bevans@ece.utexas.edu
In this problem, you'll estimate the pitch period of the recorded voice. The pitch period is the fundamental period T0. We can invert the pitch period to obtain the pitch frequency which is also the D 2 fundamental frequency f0. You'll be able to validate the estimate for by using the frequency-domain analysis in section 2.4. E 2 I 2 fundamental frequency f0 = 1 / T0. You'll be able to validate the estimate of the pitch frequency from section 2.3 with the frequency-domain analysis in section 2.4. E 2 Typically, the first peak in the plot of the magnitude of the Fourier series coefficients for positive frequencies is f0.
The spectrogram is showing the values in a matrix that has time along the horizontal dimension and frequency along the vertical dimension. So, you could automate finding the maximum value in the spectrogram after executing UTAudioFreqDomainAnalysis.m:
spectValues = spectrogram(myRecording, blockSize, overlap, blockSize, fs, 'yaxis'); [maxValue, maxIndex] = max(abs(spectValues), [], 'all', 'linear'); [row,col] = ind2sub(size(spectValues), maxIndex);The maximum value (maxValue) occurs at (row, col) in matrix abs(spectValues).
E 3 When computing the Fourier series coefficients for a continuous-time signal, we assume that the observed signal is the fundamental period of a periodic signal, whether it really is or not. This is also the case when working with a discrete-time signal, as we're doing with the recorded audio signal.
To compute the exponential Fourier series coefficients for our discrete-time signal, we'll use the Fast Fourier Transform (FFT). The FFT takes the vector of N samples for the recorded signal, and returns the N exponential Fourier series coefficients. In the discrete-time case, we have a finite number of Fourier series coefficients unlike the continuous-time Fourier series which has infinite terms.
D 2 Here's the use of the fft function in MATLAB in line 11 of UTAudioFreqDomainAnalysis.m E 2 I 2 Here's the use of the fft function in MATLAB in line 11 of UTAudioFreqDomainAnalysis.m: E 2
fourierSeriesCoeffs = fft(myRecording);The first half of the
fourierSeriesCoeffs vector contains the Fourier series coefficients for non-negative frequencies, and the second half of the vector contains the Fourier series coefficients for negative frequencies.
Here are the first three elements of the fourierSeriesCoeffs vector. Recall that MATLAB starts indexing its vectors at index 1 instead of index 0:
When plotting the Fourier series coefficients computed by the FFT, we use the
FFT shift command fftshift to swap the halves of the fourierSeriesCoeffs vector.
fourierSeriesCoeffs.
D 2 When using the FFT, the gains for Ak will need to be multiplied by 1/T0 where T0 is the fundamental period (a.k.a. pitch period).
E 2
A common approach to parts (a) and (b) is to identify frequencies of the 10 peaks
in the plot of the magnitude of the Fourier series coefficients where the frequencies are
close to being harmonically related.
For each frequency, one can look up the Fourier series coefficient in the vector
fourierSeriesCoeffs and here's how.
First, we've recorded 1s of speech at a sampling rate of 8000 samples/s, which gives
a total of 8000 samples.
Because of this, the element at index n+1 in fourierSeriesCoeffs corresponds to a
frequency of n Hz for n in [0, 3999].
Once we have the Fourier coefficient, we can compute its magnitude Ak using the abs
command and its phase Phik using the angle command.
For part (b), after computing the magnitude and phase of the Fourier series coefficient,
each frequency would be changed to be a harmonic of an estimated value of the
fundamental frequency f0.
I 2
During playback of the synthesized signal, please use the soundsc command
instead of the sound command.
E 2
bevans@ece.utexas.edu
E 1