title: ÐÐ°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ°Ñ Ð¼Ð¾Ð´ÐµÐ»Ñ Ð·Ð²ÑÑÐ°Ð½Ð¸Ñ Ð¼ÑÐ·ÑÐºÐ°Ð»ÑÐ½ÑÑ Ð¸Ð½ÑÑÑÑÐ¼ÐµÐ½ÑÐ¾Ð²
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð±Ð°ÐºÐ°Ð»Ð°Ð²ÑÐ°
titleType: Subtitle
title: Mathematical model of the sound of musical instruments
Creators: name: ÐÐ¼Ð°ÑÐ¾Ð², ÐÐ¼Ð°Ð½ÑÑÑ
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2020
Subjects: Ð³Ð°ÑÐ¼Ð¾Ð½Ð¸ÑÐµÑÐºÐ¾Ðµ-Ð¿ÐµÑÐºÑÑÑÐ¸Ð¾Ð½Ð½Ð¾Ðµ ÑÐ°Ð·Ð´ÐµÐ»ÐµÐ½Ð¸Ðµ Ð·Ð²ÑÐºÐ¾Ð²Ð¾Ð³Ð¾ ÑÐ¸Ð³Ð½Ð°Ð»Ð°
Ð¾ÐºÐ¾Ð½Ð½Ð¾Ðµ Ð¿ÑÐµÐ¾Ð±ÑÐ°Ð·Ð¾Ð²Ð°Ð½Ð¸Ðµ Ð¤ÑÑÑÐµ
Ð¼ÐµÐ´Ð¸Ð°Ð½Ð½Ð°Ñ ÑÐ¸Ð»ÑÑÑÐ°ÑÐ¸Ñ
Ð²ÑÐ¿Ð¾Ð¼Ð¾Ð³Ð°ÑÐµÐ»ÑÐ½Ð°Ñ ÑÑÐ½ÐºÑÐ¸Ñ
Ð±Ð¸Ð½Ð°ÑÐ½Ð°Ñ Ð¼Ð°ÑÐºÐ°
"Ð¼ÑÐ³ÐºÐ°Ñ" Ð¼Ð°ÑÐºÐ°
librosa
bss_eval
f-Ð¼ÐµÑÐ°
harmonic-percussion sound separation
short-time Fourier transform
median filtration
auxiliary function
binary mask
"soft" mask
f-measure

description: Ð¢ÐµÐ¼Ð° Ð²ÑÐ¿ÑÑÐºÐ½Ð¾Ð¹ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð¾Ð¹ ÑÐ°Ð±Ð¾ÑÑ: Â«ÐÐ°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ°Ñ Ð¼Ð¾Ð´ÐµÐ»Ñ Ð·Ð²ÑÑÐ°Ð½Ð¸Ñ Ð¼ÑÐ·ÑÐºÐ°Ð»ÑÐ½ÑÑ Ð¸Ð½ÑÑÑÑÐ¼ÐµÐ½ÑÐ¾Ð²Â». Ð Ð²ÑÐ¿ÑÑÐºÐ½Ð¾Ð¹ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð¾Ð¹ ÑÐ°Ð±Ð¾ÑÐµ ÑÐ°ÑÑÐ¼Ð¾ÑÑÐµÐ½Ð° Ð·Ð°Ð´Ð°ÑÐ° ÑÐ°Ð·Ð´ÐµÐ»ÐµÐ½Ð¸Ñ Ð·Ð²ÑÐºÐ¾Ð²Ð¾Ð³Ð¾ ÑÐ¸Ð³Ð½Ð°Ð»Ð° Ð½Ð° Ð³Ð°ÑÐ¼Ð¾Ð½Ð¸ÑÐµÑÐºÑÑ Ð¸ Ð¿ÐµÑÐºÑÑÑÐ¸Ð¾Ð½Ð½ÑÑ ÑÐ¾ÑÑÐ°Ð²Ð»ÑÑÑÑÑ. ÐÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ñ ÑÐ°Ð·Ð»Ð¸ÑÐ½ÑÐµ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ñ, Ð¿Ð¾Ð·Ð²Ð¾Ð»ÑÑÑÐ¸Ðµ ÑÐµÑÐ°ÑÑ Ð´Ð°Ð½Ð½ÑÑ Ð·Ð°Ð´Ð°ÑÑ. Ð ÑÐ¾Ð´Ðµ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ Ð±ÑÐ» Ð¿ÑÐ¾Ð²ÐµÐ´ÐµÐ½ ÑÑÐ°Ð²Ð½Ð¸ÑÐµÐ»ÑÐ½ÑÐ¹ Ð°Ð½Ð°Ð»Ð¸Ð· Ð¿ÑÐµÐ´Ð»Ð¾Ð¶ÐµÐ½Ð½ÑÑ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ð¾Ð² Ñ ÑÐµÐ»ÑÑ Ð²ÑÑÐ²Ð»ÐµÐ½Ð¸Ñ Ð±Ð¾Ð»ÐµÐµ ÑÑÑÐµÐºÑÐ¸Ð²Ð½Ð¾Ð³Ð¾ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ð°. ÐÐ°Ð´Ð°ÑÐ¸, ÑÐµÑÐ°ÐµÐ¼ÑÐµ Ð² ÑÐ¾Ð´Ðµ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ: 1. ÐÐ·ÑÑÐµÐ½Ð¸Ðµ ÑÑÑÑÐºÑÑÑÑ Ð¼ÑÐ·ÑÐºÐ°Ð»ÑÐ½Ð¾Ð³Ð¾ ÑÐ¸Ð³Ð½Ð°Ð»Ð° Ñ ÑÐµÐ»ÑÑ ÐµÐ³Ð¾ Ð´Ð°Ð»ÑÐ½ÐµÐ¹ÑÐµÐ³Ð¾ ÑÐ°Ð·Ð´ÐµÐ»ÐµÐ½Ð¸Ñ. 2. ÐÐ·ÑÑÐµÐ½Ð¸Ðµ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ð¾Ð² ÑÐ°Ð·Ð´ÐµÐ»ÐµÐ½Ð¸Ñ Ð·Ð²ÑÐºÐ¾Ð²Ð¾Ð³Ð¾ ÑÐ¸Ð³Ð½Ð°Ð»Ð° Ð½Ð° Ð³Ð°ÑÐ¼Ð¾Ð½Ð¸ÑÐµÑÐºÑÑ Ð¸ Ð¿ÐµÑÐºÑÑÑÐ¸Ð¾Ð½Ð½ÑÑ ÑÐ¾ÑÑÐ°Ð²Ð»ÑÑÑÐ¸Ðµ. 3. ÐÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ Ð·Ð°Ð´Ð°ÑÐ¸ Ð¾ÐºÐ¾Ð½Ð½Ð¾Ð³Ð¾ Ð¿ÑÐµÐ¾Ð±ÑÐ°Ð·Ð¾Ð²Ð°Ð½Ð¸Ñ Ð¤ÑÑÑÐµ Ð¸ Ð·Ð°Ð´Ð°ÑÐ¸ Ð¾Ð±ÑÐ°ÑÐ½Ð¾Ð³Ð¾ Ð¾ÐºÐ¾Ð½Ð½Ð¾Ð³Ð¾ Ð¿ÑÐµÐ¾Ð±ÑÐ°Ð·Ð¾Ð²Ð°Ð½Ð¸Ñ Ð¤ÑÑÑÐµ. 4. ÐÐ½Ð°Ð»Ð¸Ð· Ð¸ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ðµ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ð¾Ð². Ð ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐµ Ð±ÑÐ»Ð¸ ÑÐµÐ°Ð»Ð¸Ð·Ð¾Ð²Ð°Ð½Ñ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ñ Ð³Ð°ÑÐ¼Ð¾Ð½Ð¸ÑÐµÑÐºÐ¾Ð³Ð¾-Ð¿ÐµÑÐºÑÑÑÐ¸Ð¾Ð½Ð½Ð¾Ð³Ð¾ ÑÐ°Ð·Ð´ÐµÐ»ÐµÐ½Ð¸Ñ Ð·Ð²ÑÐºÐ¾Ð²Ð¾Ð³Ð¾ ÑÐ¸Ð³Ð½Ð°Ð»Ð° Ñ ÑÐµÐ»ÑÑ Ð¿ÑÐ¸Ð¼ÐµÐ½ÐµÐ½Ð¸Ñ Ð½Ð° ÑÑÐ´Ðµ Ð¼ÑÐ·ÑÐºÐ°Ð»ÑÐ½ÑÑ ÐºÐ¾Ð¼Ð¿Ð¾Ð·Ð¸ÑÐ¸Ð¹. ÐÐ°Ð½Ð½ÑÐµ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ñ Ð²ÐºÐ»ÑÑÐ°ÑÑ Ð² ÑÐµÐ±Ñ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼ ÑÐ°Ð·Ð´ÐµÐ»ÐµÐ½Ð¸Ñ Ð·Ð²ÑÐºÐ¾Ð²Ð¾Ð³Ð¾ Ñ Ð¿Ð¾Ð¼Ð¾ÑÑÑ Ð¼ÐµÐ´Ð¸Ð°Ð½Ð½Ð¾Ð¹ ÑÐ¸Ð»ÑÑÑÐ°ÑÐ¸Ð¸ Ð¸ Ñ Ð¿Ð¾Ð¼Ð¾ÑÑÑ ÑÐ¾Ð·Ð´Ð°Ð½Ð¸Ñ Ð²ÑÐ¿Ð¾Ð¼Ð¾Ð³Ð°ÑÐµÐ»ÑÐ½Ð¾Ð¹ ÑÑÐ½ÐºÑÐ¸Ð¸ ÑÐ°Ð·Ð´ÐµÐ»ÐµÐ½Ð¸Ñ ÑÐ¸Ð³Ð½Ð°Ð»Ð°. Ð¡Ð¸Ð½ÑÐµÐ· Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ð¾Ð² Ð¿ÑÐ¾Ð²Ð¾Ð´Ð¸Ð»ÑÑ Ð½Ð° Ð±Ð°Ð·Ðµ Ð¼Ð°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ¾Ð³Ð¾ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Ñ Ð¿Ð¾Ð¼Ð¾ÑÑÑ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð½Ð¾Ð³Ð¾ Ð¾Ð±ÐµÑÐ¿ÐµÑÐµÐ½Ð¸Ñ PyCharm Ð½Ð° ÑÐ·ÑÐºÐµ Python. ÐÐ°Ð½Ð½ÑÐµ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ñ Ð±ÑÐ»Ð¸ Ð¿ÑÐ¾ÑÐµÑÑÐ¸ÑÐ¾Ð²Ð°Ð½Ñ Ñ ÑÐµÐ»ÑÑ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ñ Ð½Ð° Ð²ÑÐ±Ð¾ÑÐºÐµ Ð¸Ð· 10 ÑÐ°Ð·Ð»Ð¸ÑÐ½ÑÑ Ð¼ÑÐ·ÑÐºÐ°Ð»ÑÐ½ÑÑ ÐºÐ¾Ð¼Ð¿Ð¾Ð·Ð¸ÑÐ¸Ð¹, Ð·Ð°ÑÐ°Ð½ÐµÐµ Ð°Ð³ÑÐµÐ³Ð¸ÑÐ¾Ð²Ð°Ð½Ð½ÑÑ Ð¸Ð· 10 Ð³Ð°ÑÐ¼Ð¾Ð½Ð¸ÑÐµÑÐºÐ¸Ñ Ð¸ 10 Ð¿ÐµÑÐºÑÑÑÐ¸Ð¾Ð½Ð½ÑÑ ÑÐ°ÑÑÐµÐ¹. ÐÐ° Ð¾ÑÐ½Ð¾Ð²Ð°Ð½Ð¸Ð¸ Ð¿ÑÐ¾Ð²ÐµÐ´ÐµÐ½Ð½ÑÑ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ð¹ Ð±ÑÐ»Ð¾ Ð¿ÑÐ¸Ð½ÑÑÐ¾ ÑÐµÑÐµÐ½Ð¸Ðµ Ð¾ Ð±Ð¾Ð»ÑÑÐµÐ¹ ÑÑÑÐµÐºÑÐ¸Ð²Ð½Ð¾ÑÑÐ¸ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ð° ÑÐ°Ð·Ð´ÐµÐ»ÐµÐ½Ð¸Ñ Ð·Ð²ÑÐºÐ¾Ð²Ð¾Ð³Ð¾ ÑÐ¸Ð³Ð½Ð°Ð»Ð° Ñ Ð¿Ð¾Ð¼Ð¾ÑÑÑ Ð¼ÐµÐ´Ð¸Ð°Ð½Ð½Ð¾Ð¹ ÑÐ¸Ð»ÑÑÑÐ°ÑÐ¸Ð¸, Ð° ÑÐ°ÐºÐ¶Ðµ Ð±ÑÐ»Ð¸ Ð¿ÑÐµÐ´Ð»Ð¾Ð¶ÐµÐ½ Ð²Ð°ÑÐ¸Ð°Ð½Ñ Ð¿Ð¾ ÑÐ»ÑÑÑÐµÐ½Ð¸Ñ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ð°, Ð¸ÑÐ¿Ð¾Ð»ÑÐ·ÑÑÑÐµÐ³Ð¾ Ð²ÑÐ¿Ð¾Ð¼Ð¾Ð³Ð°ÑÐµÐ»ÑÐ½ÑÑ ÑÑÐ½ÐºÑÐ¸Ñ ÑÐ°Ð·Ð´ÐµÐ»ÐµÐ½Ð¸Ñ.
description: The subject of the graduate qualification work is Â«Mathematical model of the sound of musical instrumentsÂ» In the graduate qualification work, the problem of dividing an audio signal into a harmonic and percussion component is considered. Various algorithms studied that allow solving this problem. During the study, a comparative analysis of the proposed algorithms carried out in order to identify a more efficient algorithm. Tasks solved during the study: 1. Study of the structure of a musical signal with a view to its further separation. 2. Study of algorithms for separating the audio signal into harmonic and percussion components. 3. Research of Short-time Fourier transform and inverse Short-time Fourier transform. 4. Analysis and comparison of algorithms. As a result, algorithms for harmonic-percussion separation of the audio signal implemented with the aim of using them on a number of musical compositions. These algorithms include an audio separation algorithm using median filtering and by creating an auxiliary signal separation function. Algorithms synthesized based on mathematical modeling using PyCharm software in Python. These algorithms tested in order to compare on a sample of 10 different musical compositions, pre-aggregated from 10 harmonic and 10 percussion parts. Based on the studies, it was decided that the algorithm for splitting the audio signal using median filtering is more effective, and an option was proposed to improve the algorithm using the auxiliary separation function.