Steven T. Wright and Justin C. Zito
EEL 6586 – Dr. John G. Harris
April 25, 2008
The goal for our project is to separate a single channel recording of two musical instruments into two individual tracks, each containing a single instrument. We created a recording of a trombone playing along with a drummer. The instruments chosen for this experiment were inspired by our individual passion for the trombone and drums, respectively. Our recording is a fifteen second long rendition of the tune “We Got the Funk,” originally performed by Positive Force in 1979. Essentially we are converting an ensemble track into two solo tracks.
Figure 1: Neal Smith of Alice Cooper ; click
on the image to hear our original recording
Motivation for our design comes from several areas. It can be used educationally, for example, in the case where a student would like to learn to play a song. The student could extract the track for the instrument of choice, allowing them to focus on learning the part of interest. It is difficult to listen to music and hear only one instrument, and even more difficult to learn from a noisy recording vs. a clean track of the instrument of interest.
It can also be useful for a musician to listen to a recording of their performance for self improvement. Tempo, tone, and dynamics may vary in playing alone vs. playing along with other musicians. A way to separate the tracks for individual playback would allow the musician to better analyze their own part for adjustments.
Recording individual tracks for each instrument or voice in a music piece is critical in the production of commercial audio. The tracks can be tweaked individually, allowing volume control, reverberation, warping and many other audio effects for each channel. Equipment such as a four-channel mixer is necessary for multi-channel input recording. This equipment, however, is not cheap. Our method eliminates the need for such equipment while still generating two instrumental tracks for individual manipulation.
The microphone used in recording is a standard desktop computer microphone. These are unidirectional and help to reduce background noise. The music is not played directly into the mic, though it is appropriately loud enough such that the mic records a rather clean audible signal. Ideally, one would use a condenser microphone in a noise free recording studio for optimal SNR. This requires access to rather expensive equipment, and is impractical for most. We use the desktop microphone in conjunction with Window’s sound recording program to save our file for processing with MATLAB software. The recordings are saved as 16 bit, PCM wav files so that they are compatible with MATLAB version 7.0.
The following method is developed in .
1. Pre-processing – extract a monaural signal with enhanced rhythmic content from a stereo signal
2. Filter bank – decompose signal into eight non-overlapping sub-bands
3. Noise subspace projection – extract the stochastic portion of each sub-band signal
4. Drum event detection – create extraction masks for bass drums, snare and cymbals
5. Drum resynthesis – create weights from the masks and weight the stochastic signals in each sub-band
Noise subspace projection: based on the Exponentially Damped Sinusoidal model. The signal can be decomposed into a harmonic component, modeled as a sum of sinusoids with an exponential decay, and a noise component defined as the difference between the original signal and the harmonic component.
We followed a method proposed by Jang and Lee  that applies to single channel observations. In this case, blind signal separation is performed upon a single-channel recording. It begins by assuming the observed signal is the summation of 2 independent source signals.
A fixed-length segment drawn from a time-varying signal is expressed as a linear superposition of basis functions. The algorithm is trained with a priori sets of time-domain basis functions that encode the sources in a statistically efficient manner. These basis functions are essentially training sets created from clean recordings of the instruments or voices. They are used in place of the second channel in our underdetermined system. Some examples of basis filters include discrete cosine transforms (DCT), Gabor wavelets, ICA and PCA.
The ICA learning algorithm searches for a linear transformation Wi that makes the components as statistically independent as possible.
The learning algorithm uses a maximum likelihood approach, given the observed channel and the basis functions. The learned basis filters maximize the likelihood of the given data.
algorithm makes use of the
The major advantage over the other time domain filtering techniques is that ICA filters utilize higher order statistics, such that there is no longer an orthogonality constraint on the subspaces . Thus, the basis functions obtained by the ICA algorithm are not required to be independently orthogonal. This algorithm is most successful at separating voice from jazz music. Jazz music typically includes bass, drums and some brass instruments.
We decided on an approach that targets the sustained tones of the trombone. Early attempts with bandpass filters had problems with windowing leakages. We realized that the trombone frequencies are set for each octave. Knowing this we decided to target these specific notes with conventional filtering methods. The technique that proved most successful was using combined IIR comb filters to remove the trombone. The comb filters remove all harmonics of the trombone while leaving the wideband transient drum beats and cymbals uncorrupted. The combination of comb filtering with emphasis on high frequency content led to our final drum track.
The drum set posed some challenges in source separation, due to the many different sounds that can be produced by the drummer. All of the drum components can be represented as transients in the time domain. The bass or kick drum has the lowest frequency, then the snare drum, and the hi-hat and crash cymbals reach the highest frequencies. We needed to develop a technique that would suppress the trombone but would not interfere with the snare and bass drum. The following section presents our results as we progressed through the stages of our single instrument extraction.
The original recording passes through a myriad of filtering techniques before generating the final track. The sound wave for the fifteen second recording is shown for each step through our progression. Our results show that we were successful only at separating the drum track from dual-instrument recording. Extracting the trombone proved to be more challenging than the drums. We then focused on extracting the drums and filtering the trombone. Since every tonal instrument plays the same frequency for a particular note, we can target and remove these specific frequencies and their harmonics, making it much easier to extract the transient drum signals. The sound files can be heard by clicking on the corresponding image. The original recording is shown below.
Figure 2: Original recording
The challenges in drum extraction, according to open literature, often point to the cymbals. The cymbals have a very sharp impulse followed by a short transient ringing, and encompass a bandwidth from 300 – 16000 Hz . To extract the trombone signal, our first step was to filter out the high frequency components of the cymbals and hi-hat. Running our signal through several bandpass filters produced the following track. The hi-hat component, which is the constant cymbal tapping throughout the drumming, is well attenuated. However, the crashing or ringing of the cymbal is not attenuated and can be heard in both places that it occurs. This early stage in our progress was demonstrated in our April 14th presentation.
Figure 3: Filtered hi-hat
The next breakthrough in our progress occurred when we changed our focus from the extraction of the trombone to that of the drums. We realized that it is much more effective to target the musical frequencies of a range of popular notes played in music. The trombone is completely eliminated with more filtering targeting lower frequencies. This allows the extraction of the snare drum and all cymbals. The drawback here is a large corresponding attenuation of the bass drum. The snare loses its low end and sounds very distorted and unnatural. The signal as a whole looses intensity as well. This file was also shown in our class presentation.
Figure 4: Cymbals and snare only
The trombone was filtered most successfully using a bank of comb filters. Using comb filters, we can target the specific frequencies for the notes of the trombone and filter them and their harmonics. We decided to use one full octave of notes in our filter bank, ranging from 110 to 220 Hz, corresponding with the 2nd octave range . Filtering over a full octave accounts for all possible trombone notes played within that range of frequencies. The drawback is obvious; if the notes are from another octave then they will not be affected at all. If the notes played are within this filtered range of frequencies, we will generate a single recording of the drum track. After comb filtering out this range of frequencies, including their harmonic parts, we recovered a somewhat robotic sounding drum track. The first five seconds, where the trombone plays alone, are almost completely attenuated. You can definitely hear the effect of filtering the complete second octave of notes in the music scale. The main benefit in this track is that the bass drum has been partially recovered from attenuation and distortion.
Figure 5: Signal after several comb filters applied to trombone
After several attempts we finally created a track consisting of the drums only. We filtered specific instruments and summed several partial signals together. For example, the high frequency components of the cymbals and snare drum were filtered in one signal and combined with another signal that was filtered several times for trombone extraction. The bass drum is more audible if you have a subwoofer.
Figure 6: Final drum track
Compared to the signal in Figure 4, when you could barely, if at all, hear the bass drum, this is a great improvement. All of the components of the drums are clearly audible. The quality of the snare drum and cymbals is much, much improved from earlier attempts. The combined tracks introduce much less attenuation to the low frequency components of the drums. The kick drum sounds appropriately ‘deep,’ and well distinguishable from the snare drum in quality.
In the end we are happy with our drum track, considering we were merely neophytes in source separation techniques four weeks ago. There are a few moments where the trombone can be heard if listening carefully. However, the drums dominate the sound we hear and have much greater intensity over the trombone. It would be easier to play along with the final drum track than the original recording for learning purposes. We did not, as we originally desired, create an individual track for the trombone as well. More work is needed in creating the individual track for the trombone (or any tonal instrument), due to the complexity of filtering the drum components. Our recording consists only of the two instruments indicated. Ultimately, the ideal goal is the separation of N instruments into N individual tracks from a single channel recording. Future developments in our algorithm are required to separate any two instruments into individual tracks. The algorithm proposed here is a small yet promising step toward SIMO instrumental source separation with an unlimited number of sources.
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 O. Gillet and G. Richard, “Extraction and Remixing of Drum Tracks from Polyphonic Music Signals,” IEEE Workshop on Applications of Signal Processing to Audio and Acoustics, New Paltz, New York, 2005, pp. 315-318.
 G. Jang and T. Lee, “A Maximum Likelihood Approach to Single-channel Source Separation,” Journal of Machine Learning Research, vol. 4, pp. 1365-1392, Dec. 2003.
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