Digital Piano Application in Acoustic Engineering

Abstract

Basically Digital piano, is an electronic musical instrument for synthesizing traditional piano timbre. This research was created to identify how the signal is transmitted through the digital piano, where the piano details are studied such as classification of the digital piano, operation and properties. Each tone of piano is having one specific key frequency and spoke to by a note like C and D etc. For the digital piano when you play traditional acoustic piano, the hammer connected to keyboard hits the string and sets it into vibration, together with the reverberation effect of wooden soundboard, then the sound comes out.

Introduction

In electrical engineering, the fundamental quantity of representing some information is called a signal. A signal is a portrayal of how one parameter different from another parameter. For example, voltage changing over time in an electronic circuit. Signal have two type, which are analog signal and digital signal. An analog signal called as continuous time signal. These signals are defined over continuous independent variables.

It’s difficult to analyze, as it carries a huge number of values and more accurate due to a large sample of values, for example human voice.

Digital piano is also called electronic piano which the pulse code modulation technology is adopted that not only has the total functions of mechanical piano, but also has the functions of special multiple timbre, storage memory, tone sandhi, audio mixing and metronome as well as the interface of MIDI, headphone and microphone [1].

Accordingly the conventional piano assembling innovation and this strategy are splendidly joined to wind up increasingly stylish.

Computerized piano has the MIDI capacity. MIDI is computerized interface which a sort of equipment among PC and MIDI gear just as to control of ongoing music transmission, advanced coding of time data and guideline of the equipment for the coding transmission. Digital piano is connected with other facilities by MDI interface, so that the function of digital piano is extended.

Further clarification of the difference between the parameters. For example, such as changing the voltage over time in an electronic circuit. The system is any process that has an output signal that responds to the input signal. The segment diagram below shows a continuous and discrete output signal that responds to a continuous and discrete input signal.

An Overview of Digital Piano History

In 1700, the main instrument that is considered today a piano was brought into the world under the name of 'pianoforte'. For the most part unassuming cost engaged this piano to end up first instrument of its form to be extensively gotten in homes of Italian goodness and power. After that, an English designer and artist starts first vast scale produce of strong and lightweight pianos in England. His plan of piano was extended enormously by an English inventor who added more octaves to cover treble and bass, included pedal and strings were considerably more vigorous and lauder.

In 1808, an inventor made first piano with agraffe, which empowered substantially more forceful utilization of consoles and mallets. This offered capacity to renowned established arranger. After few years, the first upright piano was made. In 1920, Automatic pianos end up being astoundingly predominant. Be that as it may, in the twentieth century, the advanced pianos can be found everywhere, in moderately every band.

Classification of Signals and Systems

In this section, a definition of corresponding to the main parts of the instrument, the hammer, the thread, and the radiator. In short, the algorithm is based on the decomposition of the series displacement, y (x, t) to its normal orthogonal formulas. Where yn(t) are the instantaneous amplitudes of the modes, or partials. After discretization, the input-output relation of the string block is realized as a parallel connection of N second-order all-pole resonators. Where Fstring(z) is the transversal force at the bridge, Fh(z) is the force coming from the hammer and Hmode,k(z) are the transfer functions of the normal modes. The conversion between the physical variables (i.e. force, displacement) and the modal variables is regulated by a set of input and output weights Win,k, Wout,k.

Regardless of those calculation at its center is inalienably parallelizable, it is required that it should rearrange those hammer-string cooperation from those algorithm formerly recommended clinched alongside, mostly to overcoming. Some alignment issues Also Additionally to better exploiting the competencies from claiming advanced equipment.

Optional resonators are somewhat detuned gatherings of resonators which are required for simulating the unpredictable beating envelopes found in piano partials. In addition, they are employed for the simulation of the sympathetic resonance effect, since each note filters the signal obtained as a sum of all the primary resonators. Finally, the duplex resonators model the so called duplex scale, a portion of the strings above their speaking length giving a particular brilliance to piano sound. Speaking in terms of signal processing, there is no actual feedback in the resulting diagram.

The output of the computation for each note is the total force generated at the bridge, which is then converted into the desired acoustic pressure signal using the soundboard radiation module. In the first versions of our piano synthesizers, this was implemented simply as a block-based convolution with an impulse response (IR) measured on a real piano using an instrumented hammer.

Uses a common-pole depiction in the range of the 4 regions, subsequently parallelization is workable best to the zeros of the filters and, clearly, for the concurrent processing of the two sound. Channels. If, concerning illustration done our case, the support extent is held low (64 samples) to minimize latency, those speed-up of the calculation may be in the order of 50x contrasted with direct FFT-based. There is many ways used to name the signals. First, the continuous signals use parentheses, for example: x(t) and y(t), while the discrete signals use brackets, such as: x[n] and y[n]. Signals used lower case letter while upper case letter is used for frequency domain.

There are classes of signals which are Periodic, Even and Odd, the Periodic signal is a signal that repeated in a pattern every specific period, non-periodic signal is the opposite of the periodic which has no pattern.

Even signal is called even if:

x(- t) = x(t), x[- n] = x[n],

Odd signal is called odd if:

x( -t) = - x(t), x[-n] = -x[n].

The piano has become the most versatile and popular of all musical instruments. It has a playing range of more than seven octaves (Ao to C8), and a wide dynamic range as well.

Ear is a blessing that human can get and can use in everyday life. Meanwhile, ear have its constraint as human simply typical being. One of the limit human can hear signal frequency going from 20-20 kHz. From this wide range some part is related with piano [4]. Distinctive pianos are having diverse extents.

Each tone of piano is having one specific key frequency and spoke to by a note like C, D, ...and so on as appeared in figure 5 .The later C is 12 half advances away the past one and having twofold the principal frequency. Henceforth this part (from one C prompt next C) is called one octave. Diverse octaves are separated by C1, C2, and so on.

Here is an equation for the Frequency table. The basic formula for the frequency of the notes of the equal tempered scale is given by:

fn = f0 * (a) n

Where f0 = the frequency of one fixed note which must be defined. A common choice is setting the A above middle C(A4) at f0 = 440 Hz,

n = number of half steps away from the fixed note,

fn = the frequency of the notes n half steps away,

a = (2)1/12

Frequencies for Equal Tempered Scale at A4 = 440 Hz

Digital Signal Processing for Music

Sampling

At the point when a sound wave is made by human voice (or a melodic instrument), it's a simple flood of changing gaseous tension. Be that as it may, all together for a PC to store a sound wave, it needs to record discrete values at discrete time interims. The way toward recording discrete time esteems is called examining, and the procedure of recording discrete weights is called quantizing. Recording studios utilize a standard inspecting frequency of 48 kHz, while CDs utilize the rate of 44.1 kHz. Signs ought to be tested at double the most astounding frequency exhibit in the signal. People can hear frequencies from roughly 20-20,000 Hz range.

Frequency and Fourier Transforms

A Fourier change gives the way to separate a complicated signal, similar to a melodic tone, into its constituent sinusoids. This technique includes numerous integrals and a continuous signal. It is expected to play out a Fourier change on an inspected (instead of continuous) signal, and then it is necessary to utilize the Discrete Fourier Transform [5].

The index corresponding to the maximum amplitude represents the most significant frequency component that can be found using the formula

f = ( i/f)*fs (1)

Where i = index at which maximum amplitude exists,

T = Total samples in the FFT at a time

Padding with Zeroes

Padding with zeroes, though a standard practice and useful in many applications, does not appear to significantly improve the data in this application. Though it is been twice the frequency resolution, it is not yielding any better data [5].

Quick tests cushioning with more zeroes (1 part test, 9 parts zeroes) demonstrate that however the peaks show signs of improvement frequency determination, the error between the most astounding point on the original sample and the most noteworthy point on the cushioned sample is 1 Hz at most, which implies that it is likely not worth the exertion, even at low frequencies.

Piano has a several proprieties such as the concealed hit is stacked with non-symphonious tones that promptly hose down. Starting there, the sounds change from note to note, piano to piano. The key is really a switch, somewhat like a teeter-totter however any longer toward one side than at the other. When you press down on a key, the other end of the switch (covered up inside the case) hops up in the air, forcing a small felt-covered hammer to press against the strings, making a melodic note.

In the meantime, at the extreme end of the switch behind the mallet, another mechanical part called a damper is likewise constrained in the air. When you let go of the key, the sledge and the damper fall down once more. The damper rests over the string, stops it from vibrating, and finishes the note quickly [6].

Stability

Stability is an essential idea in system, yet it is additionally one of the hardest capacity properties to demonstrate. There are a couple of particular criteria for system soundness, yet the most broadly perceived need is that the system must make a constrained output when exposed to a restricted info. For instance, if 5 volts is being associated with info terminals of a given circuit, it is needed if the circuit output did not approach boundlessness, and the circuit itself did not relax or explode. This kind of steadiness is as often as possible known as 'Limited Input, Bounded Output' dependability, or BIBO.

Stability characterizes the scope of working condition or the scope of output as per the scope of information. The system of a digital piano must be stable. That means the sound turning out from the piano must pertain with the compatibility of the system.

Memory

A system is said to have memory if the output from the system is dependent on past sources or information (or future contributions too) to the system. A system is called memoryless if the output is only dependent on the present information. Memoryless systems are less difficult to work with, yet systems with memory are progressively normal in digital signal handling applications. A memory system is moreover called a dynamic system however a memoryless system is known as a static system [7]. Let A, B and C are three continuous data sources, and A', B' and C' are particular outputs. In the event that the output an' is required when the information B is given, implies input must be put away in the system. This implies the system has a memory. Notwithstanding, advanced piano systems cannot contain any memory due to the fact that the output or output required is almost instant.

Causality

Causality is a property that is in a general sense equivalent to memory. A system is said to be causal if it is only dependent on past or current data sources. A system is said to be non-causal if the output of the system is dependent on future data sources. An extensive segment of the reasonable system is causal.

System1: y[n]=13(x[n]+x[n−1] +x[n−2]) ⟵CausalSystem2: y[n]=13(x[n−1] +x[n]+x[n+1]) ⟵Non

Causal

As it were, an output of a system must be relied upon present or past estimations of information. Subsequently, digital piano system essentially has causality in light of the fact that the system is just dependable on the off chance that it has causality.

Linearity

There are two requirements for linearity. A function must satisfy all two to be called 'linear'.

Additivity or superposition:

x1(t)⟶y1(t)x2(t)⟶y2(t)x3(t)=x1(t)+x2(t)⟶y3(t)=y1(t)+y2(t)

Homogeneity:

x1(t)⟶y1(t)ax1(t)⟶ay1(t)∀aandx1(t)

Being direct is likewise referred to in the writing as 'fulfilling the guideline of superposition'. Superposition is some help term for saying that the s is included substance and homogeneous. The terms linearity and superposition can be used proportionally.

Linearity is described as, when a lone info is given, a lone output must be taken out. Likewise, when different sources of info are given, then output for each information must be given out by the system. In the meantime, advanced piano system must be direct since a single output sound is created when a single key is being squeezed. On the off chance that two keys are pressed in an advanced piano, the output sound will comprise the two tones in the meantime. That satisfies the condition that states the more keys in piano are being pressed, the more confounded signal is delivered.

Time Invariance

Consider an information signal x(t) results a output y(t), by then at whatever point moved info, x (t + δ), brings about a time shifted output y (t + δ).

This property can be satisfied if the trade capacity of the system isn't a component of time beside conveyed by the info and output. Slack between info signals and slack between output signals must be equivalent. This is the recognizable proof of the property called time invariance. A piano system must be time invariance, in light of the fact that a steady postponement of info and output is required and those two must be corresponded.

Invertibility

The system becomes invertible if we specify its inputs and outputs. Therefore, if the system is invertible, it will produce unique outputs of any distinct input. We can find out if the system is reversible by finding the reverse system or non-reversible through outputs if the inputs produce similar to the outputs.

Conclusion

This paper presents the analysis of the main features of digital piano models based on the descriptions of the device that makes music. Signal processing of music is considered as a quickly viewed by the search field. It is clear that music is the most complex and robust of any other signal. Digital piano tune frequencies are recognized with length. The strategy used here to illustrate the guide is more advanced than the strategies already used. By converting parameters such as width and height values, we can get the desired that comes with the length of time per note.

References

1. Li, K., Zhang, S., Wang, C., & Sun, D. (2010). Distance Education of Digital Piano Based on IP Multicast and Streaming Media Technology. Second International Workshop on Education Technology and Computer Science.
2. Zambon, S., Giordani, E., Bank, B., & Fontana, F. (2013). A system to reproduce the sound of a stringed instrument.
3. Gabrielli, L. (2019). Parallel Digital Signal Processing for Efficient Piano Synthesis. University of Udine.
4. Biagetti, G., Crippa, P., Turchetti, C., & Morici, A. (2007). Efficient Synthesis of Piano Tones with Damped Bessel Functions.
5. Woodford, C. (2018). Pianos.
6. Adams, M. D. (2013). Continuous-time signals and systems.