## 3 Proposed Method
### Feature Extraction Using Sinusoidal Transform Coding  
The sampling frequency of the corpus is 44.1 kHz. However, it was observed that the most of the songs in the corpus have insignificant amount of energy behind 16 kHz. Thus, the input audio data were initially filtered with a lowpass filter that had a cutoff frequency at 16 kHz. Figure 1: (a) Harmonic peaks selected by spectral envelope estimation vocoder (SEEVOC) peak-picking routine for a song in the database, (b) short-time Fourier transforms of a C major chord played by a piano with and without a tremolo effect, and (c) their corresponding autocorrelations, \(R_{FF}\). The lowpass-filtered signals were then split into multiple frequency sub-bands utilizing the Bark frequency scale. The Bark frequency scale is defined psychoacoustically and it forms 24 critical bands. Since a critical band does not always include a sufficient number of spectral peaks, for feature extraction, a group of four neighboring critical bands of the Bark scales are grouped together to form a sub-band. The six sub-bands have the frequency ranges: [0 400), [400 920), [920 1720), [1720 3150), [3150 6400), and [6400 15,500). The sinusoidal components, \(A_{k}\) and \(f_{k}\), were found by using the SEEVOC peak-picking routine in each sub-band. An example of peak-picking results using the SEEVOC is shown in Figure 1a. As mentioned in Section 1, each musical instrument has a unique timbre. Moreover, in contemporary music, applying sound effects, such as tremolo, distortion, flange, etc., is very common. Thus, when a musical instrument is passed through an effector, the timbre of the instrument changes, and the conveyed emotions also change. For example, a spectrum of a C major chord played by a piano and another spectrum of the same chord played by the same piano with a tremolo effect are shown in Figure 1b. As shown in the figure, the overall shapes of the spectral envelops are somewhat similar; however, the tremolo effect causes more spectral peaks and sidelobes. The similar phenomenon can be observed when the autocorrelation of the spectrum are taken as shown in Figure 1c. In previous work [7], it was shown that harmonic peaks represented in an autocorrelation domain of the short-time Fourier transform, \(R_{FF}(f_{lag})\), was less susceptible to white noise than the those represented in a general frequency domain. Meanwhile both the spectrum and \(R_{FF}(f_{lag})\) can uniquely characterize the harmonic components of the input signals. For this reason, the peak locations and magnitudes of \(R_{FF}(f_{lag})\) were also extracted for feature extraction. After obtaining the sinusoidal components, their derivatives, \(\Delta\)s, were also calculated (inter-peak amplitude differences \(A_{k+1}-A_{k}\) and inter-peak frequency differences \(f_{k+1}-f_{k}\)). The six vectors (\(A_{k}\), \(f_{k}\), \(\Delta A_{k}\), \(\Delta f_{k}\), and the peak locations and magnitudes of \(R_{FF}\)) in each sub-band were then represented by statistical and regression measures as LLDs. The statistical and regression measures applied to the six vectors are marked with * in Table 1.  
Similar to human language, an emotion or impression can be expressed in a musical phrase, where the musical phrase, in general, consists of four measures [16]. Thus, the songs in the database were segmented roughly by a phrase level. For segmentation, the tempo of each song in the database was calculated using a tempo analyzer [17], then average tempo of the songs was obtained. The obtained average tempo for the songs is 117.5 beats-per-minute. In contemporary music, the time signature of 4/4, where each measure consists of four beats, is commonly used; thus, the average duration of a measure in the dataset is approximately 2 s, and a musical phrase of the songs in the database is roughly 8 s long.