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# 1. Derive from first principles the Fourier series for a Square pulse waveform shown in Figure 1 and described by equation 1:

1. Derive from first principles the Fourier series for a Square pulse waveform shown in Figure 1 and described by equation 1:

Figure 1: Square Pulse Waveform

[1]

2. Calculate the first 7 non-zero amplitude coefficients for the Fourier components.

3. Use Excel to plot the waveform over one period (from o to T) described by the Fourier series for the square wave using the first 7 non-zero harmonics.

4. It is reported that a Radio Control unit operating at 27.0 MHz is malfunctioning. On inspection it is found there is an internal digital circuit that uses a 3 MHz ‘clock’ waveform. Explain why this signal might produce an interfering signal at 27 MHz using Fourier’s theorem.

5. The 3 MHz clock signal need not be square but can be adjusted to use ‘pulses’ described by equation 2. Write down the Fourier series expression for this waveform (from the data book) and determine a suitable value of ‘a/T’ to reduce the interfering harmonic to zero.

Figure 2: Rectangular Pulse Waveform

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