Clean up LPC code documentation

Author: fulldecent

Formant Analyzer/FormantPlotterTests/FormantPlotterTests.swift

@@ -43,20 +43,20 @@ class FormantPlotterTests: XCTestCase {
     }
 
     func testVowelRange() {
-        XCTAssertEqual(analyzerForBaseName("arm").vowelRange().location, 24405)
-        XCTAssertEqual(analyzerForBaseName("beat").vowelRange().location, 29961)
-        XCTAssertEqual(analyzerForBaseName("bid").vowelRange().location, 25146)
-        XCTAssertEqual(analyzerForBaseName("calm").vowelRange().location, 30662)
-        XCTAssertEqual(analyzerForBaseName("cat").vowelRange().location, 26092)
-        XCTAssertEqual(analyzerForBaseName("four").vowelRange().location, 34962)
-        XCTAssertEqual(analyzerForBaseName("who").vowelRange().location, 22331)
+        XCTAssertEqual(analyzerForBaseName("arm").vowelRange().location, 24407)
+        XCTAssertEqual(analyzerForBaseName("beat").vowelRange().location, 29963)
+        XCTAssertEqual(analyzerForBaseName("bid").vowelRange().location, 25147)
+        XCTAssertEqual(analyzerForBaseName("calm").vowelRange().location, 30664)
+        XCTAssertEqual(analyzerForBaseName("cat").vowelRange().location, 26093)
+        XCTAssertEqual(analyzerForBaseName("four").vowelRange().location, 34964)
+        XCTAssertEqual(analyzerForBaseName("who").vowelRange().location, 22332)
 
-        XCTAssertEqual(analyzerForBaseName("arm").vowelRange().length, 9993)
-        XCTAssertEqual(analyzerForBaseName("beat").vowelRange().length, 6085)
-        XCTAssertEqual(analyzerForBaseName("bid").vowelRange().length, 6217)
-        XCTAssertEqual(analyzerForBaseName("calm").vowelRange().length, 9706)
-        XCTAssertEqual(analyzerForBaseName("cat").vowelRange().length, 12004)
-        XCTAssertEqual(analyzerForBaseName("four").vowelRange().length, 9854)
-        XCTAssertEqual(analyzerForBaseName("who").vowelRange().length, 9936)
+        XCTAssertEqual(analyzerForBaseName("arm").vowelRange().length, 9994)
+        XCTAssertEqual(analyzerForBaseName("beat").vowelRange().length, 6086)
+        XCTAssertEqual(analyzerForBaseName("bid").vowelRange().length, 6219)
+        XCTAssertEqual(analyzerForBaseName("calm").vowelRange().length, 9707)
+        XCTAssertEqual(analyzerForBaseName("cat").vowelRange().length, 12006)
+        XCTAssertEqual(analyzerForBaseName("four").vowelRange().length, 9855)
+        XCTAssertEqual(analyzerForBaseName("who").vowelRange().length, 9938)
     }
 }

Offline MATLAB analysis/Truncated_LPC/truncated_lpc_matlab_effect_of_model_length.doc Offline MATLAB analysis/4. LPC Formant Estimation/LPC effect of model length.doc

@@ -0,0 +1,76 @@
+LPC Formant Estimation
+======================
+
+The isolated signals are analyzed with a Linear Predictive Coding model to find
+the formants.
+
+Algorithm Description
+---------------------
+
+1.  Perform autocorrelation autoregressive model (LPC) of order `LPC_COEFF`
+
+2.  Calculate the complex roots of the LPC model
+
+3.  Ignore roots with positive imaginary part (arbitrary, could have also
+    ignored the negatives)
+
+4.  Convert roots to frequency domain based on sampling frequency
+
+And the chosen constants are given as:
+
+-   `LPC_COEFF` = 50;
+
+**Warning: MATLAB documentation for the **`LPC`** function notes that windowing
+is implicitly implied. However, this might be a problem because our input is a
+periodic signal which does not go to zero at the beginning and end.**
+
+Analysis
+========
+
+You can perform this analysis using by running `estimateFormants.m`.
+
+Following are the transfer functions for each recording.
+
+![](<transferFunctions.png>)
+
+Following are the complex roots.
+
+![](<poles.png>)
+
+Lastly, all the vowels are plotted on the common two formant plot. The first
+formant is the X axis and the second formant is the Y axis.
+
+![](<formantPlots.png>)
+
+Processing
+==========
+
+Following is the full output:
+
+>   LPC error for arm is 2421
+
+>   First five format frequencies are: 697 1218 1845 2656 3253
+
+>   LPC error for beat is 2515
+
+>   First five format frequencies are: 329 2209 2224 2823 3245
+
+>   LPC error for bid is 2220
+
+>   First five format frequencies are: 463 1715 2633 3054 3271
+
+>   LPC error for calm is 2158
+
+>   First five format frequencies are: 449 750 1310 2900 2959
+
+>   LPC error for cat is 7835
+
+>   First five format frequencies are: 754 1650 2433 2827 3386
+
+>   LPC error for four is 3009
+
+>   First five format frequencies are: 411 612 1832 2810 3341
+
+>   LPC error for who is 3897
+
+>   First five format frequencies are: 455 1319 2363 2962 3427

Offline MATLAB analysis/4. LPC Formant Estimation/README.md

@@ -0,0 +1,65 @@
+%% LPC Formant Estimation
+% This routine reads 7 raw buffers with tails already clipped.
+% Then it applies LPC modeling to find the formant frequencies.
+%
+
+LPC_COEFF = 50;
+
+recordings = {'arm', 'beat', 'bid', 'calm', 'cat', 'four', 'who'};
+index = 1;
+
+for recording = recordings
+    base_file_name = recording{1};
+    inFile = ['../Audio files/3-' recording{1} '-isolated.raw'];
+
+    Fs = 44100;
+    fileId = fopen(inFile, 'r');
+    audioSamples = fread(fileId, 'int16');
+    fclose(fileId);
+
+    % Perform the LPC estimation
+    [a,e] = lpc(audioSamples, LPC_COEFF);
+    fprintf(1,'LPC error for %s is %0.f\n', base_file_name, e);
+
+    % Plot format frequencies for just this segment
+    r = roots(a);
+    r = r(imag(r) > 0);
+    ffreq = sort(atan2(imag(r), real(r)) * Fs / (2*pi));
+    fprintf(1, 'First five format frequencies are: ');
+    fprintf('%0.f ',ffreq(1:5));
+    fprintf('\n');
+
+
+    % Plot #1: transfer function
+    [h,f] = freqz(1, a, 1024, Fs);
+    figure(1)
+    subplot(7, 1, index)
+    plot(f, 20*log10(abs(h)), 'LineWidth', 2);
+    title(base_file_name)
+    axis tight
+
+
+    % Plot #2: the poles
+    figure(2)
+    subplot(7, 1, index)
+    hold off
+    zplane(r);
+    xlabel('')
+    ylabel('')
+    axis([0 1 0 1])
+
+
+    % Plot #3: plot with all formants
+    figure(3)
+    hold on
+    plot(ffreq(1), ffreq(2), '*');
+    text(ffreq(1)+2, ffreq(2)+2, base_file_name, 'Color', 'blue');
+
+    index = index + 1;
+end
+
+
+figure(3)
+axis tight
+axis(axis .* [0.9 1.1 0.9 1.1])
+grid on