Description
In this lab, you will work on Matlab-based exercises designed to familiarize
you with the task of synthesizing musical notes using digital signal processing
and combining the notes to synthesize simple tunes.
You will learn to generate
an impulse train with the right pitch period which will then be applied to FIR
and IIR linear shift-invariant systems to generate the sounds for a specified
musical note. Several musical notes will be suitably combined to create simple
tunes.
You will learn to determine the pitch period for a given note frequency
and create a train of unit impulses for a desired note duration. The impulse
train is applied as excitation to a system with Impulse response h[n] and
a transfer function H(z).
The output amplitude will be shaped to produce
pleasant sounding note. Several notes so created with desired duration will
be concatenated to produce a simple tune.
We will assume that the sampling rate fs of the signal is 44100 Hz. We
will use the pitch frequencies given in the table below:
Table 1: Notes and picth frequencies
Note Pitch frequency
C4 261.61
C
#
4
/Db
4 277.18
D4 293.66
D
#
4
/Eb
4 311.13
E4 329.63
F4 349.23
F
#
4
/Gb
4 369.99
G4 392.00
G
#
4
/Ab
4 415.30
A4 440.00
A
#
4
/Bb
4 466.16
B4 493.88
C5 523.25
Values extracted from longer table at:
https://pages.mtu.edu/ suits/notefreqs.html
1 Violin sound synthesis applying impulse train excitation to a
finite-duration impulse response (FIR) filter
1.1 Creating a single note
We will use a pitch frequency fpitch = 1/Tpitch where Tpitch is the pitch period.
With fs = 44100 samples/sec, the pitch period will have Np = fsTpitch =
fs/fpitch samples with the first sample equal to 1 and the remaining Np − 1
samples zero.
Create an impulse train xA3 with impulses Np samples apart
corresponding to a pitch frequency fpitch = fA3 = 220 Hz. Use rounding to get
an integer value Np. The impulse train signal duration should be 1 second.
Apply the impulse train to an FIR filter with impulse response h[n] given
by the vector ‘impresp violin’ stored in the file irviolin.mat, which can be
accessed with the command
load(’irviolin.mat’);
Matlab command “filter” is convenient to implement the FIR filter.
The waveform envelope of the output signal yA3
should be roughly constant.
The envelope can be shaped to have a more gradual rise and fall. Shape (or
modulate) the amplitude by multiplying the signal with a suitable scaling
function. One option to do this is scale the signal with the square of half the
period of a sine wave of appropriate duration. Call the shaped signal vA3
.
Some sample code:
load(’irviolin.mat’); % loads the vector impresp_violin
a = 1; % denominator for FIR filter
b = impresp_violin;
Fs = 44100; % Sampling frequency, # of samples in 1 sec, integer
Tdur = 2; % The note should be played for 2 seconds
Ndur = round(Tdur*Fs); % # of samples in Tdur seconds
n=[0:Ndur-1]; % index set [0 1 2 3 … Ndur-1]
scalefn = sin(pi*n/(Ndur));
scalefn = scalefn.*scalefn; % modulating function for the note
Fpd = 220; % pitch frequency desired
Np = round(Fs/Fpd); % # samples in pitch period, rounded.
% Np is used in pulse train generation
tem = n/Np – round(n/Np);
% entry in tem is zero when corresponding entry in n is a multiple of Np
pt = (tem == 0); % creates pulse train
x = filter(b,a,pt);% generates signal y_{A_3} for note A3 of duration Ndur sx = x.*scalefn; % generates shaped signal v_{A_3}
note = x;
soundsc(note,Fs);
audiowrite(’note.wav’,note,Fs)
Q1: Play the sound of the output signal yA3
and the shaped signal vA3
.
Comment on the difference in the of the sound of the note produced.
1.2 Creating a tune
Now create a sequence of notes with appropriate duration and concatenate
the notes to create the following tune (from the song “Doe a deer …”)
C4 D4 E4 C4 E4 − C4 E4
Doe, a deer a female deer…
(See https://noobnotes.net/do-re-mi-sound-of-music/.
Also see http://www.choose-piano-lessons.com/piano-notes.html for other simple tunes of nursery rhymes)
You may use a different tune containing at least 6 notes including notes
with at least 3 different pitch frequencies.
Q2. Explain the details of your procedure. Load your audio file to Blackboard with your report.
2 Violin sound synthesis applying impulse train excitation to an
infinite-duration impulse response (IIR) filter
2.1 Creating a single note
Repeat the procedure as in section 1 to create an impulse train xA3 with
impulses Np samples apart corresponding to a pitch frequency fpitch = fA3 =
220 Hz.
Apply the impulse train to an IIR filter with transfer function H(z) specified by the numerator coefficient 0.1 and denominator polynomial with coefficients:
A = [1.0000 −2.4584 1.8539 −0.2387 −0.0466 −0.1614 −0.1004 0.1980 −0.0420];
3
Matlab command “filter” is convenient to implement the IIR filter.
The waveform envelope of the output signal yA3
should be roughly constant.
As before, use amplitude modulation appropriate for a pleasant sound. Again
call the shaped signal vA3
.
Q3: Plot and compare the waveform for 3 pitch periods of the output
signal yA3
in the cases of synthesis by FIR and IIR filters. Comment on the
difference in the sound of the note produced by the two methods.
2.2 Creating a tune
As before create a sequence of notes with appropriate duration and concatenate the notes to create the same tune you created in the case of FIR filter
music synthesis.
Q4. Explain the details of your procedure. Load your audio file to Blackboard with your report.
Q5: Comment on the difference in the of the sound of the tunes produced
by synthesis using FIR and IIR filters.
