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...h values with a single excitation The linear model (1) requires multiple basis functions to represent tones with different pitch values. This limitation has been addressed, for example, by FitzGerald =-=[4]-=- and Virtanen [12, pp. 57-65], who translated basis functions on logarithmic frequency axis to produce different fundamental values. In this model, each gain gn,t in (1) is replaced by gain gn,t,τ , w...

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...lapping NMF [8] which incorporates with the shiftinvariant representation, in order to restore music sources. The method is related to our earlier work [9] and the generalized prior subspace analysis =-=[10]-=-. However, the key distinction lies in a way of selecting shift-invariant basis vectors. Promising results with monaural instantaneous mixture of voice/cello and convolutive mixture of saxophone/viola...

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...for the related task of transcribing audio excerpts into musical notation [1, 3, 4, 19]. Sparsity, temporal and spectral priors have proven useful to enhance the accuracy of multiple pitch estimation =-=[3, 7, 20]-=-. Since NMF is an unsupervised technique, it can be applied in principle to an unlimited number of musical recordings without the need for ground-truth pitch labels. However, such information is often...

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...re, in this context β−1v could be a typical frequency spectrum of an unpitched instrument such as a snare drum. For example, the priors used for drum transcription using Prior Subspace Analysis (PSA) =-=[14]-=- can be used as β−1v . However, unlike PSA, the frequency basis functions are still free to adapt during analysis. 2.2. Update Equations Incorporating the above gamma priors into a cost function with ...

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...nen in [1] and by Smaragdis in [2]. If each frequency line is considered as an observation instead of each frame, the same model allows time-varying fundamental frequencies, as proposed by FitzGerald =-=[3]-=-. The model has also been used to model time-varying images [4], [5], [6]. 3. ESTIMATION CRITERIA AND ALGORITHMS Magnitude and power spectra are non-negative by their definition. Therefore, it is natu...

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...verall spectrogram with the pseudo-inverse of the frequency basis functions, to get an initial estimate for s. ICA is used to improve these estimates. In Generalized Prior Subspace Analysis, given in =-=[9]-=-, Equation 11 is essentially reinterpreted in such a way that the prior subspaces are viewed as an undercomplete signal dictionary and that the data is sparse in nature, which results in a new version...

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... Key signature estimation is based on an improved version of the algorithm presented in [5]. Polyphonic transcription of the audio is performed using an improved version of the algorithm described in =-=[6]-=-, which is based on non-negative matrix factorisation techniques. This transcription is displayed in a piano-roll format. This can be seen in Figure 2. Once transcription has been performed the system...

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... simplified version of the algorithm, where the instrument basis functions are fixed pre-learned harmonic spectra is capable of giving a reliable transcription of all notes played in a piece of music =-=[7]-=-. This simplified algorithm can be implemented on a frame-by-frame basis and is sufficiently fast to run in real time, thereby allowing real time transcription of audio signals, although at the cost o...