Revision as of 12:36, 6 November 2011

Homework 6, ECE438, Fall 2011, Yimin Xiao's solution

Questions 1

Design and perform a small experiment to investigate the following question:

"A man and a woman pronounce the same voiced phoneme. How are the formants of the phoneme pronounced by the man different from the formants of the phoneme pronounced by the woman?"

Describe your experiment and discuss your results.

Question 2

"That's one small step for a man, one giant leap for mankind", was the phrase Purdue alumnus Neil Armstrong planned to say as he stepped foot on the moon during the Apollo 11 mission. However, a careful listening of the recording indicates that the phrase he actually uttered is "That's one small step for man, one giant leap for mankind", skipping the "a" before "man" and thus creating a tautology.

First Approach: (Doesn't work out)

My first concern is the 'a' is missed due to down sampling. Then the following step was taken:

1. zeropad the signal
2. take FFT of the whole zeropadded signal
3. low pass filter the repeated part
4. IFFT back to get the upsampled signal.
   

frustratingly, the signal sounds exactly the same as the original signal.

Then I went back to examinate the original signal(ogg file), then I realize this is a 44100Hz sample file. Which must not be the original data, but had already been upsampled and processed. Since the original data is not accessible and the available data is already the result of the experiment I want to perform, I realized this is not a good approach.

Second approach:(My submission to this problem)

After abandon the first method, I replay the signal again and again, focusing on the two section between "for"s and "man".

For conveniece in notation, define

section 1 [for {a?} man]:as the section started at the instant of the first "for" is heard in this record, and end at the instant right before the word "man" is heard.

section 2 [for mankind]: as the section started at the instant of the second"for" is heard in this record, and end at the instant right before the word "mankind" is heard.

I found out that, the first section 1has a slightly higher pitch than section 2.

more precisely, both sections are constructed as two different pitches, from low to high, roughly like a major second scale.

Major second means the "for" sounds like a Do(measured with a tuner as a B note), then "man" sounds like a Re(measured as a C#).

Moreover, the section 2 sounds like two nice equal length notes, two quarter notes, perfect.

But the section 1 sounds like a 1/16 anticipation syncopation(the first note is 3/4 of a quarter note and second is 5/4 quarter note)

This observation strongly suggests that, the "a" was said, and well record. But due to the length of the "a" word, human ear cannot nicely perceive this syllable.

Play the full record again, and the first "For" sounds more like a "fur", but second "For" sounds normal.

But this is only a very subjective musical investigation, cannot support the fact that the "a" exist.

Then following steps were taken:

1. Import section 1 and section 2 in MATLAB.
2. Take DTFT of the two signals.
3. Calculate the average power of the signal with a window size of 10.
4. Plot the signals, DTFTs, Average power and compare the plots.

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