### Overview:

Every **periodic** signal can be described as a sum of sine waves with different *frequencies, amplitudes, and phase shifts*. This gives possibility of synthesizing signals with sine waves and analyze all kinds of signals to determine sine waves that makes the signal.

Decomposition of signal shape (data in time domain) to sine waves that make the signal (data in frequency domain) is done by **FFT** (Fast Fourier Transform). This algorithm is implemented in **Digilent WaveForms**.

Frequencies of the sine waves are strictly described. Every periodic signal has its own frequency **- base frequency**. It is equal to frequency of the **first** sine wave. Next sine waves in the sum have frequencies *multiplicated* by its index - for example, second sine wave has frequency equal to 2 * base frequency.

Index of the sine wave is called a **harmonic**. I will show how to measure amplitudes of harmonics in signal, that is, amplitude of specific sine wave in signal.

Unfortunately, we can't measure **phase** of the sine waves, because phase FFT algorithm is not yet implemented in Digilent WaveForms (it's possible to do this in WaveForms SDK, FFT needs only samples of the signal).

### Decomposition of the Square Wave:

### Setup:

Torun this example, you need **Analog****Discovery 2** and **PC**.

Connect **Analog Discovery 2** to your **computer**.

Connect **1+** (oscilloscope positive input) to **W1** (waveform generator output) and **1-**(oscilloscope negative input) to **GND** (ground).

We will play waveforms by **WaveGen** and observe shapes of the signal and measure harmonics (FFT) using **Scope.**

**Waveform****Generator:**

**1.** To launch the **Waveform Generator**, click on the **Wavegen** button.

**2. **Switch to the **custom** mode - we will implement **additive****generator**.

**3.** Click on **New**, paste the code provided below to the script field. By modifying **amp** and **phase** values, we will generate different shapes of signals. If you click the **generate** button, you will see the generated shape.

```
var amp =[1,0,0,0,0,0,0,0,0,0]; //amplitudevalues from 0 to 1 (0-100%)
var ph = [0,0,0,0,0,0,0,0,0,0]; //phase values from 0 to 1 (0-360degrees)
Y = amp[0] *sin((1 * 2*PI*X) + 2*PI*ph[0])
+ amp[1] *sin((2 * 2*PI*X) + 2*PI*ph[1])
+ amp[2] *sin((3 * 2*PI*X) + 2*PI*ph[2])
+ amp[3] *sin((4 * 2*PI*X) + 2*PI*ph[3])
+ amp[4] *sin((5 * 2*PI*X) + 2*PI*ph[4])
+ amp[5] *sin((6 * 2*PI*X) + 2*PI*ph[5])
+ amp[6] *sin((7 * 2*PI*X) + 2*PI*ph[6])
+ amp[7] *sin((8 * 2*PI*X) + 2*PI*ph[7])
+ amp[8] *sin((9 * 2*PI*X) + 2*PI*ph[8])
+ amp[9] * sin((10 * 2*PI*X) + 2*PI*ph[9]);
```

### Oscilloscope:

**1.** To launch the **Oscilloscope**, click on the **Scope** button.

**2.****Trigger** options (Fig. 10 below):

**Source:** Channel 1;

**Condition:** rising;

**Level:** 0V.

**3.****Time** options (Fig. 11 below):

**Position:** 0s;

**Base:** 1ms/div.

**4.****Unclick** Channel 2.

**5.****Channel** options:

**Offset:** 0V;

**Range:** 500mV/div;

Click on the sprocket wheel button and unclick **Noise** checkbox.

**6.** Click on **View->FFT** to show FFT window.

**7.****FFT** options:

**Start:** 0Hz;

**Stop:** 50kHz;

**Top:** 0dBV;

**Bottom:** -80dBV

### Measurements:

The setup is done, so we can now take some measurements.

**Examples****of****Other****Waveforms:**

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