Sine Wave Multiplication Experiment

You can demonstrate the multiplication of sinusoids that is the heart of the Fourier Transform, using the Daqarta Generator.

First, make sure that Spectrum is off and Trigger mode is set to Gen Sync. Toggle Generator on and in the Generator Stream 0 dialog set Wave to Sine and Tone Freq to 500 Hz to act as the "input" frequency. Click on the AM button to open the Amplitude Modulation dialog, and set:

• AM On
• AM Sync
• AM Source = Sine
• AM Depth = 200% (Peak mode)
• AM Mod Freq = 100 Hz

Setting AM Depth to 200% produces true multiplication instead of ordinary amplitude modulation. AM Mod Freq here acts as the reference frequency.

Notice that the extent of the waveform above the 0 volts line appears to be equal to the extent below it... if you cut a tracing of the waveform out of heavy cardboard it would balance along the 0 line.

Now set AM Mod Freq to 500 to match the input Tone Freq, and you will see that the entire product appears above the zero line, centered about a constant value that is 1/2 of whatever you set for Level.

We haven't done any averaging here, since the Daqarta averager keeps separate averages for each time point during multiple frames, whereas here we want to average together all the points from each frame to get a single average value.

You can get an approximation, however, by toggling Trigger off and letting the trace roll, then averaging a lot of frames. The average should be nearly a flat line at zero volts if the frequencies are different, or at half the input amplitude if they are the same. These would correspond to the single values obtained from averages of these respective wave products.

Next: Conceptual Analyzer

See also Spectrum (Fourier Transform) Theory