A sine wave of 60 Hz, amplitude of 117 V, and initial phase of zero (or 117 sin(

Question

A sine wave of 60 Hz, amplitude of 117 V, and initial phase of zero (or 117 sin(2*60t) is full wave rectified and sampled at 2,048 samples per second after full wave rectification. Research the Fourier series for a full wave rectified sine wave (on the Internet or in circuit theory books, such as Linear Circuits by Ronald E. Scott) and write it below.

Then write a MATLAB program that samples and stores 4,096 points of full wave rectified sine wave and performs Fourier analysis (FFT) of the full wave rectified sine wave on the stored points.

Plot the results in both linear and log scale (in two separate figures) and extract the amplitude of the DC component and the first four harmonics (first , second, third, and fourth multiple of the fundamental frequency) of the Fourier analysis, then enter them in the table given below. The DC component is given by the first number in the Fourier analysis. Hint: Full wave rectification can be achieved in MATLAB simply by taking the absolute value (abs command) of the sine wave.

                                Paste the two graphs of Fourier analysis (in linear amplitude and dB scale ) here.

Enter the theoretical expression for a Fourier series for a full wave rectified sine wave here.

Compare the results provided by the Fourier transform and fill out the following table.

Component of series

Amplitude as predicted by theoretical Fourier series

Amplitude in linear scale as predicted by FFT

Frequency as predicted by theoretical Fourier series

Frequency as predicted by FFT

DC or 0 Hz

Fundamental or 60 Hz

Second harmonic or 120 Hz

Third harmonic or 180 Hz

Fourth harmonic or 240 Hz

2. Given a cosine wave of frequency (1/) Hz and amplitude of 10, sampled at 10 samples/second, express it in a complex exponential form.

Hint:

3. Using Euler

Component of series

Amplitude as predicted by theoretical Fourier series

Amplitude in linear scale as predicted by FFT

Frequency as predicted by theoretical Fourier series

Frequency as predicted by FFT

DC or 0 Hz

Fundamental or 60 Hz

Second harmonic or 120 Hz

Third harmonic or 180 Hz

Fourth harmonic or 240 Hz

Explanation / Answer

I agrees Y Bhargav.

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