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. Mihai 4 December at 8am. See the first link on the page, to that post from a year ago.

Ed Davies 4 December at 12pm. Whoops — good catch! Kevin Kenny 6 December at 6pm. This blog is maintained by Jean-Claude Wippler. Alphabetical and Chronological index of weblog posts.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.

Using Excel to create Sin wave look up table

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.

### Sine Look Up Table Generator Calculator

Frequency is discrete and therefore a function of the sample rate. Notice the modes of the distortion behavior in the plot. They match with common sense: when retrieving from the table precisely at a point, the error is smallest; linear interpolation has a smaller error than direct lookup in between points.

What is not intuitive is that the error is relatively constant for each of the modes up to the Nyquist frequency. To take this example further, try different table precision and element counts to see the effect of each.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.

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:.

## Digital Waveform Generation: Approximating a Sine Wave

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. The way that sinesum works is that you send it a list of the amplitudes of the harmonics you wish to graph. Because the graph is the product of several sine waves being added up, the waveform can go outside the normal -1 to 1 bounds of an audio signal.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. 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.Documentation Help Center. The required parameters for the function are:. You must use at least one of the parameters errmax and nptsmax. The next section, Setting Function Parameters for the Lookup Tablegives typical settings for these parameters. If you use only the errmax parameter, without nptsmaxthe function creates a lookup table with the fewest points, for which the worst-case error is at most errmax.

See Using errmax with Unrestricted Spacing. If you use only the nptsmax parameter without errmaxthe function creates a lookup table with at most nptsmax points, which has the smallest worse case error. See Using nptsmax with Unrestricted Spacing. The section Specifying Both errmax and nptsmax describes how the function behaves when you specify both errmax and nptsmax. You can use the optional spacing parameter to restrict the spacing between breakpoints of the lookup table.

The options are. The section Restricting the Spacing and the examples that follow it explain how to use the spacing parameter. If you exit the MATLAB software after typing these commands, you must retype them before trying any of the other examples in this section. The first example shows how to create a lookup table that has the fewest data points for a specified worst-case error, with unrestricted spacing. Note that the nptsmax and spacing parameters are not specified.

The value of errworst is less than or equal to the value of errmax. In this example, the ideal function and the approximation are so close together that the two graphs appear to coincide. The lower plot displays the errors. This can sometimes reduce the maximum error. You can also change the values of xmin and xmax to evaluate the lookup table on a subset of the original interval.

To find the new maximum error after changing ydataxmin or xmaxtype. The next example shows how to create a lookup table that minimizes the worst-case error for a specified maximum number of data points, with unrestricted spacing.

The empty brackets, []tell the function to ignore the parameter errmaxwhich is not used in this example.However, when I entered an odd number as the duration, the code fails at the envelope it says matrix dimensions must agree so, when I modified it like this: it worked with any duration.

Post a Comment. Download genTone. This article deals mainly to generating sine wave tones, and genTone. From this information we can calculate how many points we need to generate a tone of a certain frequency and make it last for the correct amount of time. The first thing to do is generate a time vector with the correct number of points. This can be done in a couple of ways, for example. Linspace creates a vector from input 1 to input 2, with the number of steps specified in input 3.

Again starting from 0, so end point is the duration minus one time step. Next step is generating the sine wave. Note that Matlab's sine function expects radians as an input. This means that:. This pattern continues for values above pi, so it doesn't actually matter where we start, just so long as whatever timeVec we have runs through one full cycle every second.

Additionally, the pi range used can be shifted to shift the phase of the wave in radians simply by adding it:. To manipulate amplitude, multiply outside the sine, to manipulate frequency multiply within the sine. If the output is intended to be played from a speaker, there's another technical consideration.

It's generally advisable to add a brief rise and fall envelope 20 ms usually works well so the amplitude at the start and end doesn't change so suddenly.

This stops the speaker from clicking at the onset and offset. An easy way to do this is to create an envelope for the wave. This will be a vector of 0 to 1 of the same length as the wave.

To add a rise and fall, we'll create an envelope that starts at 0, rises to 1, remains at 1 for the majority of the wave, then falls to 0 near the end. For the rise and fall regions, a quarter of a cosine cycle will be added to the envelope. For the rise we want a rising quarter. For the fall we want a falling quarter. The rest of the points we don't want to change. The fall is simply the reverse of the rise, the end index in to rise returns rise starting with the last point and ending at the first, reversing it.

The end- nPtsRise-1 :end index on the second line selects the end of the envelope. Note the minus 1, this is because would be 21 points. The way to output a signal through speakers depends on the hardware and software setup, but the simplest way is to use Matlab's audio functions - see wavplay in older versions of Matlab and audioplayer in more recent versions.

If reliable or short latency is required, external toolboxes such as Psychtoolbox are more useful. Try this:. It takes 6 inputs, amp, freq, duration, rise duration, phase and sampling rate. It can return up to 3 outputs, the generated tone, the time vector used to generate the tone and the envelope used to modify the tone.

Older Post Home. Subscribe to: Post Comments Atom.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.

### Select a Web Site

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.

Number of output pipeline stages to insert in the generated code. Choose a web site to get translated content where available and see local events and offers. Based on your location, we recommend that you select:. Select the China site in Chinese or English for best site performance.

Other MathWorks country sites are not optimized for visits from your location. Toggle Main Navigation.