Group
Project Overview
High-Level Description
We designed our own MATLAB program to extract notes from piano music, and then synthesize those notes into music with different instrumental effects including
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8-bit
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Steel drum
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Organ
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Oboe
DSP-Course Tools
DSP Non-Course Tools
Discrete Fourier transform (DFT) - This transform allowed us to convert our audio sample from a discrete function of time into a discrete function of frequency.
Bandpass filter - We used MATLAB’s Filter Designer tool to design an FIR, Equiripple bandpass filter. This filter allowed us to isolate a certain selection of the frequency components of an audio sample. This was important to remove overtones from our audio samples, which could confuse our algorithm. An example of a bandpass filter can be seen in the image on the below.
Spectrogram analysis - Spectrograms provide us a visual representation of the spectrum of frequencies of a signal as it varies with time. This allowed us to break up our audio signal into discrete pieces, and look for the frequency with the highest power that should be included into our new, synthesized version of the sound.
Additive synthesis - Additive synthesis is a sound synthesis technique that involves summing cosines at various frequencies. This is intended to replicate the timbre of an instrument as it would include multiple harmonic or inharmonic overtones. We used this technique to create our oboe effect by summing three different cosines at fo, 1.25*fo, and 1.5*fo respectively. Note that fo represents the fundamental frequency of a desired note.
Digital Attenuation - Attenuation is the reduction of the amplitude of a signal over time. For our purposes, digital attenuation refers to the intentional reduction of signal amplitude over time for a note played by our program. We achieved this by multiplying the signal for a note with a decaying exponential. By tuning the coefficient in the exponent, we were able to control how quickly the signal’s amplitude decayed. The quicker the decay of the signal, the shorter the note sounds when played. We applied this to each of our audio effects to create brief rests when the played note is switching to a different frequency. This improved the sound of our output as it created a fading effect that would be expected from real life instruments. Digital attenuation was specifically important for our steel drum effect, as we used a relatively large coefficient on the exponent to create very short notes. This is characteristic of a steel drum as it sounds when it is struck and the note fades quickly. The steel drum effect also differed from the other effects in that it had digital attenuation applied to every time interval rather than just when the fundamental frequency is changing, since a steel drum would not be capable of producing a continuous tone without being struck repeatedly.
Frequency modulation (FM) synthesis - Frequency modulation synthesis is a tool in which the instantaneous frequency of a signal is altered to create a new signal. This is achievable by mixing (multiplying) the original signal, in our case a cosine at the fundamental frequency, with cosines at frequencies rationally related to the fundamental frequency. This effectively shifts the signal in the frequency domain, as the discrete fourier transform (DFT) of a signal multiplied with a cosine is
This alters the sound that is heard when the note is played. We utilized this tool when synthesizing organ tones by mixing (multiplying) three different cosines at 0.75*fo, fo, and 1.25*fo respectively. Note that fo represents the fundamental frequency of a desired note.
