和 type-1 及 type-2 DTW 是一樣的。
The following is a typical example of using type-3 DTW for melody alignment:
在以下的範例，我們使用 type-3 DTW 來進行音高向量對音符（只用音高）的「對位」（Alignment）：
Example 1: dtw3path01.m <![CDATA[pv=[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 47.485736 48.330408 48.917323 49.836778 50.478049 50.807818 50.478049 50.807818 50.478049 49.836778 50.154445 49.836778 50.154445 50.478049 49.524836 0 0 52.930351 52.930351 52.930351 52.558029 52.193545 51.836577 51.836577 51.836577 52.558029 52.558029 52.930351 52.558029 52.193545 51.836577 51.486821 49.218415 48.330408 48.621378 48.917323 49.836778 50.478049 50.478049 50.154445 50.478049 50.807818 50.807818 50.154445 50.154445 50.154445 0 0 0 54.505286 55.349958 55.349958 55.788268 55.788268 55.788268 55.788268 55.788268 55.788268 55.788268 55.788268 55.349958 55.349958 54.505286 54.505286 54.922471 55.788268 55.788268 56.237965 55.788268 55.349958 55.349958 55.349958 55.349958 55.349958 55.349958 55.349958 55.349958 55.349958 55.349958 54.922471 54.922471 54.097918 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 49.218415 49.218415 48.917323 49.218415 49.836778 50.478049 50.478049 50.154445 49.836778 50.154445 49.524836 49.836778 49.524836 0 0 55.788268 53.699915 53.699915 53.310858 53.310858 53.310858 53.310858 52.930351 52.930351 52.930351 52.930351 52.930351 52.558029 52.193545 51.486821 50.154445 49.836778 49.836778 50.154445 50.478049 50.478049 50.154445 49.836778 49.836778 49.524836 49.524836 49.524836 0 0 0 0 56.699654 57.661699 58.163541 58.163541 57.661699 57.661699 57.661699 57.661699 57.661699 57.661699 57.661699 57.661699 58.163541 57.173995 56.699654 56.237965 55.788268 56.237965 56.699654 56.699654 56.237965 55.788268 56.237965 56.237965 56.237965 56.237965 56.237965 56.237965 56.237965 55.788268 54.097918 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 50.154445 50.154445 50.478049 51.143991 51.143991 50.807818 50.154445 51.143991 50.154445 50.478049 50.807818 50.478049 0 0 0 60.330408 61.524836 62.154445 62.807818 62.807818 62.807818 62.807818 62.807818 63.486821 63.486821 63.486821 63.486821 62.807818 62.807818 61.524836 59.213095 58.163541 58.680365 59.213095 59.762739 59.762739 59.762739 59.762739 59.762739 59.762739];
pv(pv==0)=[]; % Delete rests (刪除休止符)
% Note representation, where the time unit of note duration is 1/64 seconds
note=[60 29 60 10 62 38 60 38 65 38 64 77 60 29 60 10 62 38 60 38 67 38 65 77 60 29 60 10 72 38 69 38 65 38 64 38 62 77 0 77 70 29 70 10 69 38 65 38 67 38 65 38];
frameSize=256; overlap=0; fs=8000;
frameRate=fs/(frameSize-overlap);
pv2=note2pv(note, frameRate);
noteMean=mean(pv2(1:length(pv))); % Take the mean of pv2 with the length of pv
pv=pv-mean(pv)+noteMean; % Key transposition
notePitch=note(1:2:end); % Use pitch only (只取音高)
notePitch(notePitch==0)=[]; % Delete rests (刪除休止符)
[minDistance, dtwPath] = dtw3(pv, notePitch, 1, 0);
dtwPathPlot(pv, notePitch, dtwPath);]]>
In the above example, before using type-3 DTW, we have performed the following preprocessing:
Key transposition: We assume the tempo of the query input is the same as the reference song. Therefore we convert the note into frame-based pitch vector for computing the mean value based on the length of the input query. We then shift the input query to have the same mean of the reference song. We can replace this simplified operation by a more precise method for key transposition.
Rest handling: We simply delete all rests in both the input query and the reference song. Again, this is a simplified operation which can be replaced by a more delicate procedure for rest handling.
在上述範例中，我們在進行 dtw3 的比對前，做了兩件事情：
音調移位：我們假設歌唱者的速度和樂譜的速度是一樣的，因此我們將 note 先轉成 mid 格式，再取用和 PV 同樣的長度來計算其平均值為 noteMean，最後再將 PV 移到同樣的平均值。這是一個簡化的處理，因為我們並無法使用「一次到位」的音調移位。
休止符的處理：我們是把 PV 和 Note 中的休止符都砍掉來進行比對。這也是一個簡化的處理，後續會提到如何使用休止符來提高比對效果。
After the alignment of type-3 DTW in the above example, we can plot the original input PV, shifted PV, and the induced PV, as follows:
經過上述範例的對位後，我們可以將每個音高點所對應的音符音高畫出來，如下：
Example 2: dtw3inducedPitch01.m <![CDATA[pv=[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 47.485736 48.330408 48.917323 49.836778 50.478049 50.807818 50.478049 50.807818 50.478049 49.836778 50.154445 49.836778 50.154445 50.478049 49.524836 0 0 52.930351 52.930351 52.930351 52.558029 52.193545 51.836577 51.836577 51.836577 52.558029 52.558029 52.930351 52.558029 52.193545 51.836577 51.486821 49.218415 48.330408 48.621378 48.917323 49.836778 50.478049 50.478049 50.154445 50.478049 50.807818 50.807818 50.154445 50.154445 50.154445 0 0 0 54.505286 55.349958 55.349958 55.788268 55.788268 55.788268 55.788268 55.788268 55.788268 55.788268 55.788268 55.349958 55.349958 54.505286 54.505286 54.922471 55.788268 55.788268 56.237965 55.788268 55.349958 55.349958 55.349958 55.349958 55.349958 55.349958 55.349958 55.349958 55.349958 55.349958 54.922471 54.922471 54.097918 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 49.218415 49.218415 48.917323 49.218415 49.836778 50.478049 50.478049 50.154445 49.836778 50.154445 49.524836 49.836778 49.524836 0 0 55.788268 53.699915 53.699915 53.310858 53.310858 53.310858 53.310858 52.930351 52.930351 52.930351 52.930351 52.930351 52.558029 52.193545 51.486821 50.154445 49.836778 49.836778 50.154445 50.478049 50.478049 50.154445 49.836778 49.836778 49.524836 49.524836 49.524836 0 0 0 0 56.699654 57.661699 58.163541 58.163541 57.661699 57.661699 57.661699 57.661699 57.661699 57.661699 57.661699 57.661699 58.163541 57.173995 56.699654 56.237965 55.788268 56.237965 56.699654 56.699654 56.237965 55.788268 56.237965 56.237965 56.237965 56.237965 56.237965 56.237965 56.237965 55.788268 54.097918 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 50.154445 50.154445 50.478049 51.143991 51.143991 50.807818 50.154445 51.143991 50.154445 50.478049 50.807818 50.478049 0 0 0 60.330408 61.524836 62.154445 62.807818 62.807818 62.807818 62.807818 62.807818 63.486821 63.486821 63.486821 63.486821 62.807818 62.807818 61.524836 59.213095 58.163541 58.680365 59.213095 59.762739 59.762739 59.762739 59.762739 59.762739 59.762739];
fs=8000; frameRate=fs/256;
%fprintf('Hit return to hear the original pitch vector...\n'); pause; pvPlay(pv, frameRate);
wavwrite(pv2wave(pv, frameRate), fs, 8, 'queryPitchWithRest.wav');
pv(pv==0)=[]; % Delete rests (刪除休止符)
%fprintf('Hit return to hear the pitch vector without rest...\n'); pause; pvPlay(pv, frameRate);
wavwrite(pv2wave(pv, frameRate), fs, 8, 'queryPitchWithoutRest.wav');
origPv=pv;
pvLen=length(origPv);
% Note representation, where the time unit of note duration is 1/64 seconds
note=[60 29 60 10 62 38 60 38 65 38 64 77 60 29 60 10 62 38 60 38 67 38 65 77 60 29 60 10 72 38 69 38 65 38 64 38 62 77 0 77 70 29 70 10 69 38 65 38 67 38 65 38];
pv2=note2pv(note, frameRate);
noteMean=mean(pv2(1:length(pv)));
shiftedPv=pv-mean(pv)+noteMean; % Key transposition
%fprintf('Hit return to hear the shifted pitch vector...\n'); pause; pvPlay(shiftedPv, frameRate);
wavwrite(pv2wave(shiftedPv, frameRate), fs, 8, 'shiftedQueryPitchWithoutRest.wav');
notePitch=note(1:2:end); % Use pitch only (只取音高)
notePitch(notePitch==0)=[]; % Delete rests (刪除休止符)
[minDistance, dtwPath] = dtw3(shiftedPv, notePitch, 1, 0);
inducedPv=notePitch(dtwPath(2,:));
plot(1:pvLen, origPv, '.-', 1:pvLen, shiftedPv, '.-', 1:pvLen, inducedPv, '.-');
legend('Original PV', 'Best shifted PV', 'Induced PV', 4);
fprintf('Min. distance = %f\n', minDistance);
inducedNote=pv2noteStrict(inducedPv, frameRate);
%fprintf('Hit return to hear the induced pitch vector...\n'); pause; notePlay(inducedNote);
wavwrite(note2wave(inducedNote, 1, fs), fs, 8, 'inducedNote.wav');]]> <![CDATA[[Warning: WAVWRITE will be removed in a future release. Use AUDIOWRITE
instead.]
[> In <a href="matlab:matlab.internal.language.introspective.errorDocCallback('wavwrite', 'E:\MATLAB\R2015a\toolbox\matlab\audiovideo\wavwrite.m', 48)" style="font-weight:bold">wavwrite</a> (<a href="matlab: opentoline('E:\MATLAB\R2015a\toolbox\matlab\audiovideo\wavwrite.m',48,0)">line 48</a>)
In <a href="matlab:matlab.internal.language.introspective.errorDocCallback('dtw3inducedPitch01', 'D:\users\jang\books\audioSignalProcessing\example\dtw3inducedPitch01.m', 4)" style="font-weight:bold">dtw3inducedPitch01</a> (<a href="matlab: opentoline('D:\users\jang\books\audioSignalProcessing\example\dtw3inducedPitch01.m',4,0)">line 4</a>)
In <a href="matlab:matlab.internal.language.introspective.errorDocCallback('goWriteOutputFile>dummyFunction', 'D:\users\jang\books\goWriteOutputFile.m', 85)" style="font-weight:bold">goWriteOutputFile>dummyFunction</a> (<a href="matlab: opentoline('D:\users\jang\books\goWriteOutputFile.m',85,0)">line 85</a>)
In <a href="matlab:matlab.internal.language.introspective.errorDocCallback('goWriteOutputFile', 'D:\users\jang\books\goWriteOutputFile.m', 55)" style="font-weight:bold">goWriteOutputFile</a> (<a href="matlab: opentoline('D:\users\jang\books\goWriteOutputFile.m',55,0)">line 55</a>)]
[Warning: WAVWRITE will be removed in a future release. Use AUDIOWRITE
instead.]
[> In <a href="matlab:matlab.internal.language.introspective.errorDocCallback('wavwrite', 'E:\MATLAB\R2015a\toolbox\matlab\audiovideo\wavwrite.m', 48)" style="font-weight:bold">wavwrite</a> (<a href="matlab: opentoline('E:\MATLAB\R2015a\toolbox\matlab\audiovideo\wavwrite.m',48,0)">line 48</a>)
In <a href="matlab:matlab.internal.language.introspective.errorDocCallback('dtw3inducedPitch01', 'D:\users\jang\books\audioSignalProcessing\example\dtw3inducedPitch01.m', 7)" style="font-weight:bold">dtw3inducedPitch01</a> (<a href="matlab: opentoline('D:\users\jang\books\audioSignalProcessing\example\dtw3inducedPitch01.m',7,0)">line 7</a>)
In <a href="matlab:matlab.internal.language.introspective.errorDocCallback('goWriteOutputFile>dummyFunction', 'D:\users\jang\books\goWriteOutputFile.m', 85)" style="font-weight:bold">goWriteOutputFile>dummyFunction</a> (<a href="matlab: opentoline('D:\users\jang\books\goWriteOutputFile.m',85,0)">line 85</a>)
In <a href="matlab:matlab.internal.language.introspective.errorDocCallback('goWriteOutputFile', 'D:\users\jang\books\goWriteOutputFile.m', 55)" style="font-weight:bold">goWriteOutputFile</a> (<a href="matlab: opentoline('D:\users\jang\books\goWriteOutputFile.m',55,0)">line 55</a>)]
[Warning: WAVWRITE will be removed in a future release. Use AUDIOWRITE
instead.]
[> In <a href="matlab:matlab.internal.language.introspective.errorDocCallback('wavwrite', 'E:\MATLAB\R2015a\toolbox\matlab\audiovideo\wavwrite.m', 48)" style="font-weight:bold">wavwrite</a> (<a href="matlab: opentoline('E:\MATLAB\R2015a\toolbox\matlab\audiovideo\wavwrite.m',48,0)">line 48</a>)
In <a href="matlab:matlab.internal.language.introspective.errorDocCallback('dtw3inducedPitch01', 'D:\users\jang\books\audioSignalProcessing\example\dtw3inducedPitch01.m', 16)" style="font-weight:bold">dtw3inducedPitch01</a> (<a href="matlab: opentoline('D:\users\jang\books\audioSignalProcessing\example\dtw3inducedPitch01.m',16,0)">line 16</a>)
In <a href="matlab:matlab.internal.language.introspective.errorDocCallback('goWriteOutputFile>dummyFunction', 'D:\users\jang\books\goWriteOutputFile.m', 85)" style="font-weight:bold">goWriteOutputFile>dummyFunction</a> (<a href="matlab: opentoline('D:\users\jang\books\goWriteOutputFile.m',85,0)">line 85</a>)
In <a href="matlab:matlab.internal.language.introspective.errorDocCallback('goWriteOutputFile', 'D:\users\jang\books\goWriteOutputFile.m', 55)" style="font-weight:bold">goWriteOutputFile</a> (<a href="matlab: opentoline('D:\users\jang\books\goWriteOutputFile.m',55,0)">line 55</a>)]
Min. distance = 204.876547
[Warning: WAVWRITE will be removed in a future release. Use AUDIOWRITE
instead.]
[> In <a href="matlab:matlab.internal.language.introspective.errorDocCallback('wavwrite', 'E:\MATLAB\R2015a\toolbox\matlab\audiovideo\wavwrite.m', 48)" style="font-weight:bold">wavwrite</a> (<a href="matlab: opentoline('E:\MATLAB\R2015a\toolbox\matlab\audiovideo\wavwrite.m',48,0)">line 48</a>)
In <a href="matlab:matlab.internal.language.introspective.errorDocCallback('dtw3inducedPitch01', 'D:\users\jang\books\audioSignalProcessing\example\dtw3inducedPitch01.m', 26)" style="font-weight:bold">dtw3inducedPitch01</a> (<a href="matlab: opentoline('D:\users\jang\books\audioSignalProcessing\example\dtw3inducedPitch01.m',26,0)">line 26</a>)
In <a href="matlab:matlab.internal.language.introspective.errorDocCallback('goWriteOutputFile>dummyFunction', 'D:\users\jang\books\goWriteOutputFile.m', 85)" style="font-weight:bold">goWriteOutputFile>dummyFunction</a> (<a href="matlab: opentoline('D:\users\jang\books\goWriteOutputFile.m',85,0)">line 85</a>)
In <a href="matlab:matlab.internal.language.introspective.errorDocCallback('goWriteOutputFile', 'D:\users\jang\books\goWriteOutputFile.m', 55)" style="font-weight:bold">goWriteOutputFile</a> (<a href="matlab: opentoline('D:\users\jang\books\goWriteOutputFile.m',55,0)">line 55</a>)]
]]>
In the above example, the green line is the original input PV, the green line is the shifted PV, and the red line is the induced PV. Since the discrepancy between the shifted and induced PVs is still too big, we can conclude that the key transposition is satisfactory. It is likely that the tempo of the query input is not close to that of the reference song. The reference song is "Happy Birthday" and we can hear the related files:
在上述範例中，由於綠色曲線（平移過的哼唱音高向量）和紅色曲線（由 dtw3 對位所產生的對應音符音高）的吻合程度並不理想，由此可以看出，我們的音調移位出了問題，所以得到的對位效果並不理想，很可能是由使用者哼唱的速度和樂譜的速度並不一致，這一首歌是「生日快樂」，我們可以直接試聽看看相關的檔案：
If we want to do a better job in the alignment, we need to improve key transposition. A straightforward method is to do a linear (exhaustive) search of 81 comparisons with the range [-2, 2], as shown in the following example:
若要進行更吻合的對位，我們就必須改善音調移位。我們可以使用一個簡單的線性搜尋法（暴力法）來找到最佳的音高平移量，換句話說，也就是進行 81 次音調移位，平移量則平均分佈於 [-2, 2] 之間，請見下列範例：
Example 3: dtw3inducedPitch02.m <![CDATA[pv=[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 47.485736 48.330408 48.917323 49.836778 50.478049 50.807818 50.478049 50.807818 50.478049 49.836778 50.154445 49.836778 50.154445 50.478049 49.524836 0 0 52.930351 52.930351 52.930351 52.558029 52.193545 51.836577 51.836577 51.836577 52.558029 52.558029 52.930351 52.558029 52.193545 51.836577 51.486821 49.218415 48.330408 48.621378 48.917323 49.836778 50.478049 50.478049 50.154445 50.478049 50.807818 50.807818 50.154445 50.154445 50.154445 0 0 0 54.505286 55.349958 55.349958 55.788268 55.788268 55.788268 55.788268 55.788268 55.788268 55.788268 55.788268 55.349958 55.349958 54.505286 54.505286 54.922471 55.788268 55.788268 56.237965 55.788268 55.349958 55.349958 55.349958 55.349958 55.349958 55.349958 55.349958 55.349958 55.349958 55.349958 54.922471 54.922471 54.097918 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 49.218415 49.218415 48.917323 49.218415 49.836778 50.478049 50.478049 50.154445 49.836778 50.154445 49.524836 49.836778 49.524836 0 0 55.788268 53.699915 53.699915 53.310858 53.310858 53.310858 53.310858 52.930351 52.930351 52.930351 52.930351 52.930351 52.558029 52.193545 51.486821 50.154445 49.836778 49.836778 50.154445 50.478049 50.478049 50.154445 49.836778 49.836778 49.524836 49.524836 49.524836 0 0 0 0 56.699654 57.661699 58.163541 58.163541 57.661699 57.661699 57.661699 57.661699 57.661699 57.661699 57.661699 57.661699 58.163541 57.173995 56.699654 56.237965 55.788268 56.237965 56.699654 56.699654 56.237965 55.788268 56.237965 56.237965 56.237965 56.237965 56.237965 56.237965 56.237965 55.788268 54.097918 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 50.154445 50.154445 50.478049 51.143991 51.143991 50.807818 50.154445 51.143991 50.154445 50.478049 50.807818 50.478049 0 0 0 60.330408 61.524836 62.154445 62.807818 62.807818 62.807818 62.807818 62.807818 63.486821 63.486821 63.486821 63.486821 62.807818 62.807818 61.524836 59.213095 58.163541 58.680365 59.213095 59.762739 59.762739 59.762739 59.762739 59.762739 59.762739];
pv(pv==0)=[]; % Delete rests (刪除休止符)
origPv=pv;
pvLen=length(origPv);
% Note representation, where the time unit of note duration is 1/64 seconds
note=[60 29 60 10 62 38 60 38 65 38 64 77 60 29 60 10 62 38 60 38 67 38 65 77 60 29 60 10 72 38 69 38 65 38 64 38 62 77 0 77 70 29 70 10 69 38 65 38 67 38 65 38];
frameRate=8000/256;
pv2=note2pv(note, frameRate);
noteMean=mean(pv2(1:length(pv)));
shiftedPv=pv-mean(pv)+noteMean; % Key transposition
notePitch=note(1:2:end); % Use pitch only (只取音高)
notePitch(notePitch==0)=[]; % Delete rests (刪除休止符)
% Linear search of 81 times within [-2 2] (上下平移 81 次，得到最短距離)
clear minDist dtwPath
shift=linspace(-2, 2, 81);
for i=1:length(shift)
newPv=shiftedPv+shift(i);
[minDist(i), dtwPath{i}] = dtw3(newPv, notePitch, 1, 0);
end
[minValue, minIndex]=min(minDist);
bestShift=shift(minIndex);
bestShiftedPv=shiftedPv+bestShift;
inducedPv=notePitch(dtwPath{minIndex}(2,:));
plot(1:pvLen, origPv, '.-', 1:pvLen, bestShiftedPv, '.-', 1:pvLen, inducedPv, '.-');
legend('Original PV', 'Best shifted PV', 'Induced PV', 4);
fprintf('Best shift = %f\n', bestShift);
fprintf('Min. distance = %f\n', minValue);
%fprintf('Hit return to hear the original pitch vector...\n'); pause; pvPlay(origPv, frameRate);
%fprintf('Hit return to hear the shifted pitch vector...\n'); pause; pvPlay(bestShiftedPv, frameRate);
inducedNote=pv2noteStrict(inducedPv, frameRate);
%fprintf('Hit return to hear the induced pitch vector...\n'); pause; notePlay(inducedNote);
fs=16000;
wavwrite(note2wave(inducedNote, 1, fs), fs, 8, 'inducedNote2.wav');]]> <![CDATA[Best shift = 1.300000
Min. distance = 103.332368
[Warning: WAVWRITE will be removed in a future release. Use AUDIOWRITE
instead.]
[> In <a href="matlab:matlab.internal.language.introspective.errorDocCallback('wavwrite', 'E:\MATLAB\R2015a\toolbox\matlab\audiovideo\wavwrite.m', 48)" style="font-weight:bold">wavwrite</a> (<a href="matlab: opentoline('E:\MATLAB\R2015a\toolbox\matlab\audiovideo\wavwrite.m',48,0)">line 48</a>)
In <a href="matlab:matlab.internal.language.introspective.errorDocCallback('dtw3inducedPitch02', 'D:\users\jang\books\audioSignalProcessing\example\dtw3inducedPitch02.m', 34)" style="font-weight:bold">dtw3inducedPitch02</a> (<a href="matlab: opentoline('D:\users\jang\books\audioSignalProcessing\example\dtw3inducedPitch02.m',34,0)">line 34</a>)
In <a href="matlab:matlab.internal.language.introspective.errorDocCallback('goWriteOutputFile>dummyFunction', 'D:\users\jang\books\goWriteOutputFile.m', 85)" style="font-weight:bold">goWriteOutputFile>dummyFunction</a> (<a href="matlab: opentoline('D:\users\jang\books\goWriteOutputFile.m',85,0)">line 85</a>)
In <a href="matlab:matlab.internal.language.introspective.errorDocCallback('goWriteOutputFile', 'D:\users\jang\books\goWriteOutputFile.m', 55)" style="font-weight:bold">goWriteOutputFile</a> (<a href="matlab: opentoline('D:\users\jang\books\goWriteOutputFile.m',55,0)">line 55</a>)]
]]>
Due to a better key transposition, the alignment of type-3 DTW is improved significantly with a much less DTW distance. The related files are shown next:
由上述範例可以看出，type-3 DTW 對位的效果已經大幅改善，最短距離也大幅降低。相關檔案如下：
Hint In general, if we want to perform melody recognition, the exhaustive search for key transposition is impractical due to its excessive computational load. Some heuristic search, such as the binary-like search mentioned in section 2 of this chapter, should be employed instead for such purpose.
Hint 一般而言，若要進行旋律辨識，是無法進行上述線性搜尋法的音調移位，只能採取計算量較小的計算方法，例如第二節所提到的二元搜尋法。
In the above example, we can still find some obvious mistake for the alignment. For instance, the fifth induced is too short since it only covers 3 frames. To solve this problem and to improve type-3 DTW in general, we have the following strategies:
Set the range of frame numbers being mapped to each note: For instance, the duration of the frames being mapped to a note should between the range [0.5, 2] of the duration of the note. This can enhance the performance since the duration of each note is used.
Use rests: Except for the leading and trailing rests, any rest in the query input indicates the end of the previous note and the beginning of the next note. We can use this cue for better alignment and query by singing/humming.
但是在上述範例中，我們還是可以發現對位的錯誤，例如在第一句「祝你生日快樂」的「樂」這個音符，只有被分配到三個音框，很明顯的過少。若要解決這個問題，有幾個可能的方向：
限制每一個音符所能分配的音框個數：例如每個音符所對應的音框總長度，不得小於音符長度的一半，也不得大於音符長度的兩倍。此規則的加入，使我們可以同時用到音符的音高及音長資訊。
使用休止符：在使用者哼唱的音高向量中，除了頭尾的休止符不算外，只要遇到一個休止區間，就代表一個舊音符的結束及新音符的開始，此規則可以適用到一般的哼唱選歌輸入。
We can simply modify our type-3 DTW to meet the above two requirement in order to increase the precision of alignment and the recognition rates of query by singing/humming.
我們可以修改 DTW 以符合上述規範，以便提高對位的準確度及旋律辨識的辨識率。
We can employ a modifed version of type-3 DTW which take rests into consideration, as follows:
Example 4: dtw3inducedPitch03.m <![CDATA[% ====== Read db
songDb=songDbRead('childSong');
for i=1:length(songDb)
terms=split(songDb(i).songName, '_');
songDb(i).songName=terms{1};
end
% ====== Find the right track
index=find(strcmp('生日快樂', {songDb.songName}));
note=double(songDb(index).track)';
% ====== Pitch tracking
waveFile='happyBirthday.wav';
%waveFile='twinkle_twinkle_little_star.wav';
au=myAudioRead(waveFile);
pfType=1; % 0 for AMDF, 1 for ACF
ptOpt=ptOptSet(au.fs, au.nbits, pfType);
ptOpt.mainFun='maxPickingOverPf';
showPlot=0;
[pv, clarity]=pitchTrack(au, ptOpt, showPlot);
% ====== Compute pv from the given note sequence
index=find(pv~=0); pv=pv(index(1):end); leadingZeroNum=index(1)-1; % Cut off leading zeros
pvNoRest=pv; pvNoRest(pvNoRest==0)=[];
pvLen=length(pv);
pvMean=mean(pvNoRest);
zeroIndex=find(pv==0);
pv(zeroIndex)=nan;
frameRate=au.fs/(ptOpt.frameSize-ptOpt.overlap);
pv2=note2pv(note, frameRate);
noteMean=mean(pv2(1:length(pv)));
shiftedPv=pv-pvMean+noteMean; % Key transposition
notePitch=note(1:2:end); % Use pitch only (只取音高)
notePitch(notePitch==0)=[]; % Delete rests (刪除休止符)
% ====== Linear search of 101 times within [-2 2] (上下平移 101 次，得到最短距離)
clear minDist dtwPath
dtwOpt=dtw3withRestM('defaultOpt');
dtwOpt.endCorner=0;
shift=linspace(-2, 2, 101);
for i=1:length(shift)
newPv=shiftedPv+shift(i);
[minDist(i), dtwPath{i}] = dtw3withRestM(newPv, notePitch, dtwOpt);
end
[minValue, minIndex]=min(minDist);
bestShift=shift(minIndex);
bestShiftedPv=shiftedPv+bestShift;
inducedPv=notePitch(dtwPath{minIndex}(2,:));
inducedPv(zeroIndex)=nan;
% ====== Add back the leading zeros
pv=[nan*ones(1,leadingZeroNum), pv];
bestShiftedPv=[nan*ones(1,leadingZeroNum), bestShiftedPv];
inducedPv=[nan*ones(1,leadingZeroNum), inducedPv];
pvLen=length(pv);
% ====== Plotting and playback
% === Plot the pitch without rest
plot(1:pvLen, pv, '.-', 1:pvLen, bestShiftedPv, '.-', 1:pvLen, inducedPv, '.-');
legend('Original PV', 'Best shifted PV', 'Induced PV', 'location', 'NorthEast');
fprintf('Best shift = %f\n', bestShift);
fprintf('Min. distance = %f\n', minValue);
fprintf('Hit return to hear the original pitch vector...\n'); pause; pvPlay(pv, frameRate);
fprintf('Hit return to hear the shifted pitch vector...\n'); pause; pvPlay(bestShiftedPv, frameRate);
inducedNote=pv2noteStrict(inducedPv, frameRate);
fprintf('Hit return to hear the induced pitch vector...\n'); pause; notePlay(inducedNote, 1);
fs=16000;
%wavwrite(note2wave(inducedNote, 1, fs), fs, 8, 'inducedNote2.wav');]]> <![CDATA[Best shift = 0.880000
Min. distance = 87.066652
Hit return to hear the original pitch vector...
Hit return to hear the shifted pitch vector...
Hit return to hear the induced pitch vector...
]]> Audio Signal Processing and Recognition (音訊處理與辨識)
