### Sine wave data table

29.04.2021

One way to do so is to use a resistor ladder networktied to a number of digital output pins. With 8 output bits, you get an 8-bit DAC which can output voltages The next step is to approximate a sine wave by rapidly adjusting the output bits to the values of a sine wave. This toneGen sketch from the weblog post does precisely that:.

This lets us generate an decent sine wave by stepping voltages in the proper sequence, looping forever:. Fortunately, this is usually very easy to fix with a low-pass filter even just a single R-C filtersince these artifacts are at a much higher frequency than the generated sine wave itself. The AD chip used in the Sine Wave Generator works the same way, but it has one more clever trick up its sleeve, which lets it generate arbitrary frequencies using a single fixed crystal-based master clock.

Then every microsecond, a new value is looked up, and after lookups we can start over. The result would be a Hz sine wave. Now suppose we want a Hz sine wave, driven by the same 1 MHz clock source: we can simply re-use the same table entry twice, before moving on to the next.

How about Hz? But what we can do, is represent the step time as a fractional value, i. And now the big trick: ignore the fractional part while deciding which table entry to use! This causes the table entries to be used in sequence, but possibly with a slight jitter as the stepping progresses in such a way that the full table will be cycled through exactly fast enough to produce the desired frequency.

So 1 Hz output is produced with a 0. All you need to do is allow the fractional step rate to be larger than 1. Stepping through the table with rate So its amplitude changes will not be as fine-grained, but its frequency will be exact.

For completeness: an Arbitrary Waveform Generator AWG works similar to a DDS in that it also synthesizes a wave by running samples through an DAC from a table, but now the table may contain anything, not just a pure sine wave.

The entries in the table describe one full wave. Instead, an AWG really has to accurately control its step time from table entry to table entry to produce the desired frequency. How is performance on very low frequencies, especially: how much does a 50 Hz sine wave drift? Compare differentially mains on one pin and a crystal-derived frequency on other JeeNode pin.This chapter will cover generating sawtooth, triangle and square waveforms from a combination of sine wave harmonics, graphing these waveforms to an array and playing this array back as an oscillator.

When written to an arraythese waveforms can be played back as an oscillator. The first advantage is that the resulting waveforms will be bandlimited. This means the number of harmonics they produce will be limited, and will cause less aliasing noise. The second advantage is that these waveforms much more closely resemble the kinds of waveforms generated by analog electronics.

Real world analog waveforms do not have the completely sharp angles of their idealized, digital counterparts due to the "rippling" effect inherent in the resonance of their circuitry.

Embedded System Practical - Sine Wave Generation using Keil uVision

The basic principle we will use here comes from the Fourier theorem. This theorem states that any complex waveform can be broken down into a series of simpler sine waves which, when added back together, can reproduce that waveform. The more sine waves used to represent the complex wave, the more accurate the reproduction will be. While a full explanation of the math behind this is outside the scope of this manual, we will cover the use of this theorem to create three basic wave forms, the sawtooth, the triangle and the square.

In Pd, we can write waveforms to a table using an internal message. An internal message is a message box which, when clicked, sends the message inside to the Pd application itself. An example would be the messages we can use to turn audio processing on and off in Pd:. So to create and load a table with a waveform, we must first create an array from the Put menu.

Then we give it the name "waveform" in the properties:. After that, we create a message, and type the following in it using the Return key after the semicolon to start a new line :.

The semicolon indicates that the message is an internal message, and "waveform" indicates that we are sending information to the array named "waveform". The word "sinesum" tells the array that we will be sending it a series of harmonics to graph.

The number "" tells the array that we want to graph those harmonics out on units on the X range, so the array will be resized from its default size to Finally, the number "1" indicates that we want to write a single sine wave with a peak amplitude of 1 to the array.Documentation Help Center.

Implement fixed-point sine or cosine wave using lookup table approach that exploits quarter wave symmetry. The block can output the following functions of the input signal, depending upon what you select for the Output formula parameter:. You define the number of lookup table points in the Number of data points for lookup table parameter. Use the Output word length parameter to specify the word length of the fixed-point output data type.

The fraction length of the output is the output word length minus 2. Input signal, u, specified as a real-valued scalar, vector, or matrix. To obtain meaningful block output, the block input values should fall within the range [0, 1. For input values that fall outside this range, the values are cast to an unsigned data type, where overflows wrap.

For these out-of-range inputs, the block output might not be meaningful. Data Types: single double int8 int16 int32 int64 uint8 uint16 uint32 uint64 Boolean fixed point. The block uses double-precision floating-point values to construct lookup tables. Therefore, the maximum amount of precision you can achieve in your output is 53 bits.

Setting the word length to values greater than 53 bits does not improve the precision of your output. Select Speed for faster calculations.

If you do, a loss of accuracy might occur, usually up to 2 bits. Some of the main steps needed to design and evaluate a sine wave data table for use in digital waveform synthesis applications in embedded systems and arbitrary waveform generation instruments.

Boolean double fixed point integer single. The HDL code implements Cosine and Sine blocks by using the quarter-wave lookup table that you specify in the Simulink block parameters. Number of registers to place at the outputs by moving existing delays within your design. Distributed pipelining does not redistribute these registers. The default is 0. Number of input pipeline stages to insert in the generated code. Distributed pipelining and constrained output pipelining can move these registers.Documentation Help Center. The Sine Wave block generates a multichannel real or complex sinusoidal signal, with independent amplitude, frequency, and phase in each output channel.

The block supports floating point and signed fixed-point data types. The block generates a real sinusoidal signal when you set the Output complexity parameter to Real. The real sinusoidal output is defined by an expression of the type.

### Generating Waveforms

The block generates a complex exponential signal when you set the Output complexity parameter to Complex. This complex exponential signal is defined by an expression of the type. When you specify at least one of these parameters as a length- N vector, scalar values specified for the other parameters are applied to every channel. For example, to generate the three-channel output containing the following real sinusoids, set the block parameters as shown:.

Output a sinusoidal signal as a scalar or vector. For more information about output complexity, see Description.

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For information about multichannel support, see Generating Multichannel Outputs. To output fixed-point data types, you must set Sample mode to Discrete and Computation method to Table lookup. A length- N vector containing the amplitudes of the sine waves in each of N output channels, or a scalar to be applied to all N channels.

The vector length must be the same as that specified for the Frequency and Phase offset parameters. This parameter is tunable Simulink only when the Computation method is Trigonometric fcn or Differential. A length- N vector containing frequencies, in hertz, of the sine waves in each of N output channels, or a scalar to be applied to all N channels.

The vector length must be the same as that specified for the Amplitude and Phase offset parameters. You can specify positive, zero, or negative frequencies.

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This parameter is tunable Simulink when you set either:. Sample mode to Continuous. Sample mode to Discrete and Computation method to Trigonometric fcn. A length- N vector containing the phase offsets, in radians, of the sine waves in each of N output channels, or a scalar to be applied to all N channels. The vector length must be the same as that specified for the Amplitude and Frequency parameters. Specify the sampling mode as Continuous or Discrete :. In continuous mode, the sinusoid in the i th channel, y iis computed as a continuous function.

This mode offers high accuracy, but requires trigonometric function evaluations at each simulation step, which is computationally expensive. Also, because this method tracks absolute simulation time, a discontinuity will eventually occur when the time value reaches its maximum limit.

In discrete mode, the block can generate discrete-time output by directly evaluating the trigonometric function, by table lookup, or by a differential method. For more information on these computation methods, see Algorithms. The type of waveform to generate: Real specifies a real sine wave, Complex specifies a complex exponential. The method by which discrete-time sinusoids are generated: Trigonometric fcnTable lookupor Differential.In Digital Signal Processing, often is required the implementation of transcendental math function as trigonometric functions sine, cosine, tan, atan or exponential and logarithmic functions and so on.

An efficient way, when possible, is to implement an approximation of these functions using Look Up Table or LUT as the sine example in Figure1. For example, using a system clock of MHz the Figure reports the configuration for a sine wave output frequency of 3. Of course, the VHDL code for generating a sine wave table is not a synthesizable code. In Figure4 is reported an example of a 32 sine wave samples quantized using 8 bit.

The X axis reports the sample and Y axis reports the quantized amplitude. In other words, we need to generate the quantized version of the following trigonometric sinusoidal function:. Using Matlab a possible simple code for sine wave generation of 32 samples and maximum quantized value of can be the following:. Here below there is an example of a VHDL code generating a sine wave samples and write it to an external file.

It is clear that, if you change the transcendent function you can generate the all the LUTs you need. In this function, the test on the positive or negative number is performed. This value is 0.

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The sum is performed by the XOR function on the sign bit. It is worth of notice that in this example we are using a fake or artificial clock only to allow the plot of the sine wave samples on the Modelsim simulation wave of Figure5.

Line 84 print to file the sine samples as 16 columns per row integer separated by a comma, so you can easy generate the ROM code for a sine waveform as Figure5. Here an example of how to use the sine samples to write the code of a ROM containing the sine values. You can use the VHDL code above to generate all the transcendent function you need in your VHDL design simply modifying the function, number of bit for sample and quantization.

I am having a difficult time following the flow of the first VHDL code. The second part in Figure 5 is pretty easy to follow. I think the first section is trying to take in samples of a file to create a sine wave table and store the samples in the respective ROM locations?

Is there a way to break this down into block diagrams so that it can be easier understood? I understand block diagrams easier than the declarations etc.

Thank you. It implements the ROM with sine samples. Thanks in advance. For example, I want to generate x,y points from cost at,btsin at,bt where t is the timer and A,B are any int value.

Additionally, we will be incorporating potentiometers for volume and frequency control of the sine wave. In the Music With a Piezo Element project, we created a square waveform by toggling a digital pin on and off at the desired frequency. For that project, we did not take into consideration bit depth or sample rate because we were changing the amplitude of the waveform at exact points. Figure 1 shows an example of that method, illustrating the waveform that would be generated by the following code.

The line numbers of the code relate directly to labels in the figure. Complex waveforms like sine waves, and especially audio from your mp3 player have to use a more sophisticated way of reconstructing sound that involves sampling. Sampling works by updating the amplitude of an output signal at a fixed interval of time that is much faster than the signal you are trying to produce. This interval is the sample ratewhich is defined as the number of samples taken per second used to reconstruct a waveform.

You could think of this method as if plotting points on a graph of a waveform; with enough points you get an accurate picture of the waveform.

Figure 2 shows the sampling method of recreating a waveform the red dots in the graph are sample points. You can see that with enough points, the same square wave is reproduced. While this may seem a bit excessive for just a square wave, you may begin to see how any waveform can be created in this manner.

Bit depth is defined as the number of bits used to represent the amplitude at each sample point. Most often, amplitude values in digital systems are stored as integers mainly due to hardware limitationswhich means there is a discrete number of values which can be used to represent the signal.

Using the graph plotting example, you can think of bit depth as the number of vertical divisions on the graph. Figure 3 shows an example of bit depth. In this example, the same continuous time waveform is represented by three signals of different bit depths. By using enough bits, a reasonable approximation of the original waveform can be achieved. As a point of reference, CD quality audio is reproduced at a sample rate of For our project, we will be using a sample rate of This will be how we create our sample points as described above.

Follow the link to the right for a more in-depth explanation of how SPI functions to transmit data. SPI normally requires four signal pins, but for this project we will only be using three. For the other chipKIT boards, the pinout for SPI is listed in the reference manual, which can be found on the digilent website.

For SPI you simply have to set the following two lines of code in the setup portion of your sketch to initialize communication. The begin method simply initializes the SPI hardware, and setBitOrder tells the chipKIT board to either send the least or most significant bit of transmitting data first.Documentation Help Center. This example shows some of the main steps needed to design and evaluate a sine wave data table for use in digital waveform synthesis applications in embedded systems and arbitrary waveform generation instruments.

Real-Time direct digital synthesis of analog waveforms using embedded processors and digital signal processors DSPs connected to digital-to-analog converters DACs is becoming pervasive even in the smallest systems. In real-time systems, the computational burden is typically too large to permit this approach.

Similar analysis is needed when performing your own waveform designs. The table data and look-up algorithm alone do not determine performance in the field. Additional considerations such as the accuracy and stability of the real-time clock, and digital to analog converter are also needed in order to assess overall performance.

The Givens rotation-based CORDIC algorithm is among one of the most hardware-efficient algorithms because it requires only shift-add iterative operations. The following commands make a point sine wave and measure its total harmonic distortion when sampled first on the points and then by jumping with a delta of 2. For frequency-based applications, spectral purity can be more important than absolute error in the table. The file ssinthd. It is used for calculating total harmonic distortion THD for digital sine wave generation with or without interpolation.

This THD algorithm proceeds over an integral number of waves to achieve accurate results. The number of wave cycles used is A. You can put the sine wave designed above into a Simulink model and see how it works as a direct lookup, with linear interpolation, and with CORDIC approximation. This model compares the output of the floating point tables to the sin function. As expected from the THD calculations, the linear interpolation has a lower error than the direct table lookup in comparison to the sin function.

You can typically achieve greater accuracy by increasing the number of iterations corresponding to a longer computation time. It is used when multipliers are less efficient or non-existent in hardware. Zooming in on the signals between 4. Now convert the floating point table into a 24 bit fractional number using 'nearest' rounding.

The new table is tested for total harmonic distortion in direct lookup mode at 1, 2, and 3 points per step, then with fixed point linear interpolation.

Choosing a table step rate of 8. Simulink also includes a Sine Wave source block with continuous and discrete modes, plus fixed point Sin and Cosine function blocks that implement the function approximation with a linearly interpolated lookup table that exploits the quarter wave symmetry of sine and cosine. The model also compares the sine wave source reference with the sin function whose input angle in radians is time based computed using a clock.

The following plot shows that the sin function accumulates error when its input is time based. This also shows that a sampled sine wave source is more accurate to use as a waveform generator.

N is points in this example; the 1, 2, 2. Frequency is discrete and therefore a function of the sample rate. Notice the modes of the distortion behavior in the plot.