Abstract: Modified Discrete Cosine Transform (MDCT) is a modified form of Discrete Cosine Transform which ensures 50% overlapping of the segments. It is most widely used in audio coding, audio compression and audio signal analysis based applications. MDCT is a real transform and it does not contain any phase information. MDCT eliminates aliasing that occurs in time domain due to the overlapping of the segments. It is used in most of the audio coders for time domain to frequency domain transformation. In this paper, we propose a method for audio signal analysis using MDCT with different types of windows. This method consists of analysis and synthesis stages. Time domain aliasing that occurs in the analysis stages due to the overlapping of the …show more content…
In paper [5] Modified Discrete Cosine Transform is used in Psychoacoustic model for the perception of audio quality. In paper [3, 11] MDCT is widely used in audio coders due to the property of perfect reconstruction with critical sampling mostly with sine window. In both the papers analysis of audio signals are done using MDCT and exact results was discussed. It is not suitable for spectral analysis for several causes: it vectors are not shift-invariant, it does not conserve energy, and it cannot be understood by means of magnitude and phase [13]. Various window functions are used in practice for MDCT [11, 12]. Using adjustable window the main lobe width can be increased by reducing the side lobe. For audio signal analysis and processing mostly sine window or Kaiser Bessel Derived (KBD) window are used. Certainly, Hamming or Hanning Window is used for spectral analysis and …show more content…
3.1 Modified Discrete Cosine Transform The forward and inverse transform of MDCT are described as, X_k=√(4/N) ∑_(n=0)^(N-1)▒〖x_n cos(π/N (n+1/2+N/2)(K+1/2) ) 〗 k=0, 1.. ( N)/2-1 (1) Y_n=√(4/N) ∑_(K=0)^(N/2-1)▒〖X_k cos(π/N (n+1/2+N/2)(K+1/2) ) 〗 n=0, 1,…N-1 (2) In the above equation 1 & 2 x_n is the windowed input signal, X_k represents the transformed input signal,Y_n represents inverse transformed input signal, N represents length of the input signal. Window Functions Sine window or Kaiser Bessel Derived (KBD) window are the most widely used window in audio coding, audio signal processing and audio compression applications [11]. The other windows that can be applied for MDCT are rectangular, triangular, trapezoidal, Welch window etc. 3.2.1 Sine Window Sine window is a simple window which can be used for any transforms due to its spectral property and reconstruction property. When a sine window convolved itself it is known as Bohman window. The expression for sine window function W (n) can be given as in equation
This equation shifts from the parent function based on the equation f(x) = k+a(x-h) . In this equation, k shifts the parent function vertically, up or down, depending on the value of k. The h value shifts the parent function to the left or right. If h equals 1, it goes to the right 1 unit, if it is negative 1, it goes to the left 1 unit. If a is negative, the parent function is reflected on the x-axis. If x is negative, the parent function is reflected on the y-axis.
In this equation, Y is the dependent variable, and X is the independent variable. α is the intercept of the regression line, and β is the slope of the regression line. e is the random disturbance term.
(MPEG Audio Layer 3) An audio compression technology that is part of the MPEG-1 and
…………………… Early Commercial Applications of the Computer Within Music 6 ……………… ……………………. The Application of Music Programming 7 ……………… …………………… The Digital Revolution 8 ……………… …………………… My Conclusion
Now we can use techniques from linear regression to solve the problem. After the transformation, the least squares method will be used to predict those unknown betas. The core concept of the least squares method is to make the sum of (y-ye)2 the least (Jia, 2011). There is no need to calculate them by ourselves because the process is complex. We usually use computer to assist us to get the results of the least squares method.
in computer speakers or stereo or a telephone. And becuase of the common use of
Henry V Examines how historical fiction in drama and film comments upon and reflects their own contexts, offering enduring insights into society. Historical fiction in drama and film explores the enduring principles of realpolitik, revealing the complexities of leadership and the value of religion that provide insight into Elizabethan and Napoleonic societies. The perpetual play Henry V by William Shakespeare depicts the harsh materialities of leadership and how personal sacrifice is crucial. It cultivates the religious beliefs of the time while also paralleling Elizabethan society, based on the sacrifices Queen Elizabeth made during her reign. Correspondingly, Peter Weir’s film “Master and Commander: The Far Side of the World” corroborates
Music and the relationships of music have changed drastically in our society. The course of studies and the evaluations of the applications of the technology of music, the making and the listening of music have changed in the way we listen to music, the styles of music in our society and in the media. The importance of the technology in music today, has, over the past century been charted through the study of musical examples and through viewing how human values are reflected in this century's timely music. There are very many different types of music that are listened to. There are readings, writings, lectures and discussions on all the different types of music.
Most of the applications in terms of speech and audio compression may seem obvious at first, but what most do not realize is the scale at which it is used. Some of the more common examples include: telephone communications, compact disc players in the form of digital audio coding, stereo sound systems, speech recognition and playback, noise reduction/filtering after voice recognition and speech synthesis [1]. The uses of DSP for speech and audio compression is certainly not limited to these examples, but just these alone are examples that the general public use through various devices on a daily basis often without realizing the function of the systems and processes that go into their operation.
Fourier series has been proposed by Fourier in the late 18 century to deal with some mathematical heat problems [4]. Fourier insight was that any signal can be decomposed to periodic components in terms of trigonometric functions. Euler and Lagrange has shown before Fourier that periodic functions can be decomposed to such an expansion but Fourier’s contribution has been in proposing that any function can be decomposed in such a way although he wasn’t able to prove it [5]. It took almost one hundred years for mathematicians to prove that Fourier’s claim was ...
In acoustical problems the sound intensity is expressed by another convenient unit called decibel (dB) which 1/10 of bel unit.
The sound system used in the theatre is DTS is a series of multichannel audio technologies owned by DTS, Inc (formerly known as Digital Theater Systems, Inc), a U.S. company specializing in digital surround sound formats used for commercial / theatrical and consumer grade applications.
In this case, analysis would show that soundwaves from all the sound sources in the environment -- the various instruments of the performance, perhaps the stirring of the audience, or the sound of vehicles passing beyond the confines of the performance context -- the multitude of acoustic elements that make up each of these sounds do not conveniently remain grouped by source. Rather, the components of all these sounds mix together, combining into a single, very complex waveform which is represented on the tape and revealed through analysis. This is because sound waves are additive, like waves in water, multiplying in quality rather than quantity. In the simplest possible terms, what digital analysis uncovers are the acoustic features of the sounds captured by the tape recorder; what are actually heard are the perceptual features of the same sounds. The acoustic and perceptual characteristics of sound are not the same, nor in many cases is there a one-to-one correspondence between them.
Just as was true for other media, the conversion to digital offers radio a wealth of benefits not available from current AM or FM analog systems. Radio is an audio service, so consumers naturally compare it to the most pervasive high-quality audio technology, the compact disk (CD). A good FM signal played by a high-quality, stationary rec...